View source for Atomic clock

{{Short description|Clock that monitors the resonant frequency of atoms}}
{{About||a clock updated by radio signals|Radio clock|the clock as a measure for risk of catastrophic destruction|Doomsday Clock|other topics|Atomic Clock (disambiguation)}}
{{Use dmy dates|date=July 2022}}
[[File:Caesium clock block.svg|thumb|upright=1.8|Simplified block diagram of typical commercial cesium beam frequency reference]]
[[File:NIST-F2 cesium fountain atomic clock.jpg|thumb|NIST physicists Steve Jefferts (foreground) and Tom Heavner with the NIST-F2 caesium fountain atomic clock, a civilian time standard for the United States]]
[[File:Usno-mc.jpg|thumb|upright=1.2|The master atomic clock ensemble at the [[United States Naval Observatory|U.S. Naval Observatory]] in [[Washington, D.C.]], which provides the time standard for the U.S. Department of Defense.<ref>{{Cite web |url=http://www.usno.navy.mil/USNO/time/master-clock/ |title=USNO Master Clock |access-date=23 November 2010 |archive-date=7 December 2010 |archive-url=https://web.archive.org/web/20101207082711/http://www.usno.navy.mil/USNO/time/master-clock |url-status=live }}</ref> The rack mounted units in the background are HP 5071A cesium beam clocks. The black units in the foreground are Sigma-Tau MHM-2010 hydrogen maser standards.]]
An '''atomic clock''' is a [[clock]] that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different [[energy level]]s. Electron states in an atom are associated with different energy levels, and in transitions between such states they interact with a very specific [[frequency]] of [[electromagnetic radiation]]. This phenomenon serves as the basis for the [[International System of Units]]' (SI) definition of a [[second]]:
<blockquote>
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, <math>\Delta \nu_\text{Cs}</math>, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be {{val|9192631770}} when expressed in the unit Hz, which is equal to s<sup>−1</sup>.
</blockquote>
This definition is the basis for the system of [[International Atomic Time]] (TAI), which is maintained by an ensemble of atomic clocks around the world. The system of [[Coordinated Universal Time|Coordinated Universal Time (UTC)]] that is the basis of civil time implements [[leap seconds]] to allow clock time to track changes in [[Earth's rotation]] to within one second while being based on clocks that are based on the definition of the second, though leap seconds will be phased out in 2035.<ref>{{cite news |last1=Brumfiel |first1=Geoff |title=The world is doing away with the leap second |url=https://www.npr.org/2022/11/27/1139307736/the-world-is-doing-away-with-the-leap-second |access-date=April 30, 2024 |work=Weekend Edition Sunday |agency=National Public Radio |date=November 27, 2022}}</ref>

The accurate timekeeping capabilities of atomic clocks are also used for navigation by [[Satellite navigation|satellite networks]] such as the [[European Union]]'s [[Galileo (satellite navigation)|Galileo Programme]] and the United States' [[GPS]]. The timekeeping [[Accuracy and precision|accuracy]] of the involved atomic clocks is important because the smaller the error in time measurement, the smaller the error in distance obtained by multiplying the time by the [[speed of light]] is (a timing error of a [[nanosecond]] or 1&nbsp;billionth of a second (10{{sup|−9}} or {{frac|1|1,000,000,000}} second) translates into an almost {{convert|30|cm|1|adj=on}} distance and hence positional error).

The main variety of atomic clock uses [[caesium]] atoms cooled to [[temperatures]] that approach [[absolute zero]]. The primary standard for the United States, the [[National Institute of Standards and Technology|National Institute of Standards and Technology (NIST)]]'s caesium fountain clock named [[NIST-F2]], measures time with an [[Measurement uncertainty|uncertainty]] of 1 second in 300 million years (relative uncertainty {{val|e=-16}}). NIST-F2 was brought online on 3 April 2014.<ref name="nistlaunch">{{Cite journal|url=https://www.nist.gov/news-events/news/2014/04/nist-launches-new-us-time-standard-nist-f2-atomic-clock|title=NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock|date=3 April 2014|journal=NIST|via=www.nist.gov}}</ref><ref name="Jefferts">{{cite journal |url=http://tf.boulder.nist.gov/general/pdf/2704.pdf |title=First Accuracy Evaluation of NIST-F2 |author1=Thomas P. Heavner  |author2=Elizabeth A. Donley |author3=Filippo Levi |author4=Giovanni Costanzo |author5=Thomas E. Parker |author6=Jon H. Shirley |author7=Neil Ashby |author8=Stephan Barlow |author9=Steven R. Jefferts |date=May 2014 |journal=[[Metrologia]] |volume=51 |issue=3 |pages=174–182 |doi=10.1088/0026-1394/51/3/174 |bibcode=2014Metro..51..174H |quote=Currently, the type B fractional uncertainty in NIST-F1 is {{val|0.31|e=-15}} and is dominated by the uncertainty in the blackbody radiation (BBR) shift correction, which is {{val|0.28|e=-15}} (this corresponds to a 1 degree uncertainty in the radiation environment as seen by the atoms in NIST-F1). To improve the performance of the NIST primary frequency standard, we sought to reduce the uncertainty due to the BBR effect. To accomplish this goal and to better understand the accepted model of the BBR shift, we developed NIST-F2, a laser-cooled Cs fountain primary frequency standard in which the microwave cavity structure and flight tube operate at cryogenic temperatures ({{val|80|u=K}}).}}</ref>

== History ==
[[File:Atomic Clock-Louis Essen.jpg|thumb|upright=1.2|[[Louis Essen]] (right) and Jack Parry (left) standing next to the world's first caesium-133 atomic clock in 1955, at the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]] in west London, England.]]

The Scottish physicist [[James Clerk Maxwell]] proposed measuring time with the vibrations of [[Electromagnetic radiation|light waves]] in his 1873 Treatise on Electricity and Magnetism: 'A more universal unit of time might be found by taking the periodic time of vibration of the particular kind of light whose wave length is the unit of length.'<ref>{{Cite journal |last=Ramsey |first=Norman F. |date=June 2006 |title=History of early atomic clocks |url=https://iopscience.iop.org/article/10.1088/0026-1394/42/3/S01 |journal=Metrologia |language=en |volume=42 |issue=3 |pages=S1–S3 |doi=10.1088/0026-1394/42/3/s01 |issn=0026-1394 |s2cid=122631200}}</ref><ref name=":9">{{Citation |last=Achard |first=F. |title=James Clerk Maxwell, A treatise on electricity and magnetism, first edition (1873) |date=2005 |url=http://dx.doi.org/10.1016/b978-044450871-3/50125-x |work=Landmark Writings in Western Mathematics 1640–1940 |pages=564–587 |publisher=Elsevier |doi=10.1016/b978-044450871-3/50125-x |isbn=9780444508713 |access-date=20 June 2022}}</ref> Maxwell argued this would be more accurate than the [[Earth's rotation]], which defines the [[Second#History of definition|mean solar second]] for timekeeping.<ref>{{Cite web |date=14 June 2022 |title=Milestones:First Atomic Clock, 1948 |url=https://ethw.org/Milestones:First_Atomic_Clock,_1948 |access-date=20 June 2022 |website=ETHW |language=en}}</ref>

During the 1930s, the American physicist [[Isidor Isaac Rabi]] built equipment for atomic beam [[magnetic resonance]] frequency clocks.<ref>{{Cite journal |last=Rabi |first=I. I. |date=15 April 1937 |title=Space Quantization in a Gyrating Magnetic Field |url=http://dx.doi.org/10.1103/physrev.51.652 |journal=Physical Review |volume=51 |issue=8 |pages=652–654 |doi=10.1103/physrev.51.652 |bibcode=1937PhRv...51..652R |issn=0031-899X}}</ref><ref>{{Cite journal |last1=Rabi |first1=I. I. |last2=Zacharias |first2=J. R. |last3=Millman |first3=S. |last4=Kusch |first4=P. |date=15 February 1938 |title=A New Method of Measuring Nuclear Magnetic Moment |journal=Physical Review |volume=53 |issue=4 |pages=318 |doi=10.1103/physrev.53.318 |bibcode=1938PhRv...53..318R |issn=0031-899X|doi-access=free }}</ref>

The accuracy of mechanical, [[Shortt–Synchronome clock|electromechanical]] and [[quartz clock]]s is reduced by temperature fluctuations. This led to the idea of measuring the frequency of an atom's vibrations to keep time much more accurately, as proposed by James Clerk Maxwell, [[William Thomson, 1st Baron Kelvin|Lord Kelvin]], and Isidor Rabi.<ref name="Lombardi">{{Cite journal |last1=Lombardi |first1=M. A. |last2=Heavner |first2=T. P. |last3=Jefferts |first3=S. R. |year=2007 |title=NIST Primary Frequency Standards and the Realization of the SI Second |url=http://tf.nist.gov/general/pdf/2039.pdf |url-status=live |journal=[[Journal of Measurement Science]] |volume=2 |issue=4 |pages=74–89 |archive-url=https://web.archive.org/web/20210212011250/https://tf.nist.gov/general/pdf/2039.pdf |archive-date=12 February 2021 |access-date=24 October 2009}}</ref> He proposed the concept in 1945, which led to a demonstration of a clock based on [[ammonia]] in 1949.<ref>{{cite conference |author=Sullivan |first=D. B. |year=2001 |title=Time and frequency measurement at NIST: The first 100 years |url=http://ethw.org/w/images/a/aa/Sullivan_IEEE_FCS_2001.pdf |conference=IEEE International Frequency Control Symposium |publisher=[[National Institute of Standards and Technology|NIST]] |pages=4–17 |archive-url=https://web.archive.org/web/20191229045628/https://ethw.org/w/images/a/aa/Sullivan_IEEE_FCS_2001.pdf |archive-date=29 December 2019 |access-date=1 May 2018 |url-status=live}}</ref> This led to the first practical accurate atomic clock with caesium atoms being built at the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]] in the United Kingdom in 1955<ref>
{{Cite journal|last1=Essen|first1=L.|author-link1=Louis Essen|last2=Parry|first2=J. V. L.|year=1955|title=An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator|journal=Nature|volume=176|issue=4476|pages=280–282|bibcode=1955Natur.176..280E|doi=10.1038/176280a0|s2cid=4191481}}</ref><ref>{{Cite web|title=60 years of the Atomic Clock|url=http://www.npl.co.uk/60-years-of-the-atomic-clock/|url-status=live|archive-url=https://web.archive.org/web/20171017151756/http://www.npl.co.uk/60-years-of-the-atomic-clock/|archive-date=17 October 2017|access-date=17 October 2017|website=National Physical Laboratory}}</ref> by [[Louis Essen]] in collaboration with Jack Parry.<ref>{{Cite journal | last1 = Essen | first1 = L. | author-link1 = Louis Essen| last2 = Parry | first2 = J. V. L. | doi = 10.1038/176280a0  |bibcode=1955Natur.176..280E| title = An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator | journal = Nature | volume = 176 | issue = 4476 | pages = 280 | year = 1955 | s2cid = 4191481 }} p.280.</ref>

[[File:President Piñera receives ESO's first atomic clock.jpg|thumb|upright=1.2|A caesium atomic clock from 1975 (upper unit) and battery backup (lower unit)<ref>{{cite news|date=15 November 2013|title=President Piñera Receives ESO's First Atomic Clock|newspaper=ESO Announcement|url=http://www.eso.org/public/announcements/ann13092/|url-status=live|access-date=20 November 2013|archive-url=https://web.archive.org/web/20140401072904/http://www.eso.org/public/announcements/ann13092/|archive-date=1 April 2014}}</ref>]]

In 1949, [[Alfred Kastler]] and [[Jean Brossel]]<ref>{{Cite journal |last=Ramsey |first=N. F. |date=September 1983 |title=History of Atomic Clocks |url=http://dx.doi.org/10.6028/jres.088.015 |journal=Journal of Research of the National Bureau of Standards |volume=88 |issue=5 |pages=301–320 |doi=10.6028/jres.088.015 |issn=0160-1741 |pmc=6768155 |pmid=34566107}}</ref> developed a technique called [[optical pumping]] for electron energy level transitions in atoms using light. This technique is useful for creating much stronger [[magnetic resonance]] and microwave absorption signals. Unfortunately, this caused a side effect with a light shift of the resonant frequency. [[Claude Cohen-Tannoudji]] and others managed to reduce the light shifts to acceptable levels.

Ramsey developed a method, commonly known as [[Ramsey interferometry]] nowadays, for higher frequencies and narrower resonances in the oscillating fields. Kolsky, Phipps, Ramsey, and Silsbee used this technique for molecular beam spectroscopy in 1950.<ref>{{Citation |title=Paper 1.15: "Experiments with Separated Oscillatory Fields and Hydrogen Masers," (Nobel Lecture), N. F. Ramsey, ''Les Prix Nobel'' (1989, The Nobel Foundation) and ''Rev. Mod. Phys.'' '''62''', 541–552 (1990) |date=June 1998 |url=http://dx.doi.org/10.1142/9789812795717_0015 |work=Spectroscopy With Coherent Radiation |series=World Scientific Series in 20th Century Physics |volume=21 |pages=115–127 |publisher=WORLD SCIENTIFIC |doi=10.1142/9789812795717_0015 |isbn=978-981-02-3250-4 |access-date=20 June 2022}}</ref>

After 1956, atomic clocks were studied by many groups, such as the [[National Institute of Standards and Technology]] (formerly the National Bureau of Standards) in the USA, the [[Physikalisch-Technische Bundesanstalt]] (PTB) in Germany, the [[National Research Council Canada|National Research Council]] (NRC) in Canada, the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]] in the United Kingdom, [[International Time Bureau]] ([[French language|French]]: ''Bureau International de l'Heure'', abbreviated BIH), at the [[Paris Observatory]], the [[National Radio Company]], Bomac, [[Varian Medical Systems|Varian]], [[Hewlett-Packard|Hewlett–Packard]] and Frequency & Time Systems.<ref>{{Cite journal |last1=Hellwig |first1=Helmut |last2=Evenson |first2=Kenneth M. |last3=Wineland |first3=David J. |date=December 1978 |title=Time, frequency and physical measurement |url=http://dx.doi.org/10.1063/1.2994867 |journal=Physics Today |volume=31 |issue=12 |pages=23–30 |doi=10.1063/1.2994867 |bibcode=1978PhT....31l..23H |issn=0031-9228}}</ref>

During the 1950s, the [[National Radio Company]] sold more than 50 units of the first atomic clock, the [[Atomichron]].<ref>{{Cite web|last=Forman|first=Paul|date=1998|title=Atomichron: The Atomic Clock from Concept to Commercial Product|url=http://ieee-uffc.org/freqcontrol/atomichron/automichron.htm|archive-url=https://web.archive.org/web/20071021044529/http://ieee-uffc.org/freqcontrol/atomichron/automichron.htm|archive-date=21 October 2007|access-date=16 February 2022}}</ref> In 1964, engineers at [[Hewlett-Packard]] released the 5060 rack-mounted model of caesium clocks.<ref name="Lombardi" />

=== Definition of the second ===
{{main|Second}}

In 1968, the SI defined the duration of the second to be {{val|9192631770}} vibrations of the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom. Prior to that it was defined by there being {{val|31556925.9747}} seconds in the [[tropical year]] 1900.<ref>{{Cite book
|pages=191–195
|last1=McCarthy
|first1=D. D.
|last2=Seidelmann
|first2=P. K.
|author-link1=Dennis McCarthy (scientist)
|year=2009
|title=TIME—From Earth Rotation to Atomic Physics
|location=Weinheim
|publisher=Wiley-VCH
|isbn=978-3-527-40780-4}}</ref> In 1997, the [[International Committee for Weights and Measures]] (CIPM) added that the preceding definition refers to a caesium atom at rest at a temperature of [[absolute zero]].<ref>{{SIbrochure8th}}</ref>{{rp|113}} Following the [[2019 revision of the SI]], the definition of every [[SI base unit|base unit]] except the [[mole (unit)|mole]] and almost every [[SI derived unit|derived unit]] relies on the definition of the second.

Timekeeping researchers seek an even more stable atomic reference for the second, with a plan to find a [[Atomic clock#Redefining the second|more precise definition]] of the second as atomic clocks improve based on [[Optical clock|optical clocks]] or the [[Rydberg constant]] around 2030.<ref>{{Cite web|last1=Fox|first1=Alex|title=New Atomic Clocks May Someday Redefine the Length of a Second|url=https://www.smithsonianmag.com/smart-news/new-atomic-clocks-hone-length-second-180977387/|access-date=16 February 2022|website=Smithsonian Magazine|language=en}}</ref><ref name=":6">{{Cite journal|last=Lodewyck|first=Jérôme|date=16 September 2019|title=On a definition of the SI second with a set of optical clock transitions|url=https://iopscience.iop.org/article/10.1088/1681-7575/ab3a82|journal=Metrologia|language=en|volume=56|issue=5|article-number=055009|doi=10.1088/1681-7575/ab3a82|arxiv=1911.05551|bibcode=2019Metro..56e5009L|s2cid=202129810|issn=0026-1394}}</ref>

=== Metrology advancements and optical clocks ===
[[File:Ytterbium Lattice Double Clock with Photons at NIST.jpg|thumb|upright=1.2|A [[ytterbium]] lattice clock that uses [[photon]]s to measure time precisely]]

Technological developments such as [[lasers]] and [[Frequency comb|optical frequency combs]] in the 1990s led to increasing accuracy of atomic clocks.<ref name="Hollberg">{{Cite journal |last1=Ye |first1=J. |last2=Schnatz |first2=H. |last3=Hollberg |first3=L. W. |year=2003 |title=Optical frequency combs: From frequency metrology to optical phase control |url=http://tf.nist.gov/general/pdf/1875.pdf |url-status=live |journal=[[IEEE Journal of Selected Topics in Quantum Electronics]] |volume=9 |issue=4 |pages=1041–1058 |bibcode=2003IJSTQ...9.1041Y |doi=10.1109/JSTQE.2003.819109 |archive-url=https://web.archive.org/web/20160306015838/http://tf.nist.gov/general/pdf/1875.pdf |archive-date=6 March 2016 |access-date=25 February 2016}}</ref><ref>{{Cite journal|last=NIST|date=31 December 2009|title=Optical Frequency Combs|url=https://www.nist.gov/topics/physics/optical-frequency-combs|access-date=16 February 2022|journal=NIST|language=en}}</ref> Lasers enable the possibility of optical-range control over atomic states transitions, which has a much higher frequency than that of microwaves; while optical frequency comb measures highly accurately such high frequency oscillation in light.

The first advance beyond the precision of caesium clocks occurred at NIST in 2010 with the demonstration of a "quantum logic" optical clock that used aluminum ions to achieve a precision of {{val|e=-17}}.<ref>{{Cite journal|last=swenson|date=4 February 2010|title=NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock|url=https://www.nist.gov/news-events/news/2010/02/nists-second-quantum-logic-clock-based-aluminum-ion-now-worlds-most-precise|access-date=21 February 2022|journal=NIST|language=en}}</ref> Optical clocks are a very active area of research in the field of metrology as scientists work to develop clocks based on elements [[ytterbium]], [[Mercury (element)|mercury]], [[Aluminium|aluminum]], and [[strontium]]. Scientists at [[JILA]] demonstrated a strontium clock with a [[frequency]] precision of {{val|e=-18}} in 2015.<ref>{{Cite journal |last1=Nicholson |first1=T. L. |last2=Campbell |first2=S. L. |last3=Hutson |first3=R. B. |last4=Marti |first4=G. E. |last5=Bloom |first5=B. J. |last6=McNally |first6=R. L. |last7=Zhang |first7=W. |last8=Barrett |first8=M. D. |last9=Safronova |first9=M. S. |last10=Strouse |first10=G. F. |last11=Tew |first11=W. L. |date=21 April 2015 |title=Systematic evaluation of an atomic clock at {{val|2|e=-18}} total uncertainty |journal=Nature Communications |language=en |volume=6 |issue=1 |arxiv=1412.8261 |bibcode=2015NatCo...6.6896N |doi=10.1038/ncomms7896 |issn=2041-1723 |pmc=4411304 |pmid=25898253 |article-number=6896}}</ref> Scientists at NIST developed a quantum logic clock that measured a single aluminum ion in 2019 with a frequency uncertainty of {{val|9.4|e=-19}}.<ref>{{Cite journal|last=sarah.henderson@nist.gov|date=15 July 2019|title=NIST's Quantum Logic Clock Returns to Top Performance|url=https://www.nist.gov/news-events/news/2019/07/nists-quantum-logic-clock-returns-top-performance|access-date=21 February 2022|journal=NIST|language=en}}</ref><ref name="journals.aps.org">{{Cite journal|last1=Brewer|first1=S. M.|last2=Chen|first2=J.-S.|last3=Hankin|first3=A. M.|last4=Clements|first4=E. R.|last5=Chou|first5=C. W.|last6=Wineland|first6=D. J.|last7=Hume|first7=D. B.|last8=Leibrandt|first8=D. R.|date=15 July 2019|title=Al+27 Quantum-Logic Clock with a Systematic Uncertainty below {{val|e=-18}}|url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.033201|journal=Physical Review Letters|volume=123|issue=3|article-number=033201|doi=10.1103/physrevlett.123.033201|pmid=31386450|arxiv=1902.07694 |s2cid=119075546|issn=0031-9007}}</ref>

At JILA in September 2021, scientists demonstrated an optical strontium clock with a differential frequency precision of {{val|7.6|e=-21}} between atomic ensembles{{clarify|reason=what is an atomic ensemble?|date=September 2024}} separated by {{val|1|u=mm}}.<ref>{{Cite journal|last1=Bothwell|first1=Tobias|last2=Kennedy|first2=Colin J.|last3=Aeppli|first3=Alexander|last4=Kedar|first4=Dhruv|last5=Robinson|first5=John M.|last6=Oelker|first6=Eric|last7=Staron|first7=Alexander|last8=Ye|first8=Jun|date=16 February 2022|title=Resolving the gravitational redshift across a millimetre-scale atomic sample|url=http://dx.doi.org/10.1038/s41586-021-04349-7|journal=Nature|volume=602|issue=7897|pages=420–424|doi=10.1038/s41586-021-04349-7|pmid=35173346|arxiv=2109.12238|bibcode=2022Natur.602..420B|s2cid=246902611|issn=0028-0836}}</ref><ref>{{Cite web|date=18 October 2021|title=An atomic clock measured how general relativity warps time across a millimeter|url=https://www.sciencenews.org/article/atomic-clock-general-relativity-time-warp-millimeter-physics|access-date=22 February 2022|website=Science News|language=en-US}}</ref> The second is expected to be redefined when the field of optical clocks matures, sometime around the year 2030 or 2034.<ref>{{Cite journal|last1=Dimarcq|first1=Noel|last2=Gertsvolf|first2=Marina|last3=Mileti|first3=Gaetano|last4=Bize|first4=Sebastien|last5=Oates|first5=Christopher|last6=Peik|first6=Ekkehard|last7=Calonico|first7=Davide|last8=Ido|first8=Tetsuya|last9=Tavella|first9=Patrizia|last10=Meynadier|first10=Frédéric|date=2024|title=Roadmap towards the redefinition of the second|url=https://iopscience.iop.org/article/10.1088/1681-7575/ad17d2|journal=Metrologia|volume=61|issue=1|page=012001 |doi=10.1088/1681-7575/ad17d2|arxiv=2307.14141|bibcode=2024Metro..61a2001D }}</ref> In order for this to occur, optical clocks must be consistently capable of measuring frequency with accuracy at or better than {{val|2|e=-18}}. In addition, methods for reliably comparing different optical clocks around the world in national metrology labs must be demonstrated{{clarify|reason=to whom?|date=September 2024}}, and the comparison must show relative clock frequency accuracies at or better than {{val|5|e=-18}}.

=== Chip-scale atomic clocks ===
[[File:18pml015 clock-chip-with-coffee-bean 2mb.jpg|thumb|The heart of NIST's next-generation miniature atomic clock{{snd}} ticking at high "optical" frequencies{{snd}} is this vapor cell on a chip, shown next to a coffee bean for scale.]]
Reducing the size and power consumption of optical clocks is necessary to enable their use in geodesy and GPS navigation. In August 2004, [[National Institute of Standards and Technology|NIST]] scientists demonstrated a [[chip-scale atomic clock]] that was 100 times smaller than an ordinary atomic clock and had a much smaller power consumption of {{val|125|ul=mW}}.<ref name="Symmetricon-CSAC">
{{cite web
 |year=2011
 |title=SA.45s CSAC Chip Scale Atomic Clock (archived version of the original pdf)
 |url=http://www.symmetricom.com/media/files/downloads/product-datasheets/DS%5FSA%2045s%5FCSAC.pdf
 |archive-url=https://web.archive.org/web/20130525160417/http://www.symmetricom.com/media/files/downloads/product-datasheets/DS_SA%2045s_CSAC.pdf
 |url-status=dead
 |archive-date=25 May 2013
 |access-date=12 June 2013
}}</ref><ref name="Chip-Scale">{{cite web|year=2007|title=Chip-Scale Atomic Devices at NIST|url=http://tf.nist.gov/timefreq/ofm/smallclock/index.htm|url-status=dead|archive-url=https://web.archive.org/web/20080107133256/http://tf.nist.gov/timefreq/ofm/smallclock/index.htm|archive-date=7 January 2008|access-date=17 January 2008|publisher=[[National Institute of Standards and Technology|NIST]]}}  Available on-line at: [http://tf.nist.gov/general/pdf/2067.pdf NIST.gov]. {{Webarchive|url=https://web.archive.org/web/20210107194040/https://tf.nist.gov/general/pdf/2067.pdf|date=7 January 2021}}</ref> The atomic clock was about the size of a grain of rice with a frequency of about 9&nbsp;GHz. This technology became available commercially in 2011.<ref name="Symmetricon-CSAC" />  

== Measuring time with atomic clocks ==

=== Clock mechanism ===
An atomic clock is based on a system of atoms which may be in one of two possible energy states. A group of atoms in one state is prepared, then subjected to [[microwave]] radiation. If the radiation is of the correct frequency, a number of atoms will transition to the other [[Energy level|energy state]]. The closer the frequency is to the inherent oscillation frequency of the atoms, the more atoms will switch states. Such correlation allows very accurate tuning of the frequency of the microwave radiation. Once the microwave radiation is adjusted to a known frequency where the maximum number of atoms switch states, the atom and thus, its associated transition frequency, can be used as a timekeeping oscillator to measure elapsed time.<ref>{{Cite web |title=How Do Atomic Clocks Work? |url=https://www.timeanddate.com/time/how-do-atomic-clocks-work.html |access-date=17 February 2022 |website=www.timeanddate.com |language=en}}</ref>

All timekeeping devices use oscillatory phenomena to accurately measure time, whether it is the rotation of the Earth for a [[sundial]], the swinging of a [[pendulum]] in a [[grandfather clock]], the vibrations of springs and gears in a [[watch]], or [[voltage]] changes in a [[quartz]] [[Quartz clock|crystal watch]]. However all of these are easily affected by [[temperature]] changes and are not very accurate. The most accurate clocks use atomic vibrations to keep track of time. Clock transition states in atoms are insensitive to temperature and other environmental factors and the oscillation frequency is much higher than any of the other clocks (in microwave frequency regime and higher).

One of the most important factors in a clock's performance is the atomic line quality factor, {{math|''Q''}}, which is defined as the ratio of the absolute frequency <math>\nu_0</math> of the [[resonance]] to the linewidth of the resonance itself <math>\Delta \nu</math>. Atomic resonance has a much higher {{math|''Q''}} than mechanical devices. Atomic clocks can also be isolated from environmental effects to a much higher degree. Atomic clocks have the benefit that atoms are universal, which means that the oscillation frequency is also universal. This is different from quartz and mechanical time measurement devices that do not have a universal frequency.

A clock's quality can be specified by two parameters: accuracy and stability. Accuracy is a measurement of the degree to which the clock's ticking rate can be counted on to match some absolute standard such as the inherent hyperfine frequency of an isolated atom or ion. Stability describes how the clock performs when averaged over time to reduce the impact of noise and other short-term fluctuations (see [[Accuracy and precision|precision]]).<ref>{{Cite journal |last=Poli |first=N |year=2014 |title=Optical atomic clocks |journal=La Rivista del Nuovo Cimento |volume=36 |issue=12 |page=555 |arxiv=1401.2378 |bibcode=2013NCimR..36..555P |doi=10.1393/ncr/i2013-10095-x |s2cid=118430700}}</ref>

The instability of an atomic clock is specified by its [[Allan deviation]] <math>\sigma_y(\tau)</math>.<ref name="Allan1966">Allan, David W. [http://tf.nist.gov/general/pdf/7.pdf ''Statistics of Atomic Frequency Standards''], pp. 221–230. Proceedings of the IEEE, Vol. 54, No 2, February 1966.</ref> The limiting instability due to atom or ion counting statistics is given by 
: <math>
\sigma_{y,\, {\rm atoms}}(\tau) \approx \frac{\Delta \nu}{\nu_0 \sqrt{N}} \sqrt{\frac{T_\text{c}}{\tau}},
</math>
where <math>\Delta \nu</math> is the [[Spectroscopy|spectroscopic]] linewidth of the clock system, <math>N</math> is the number of atoms or ions used in a single measurement, <math>T_\text{c}</math> is the time required for one cycle, and <math>\tau</math> is the averaging period. This means instability is smaller when the linewidth <math>\Delta \nu</math> is smaller and when <math>\sqrt{N}</math> (the [[Signal-to-noise ratio|signal to noise ratio]]) is larger. The stability improves as the time <math>\tau</math> over which the measurements are averaged increases from seconds to hours to days. The stability is most heavily affected by the oscillator frequency <math>\nu_0</math>. This is why optical clocks such as strontium clocks (429 terahertz) are much more stable than caesium clocks (9.19&nbsp;GHz).

Modern clocks such as atomic fountains or optical lattices that use sequential interrogation are found to generate type of noise that mimics and adds to the instability inherent in atom or ion counting. This effect is called the [[Dick effect]]<ref name="Dick 1987">
{{cite conference |author=Dick |first=G. J. |year=1987 |title=Local oscillator induced instabilities in trapped ion frequency standards |url=https://tycho.usno.navy.mil/ptti/1987papers/Vol%2019_13.pdf |conference=Precise Time and Time Interval (PTTI) Conference |location=Redondo Beach}}</ref> and is typically the primary stability limitation for the newer atomic clocks. It is an aliasing effect; high frequency noise components in the [[local oscillator]] ("LO") are heterodyned to near zero frequency by harmonics of the repeating variation in feedback sensitivity to the LO frequency. The effect places new and stringent requirements on the LO, which must now have low phase noise in addition to high stability, thereby increasing the cost and complexity of the system. For the case of an LO with [[Allan variance#Power-law noise|Flicker frequency noise]]<ref name="NBS Tech Note 394">J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. C. Vessot, G. M. R. Winkler: ''[https://tf.nist.gov/general/tn1337/Tn146.PDF Characterization of Frequency Stability]'', NBS Technical Note 394, 1970.</ref> where <math>\sigma_y^{\rm LO}(\tau)</math> is independent of <math>\tau</math>, the interrogation time is <math>T_i</math>, and where the duty factor <math>d=T_i/T_c</math> has typical values <math>0.4<d<0.7</math>, the [[Allan deviation]] can be approximated as<ref name="Santarelli 1998">
{{cite journal |author1=Santarelli, G. |author2=Audoin, C. |author3=Makdissi, A. |author4=Laurent, P. |author5=Dick, G.J. |author6=Clairon, A. |year=1998 |title=Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator |url= |journal=[[IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control]] |volume=45 |issue=4 |pages=887–894 |doi=10.1109/58.710548 |pmid=18244242 |s2cid=12303876}}</ref> 
: <math>\sigma_{y,\,{\rm Dick}}(\tau) \approx \frac{\sigma_y^{\rm LO}}{\sqrt{2\ln(2)}} \cdot \left|\frac{\sin(\pi d)}{\pi d}\right| \cdot \sqrt{\frac{T_c}{\tau}}.
</math>

This expression shows the same dependence on <math>T_c / {\tau} </math> as does <math> \sigma_{y,\, {\rm atoms}}(\tau)</math>, and, for many of the newer clocks, is significantly larger. Analysis of the effect and its consequence as applied to optical standards has been treated in a major review (Ludlow, et al., 2015)<ref name="Ludlow etal 2015">
{{cite journal |last1=Ludlow |first1=A. D. |last2=Boyd |first2=M. M. |last3=Ye |first3=Jun |last4=Peik |first4=E. |last5=Schmidt |first5=P. O. |date=June 26, 2015 |title=Optical atomic clocks |url= |journal=[[Reviews of Modern Physics]] |volume=87 |issue=2 |pages=637–701 |arxiv=1407.3493 |bibcode=2015RvMP...87..637L |doi=10.1103/RevModPhys.87.637 |s2cid=119116973}}</ref> that lamented on "the pernicious influence of the Dick effect", and in several other papers.<ref name="Quessada etal 2003">
{{cite journal |author1=Quessada, A. |author2=Kovacich, R. P. |author3=Courtillot, I. |author4=Clairon, A. |author5=Santarelli, G. |author6=Lemonde, P. |date=April 2, 2003 |title=The Dick effect for an optical frequency standard |url=https://www.researchgate.net/publication/231075532 |journal=[[Journal of Optics B: Quantum and Semiclassical Optics]] |volume=5 |issue=2 |pages=S150–S154 |bibcode=2003JOptB...5S.150Q |doi=10.1088/1464-4266/5/2/373}}</ref><ref name="Westergaard etal 2010">{{Cite journal |last1=Westergaard |first1=P. G. |last2=Lodewyck |first2=J. |last3=Lemonde |first3=P. |date=March 2010 |title=Minimizing the Dick effect in an optical lattice clock. |url=https://www.researchgate.net/publication/41825159 |journal=[[IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control]] |volume=57 |issue=3 |pages=623–628 |arxiv=0909.0909 |doi=10.1109/TUFFC.2010.1457 |pmid=20211780 |s2cid=10581032}}</ref>

=== Tuning and optimization ===
The core of the traditional [[radio frequency]] atomic clock is a tunable [[microwave cavity]] containing a gas. In a [[hydrogen maser]] clock the gas emits [[microwave]]s (the gas ''[[maser|mases]]'') on a hyperfine transition, the field in the cavity oscillates, and the cavity is tuned for maximum microwave amplitude. Alternatively, in a caesium or rubidium clock, the beam or gas absorbs microwaves and the cavity contains an electronic amplifier to make it oscillate. For both types, the atoms in the gas are prepared in one hyperfine state prior to filling them into the cavity. For the second type, the number of atoms that change hyperfine state is detected and the cavity is tuned for a maximum of detected state changes.

Most of the complexity of the clock lies in this adjustment process. The adjustment tries to correct for unwanted side-effects, such as frequencies from other electron transitions, temperature changes, and the spreading in frequencies caused by the vibration of molecules including [[Doppler broadening]].<ref name=":4">{{Cite journal |last=NIST |date=December 2007 |title=NIST Primary Frequency Standards and the Realization of the SI Second |url=https://tf.nist.gov/general/pdf/2039.pdf |journal=NCSL International Measure |volume=2 |pages=77 |no-pp=}}</ref> One way of doing this is to sweep the microwave oscillator's frequency across a narrow range to generate a [[Modulation|modulated]] [[signal]] at the detector. The detector's signal can then be [[Demodulation|demodulated]] to apply feedback to control long-term drift in the radio frequency.<ref>{{Cite journal |last1=Jain |first1=Pratik |last2=Priya |first2=Priyanka |last3=Ram |first3=T. V. S. |last4=Parikh |first4=K. S. |last5=Bandi |first5=Thejesh N. |date=1 December 2021 |title=Digital lock-in amplifier for space rubidium atomic clock |journal=Review of Scientific Instruments |volume=92 |issue=12 |bibcode=2021RScI...92l4705J |doi=10.1063/5.0061727 |pmid=34972462 |s2cid=245079164 |article-number=124705}}</ref>

In this way, the [[Quantum mechanics|quantum-mechanical]] properties of the atomic transition frequency of the caesium can be used to tune the microwave oscillator to the same frequency, except for a small amount of [[Observational error|experimental error]]. When a clock is first turned on, it takes a while for the oscillator to stabilize. In practice, the feedback and monitoring mechanism is much more complex.<ref>{{Cite journal |last1=Poli |first1=N. |last2=Oates |first2=C. W. |last3=Gill |first3=P. |last4=Tino |first4=G. M. |date=13 January 2014 |title=Optical Atomic Clocks |url=https://tf.nist.gov/general/pdf/2707.pdf |journal=Rivista del Nuovo Cimento |volume=36 |issue=12 |pages=555–624 |arxiv=1401.2378 |bibcode=2013NCimR..36..555P |doi=10.1393/ncr/i2013-10095-x |s2cid=118430700}}</ref>

Many of the newer clocks, including microwave clocks such as trapped ion or fountain clocks, and optical clocks such as lattice clocks use a sequential interrogation protocol rather than the frequency modulation interrogation described above.<ref name="Ludlow etal 2015" /> An advantage of sequential interrogation is that it can accommodate much higher Q's, with ringing times of seconds rather than milliseconds. These clocks also typically have a ''dead time'', during which the atom or ion collections are analyzed, renewed and driven into a proper quantum state, after which they are interrogated with a signal from a ''local oscillator'' (LO) for a time of perhaps a second or so. Analysis of the final state of the atoms is then used to generate a correction signal to keep the LO frequency locked to that of the atoms or ions.

== Accuracy ==
[[File:Clock accuracy.svg|thumb|upright=1.4|The historical accuracy of atomic clocks from [[NIST]]]]

The accuracy of atomic clocks has improved continuously since the first prototype in the 1950s. The first generation of atomic clocks were based on measuring caesium, rubidium, and hydrogen atoms. In a time period from 1959 to 1998, [[National Institute of Standards and Technology|NIST]] developed a series of seven caesium-133 microwave clocks named NBS-1 to NBS-6 and NIST-7 after the agency changed its name from the National Bureau of Standards to the National Institute of Standards and Technology.<ref name="Lombardi" /> The first clock had an accuracy of {{val|e=-11}}, and the last clock had an accuracy of {{val|e=-15}}. The clocks were the first to use a [[Atomic fountain|caesium fountain]], which was introduced by [[Jerrold R. Zacharias|Jerrod Zacharias]], and laser cooling of atoms, which was demonstrated by [[David J. Wineland|Dave Wineland]] and his colleagues in 1978.

The next step in atomic clock advances involves going from accuracies of {{val|e=-15}} to accuracies of {{val|e=-18}} and even {{val|e=-19}}.{{efn|Researchers at the [[University of Wisconsin-Madison]] have demonstrated a clock that will not lose a second in 300 billion years.<ref name="auto">{{cite web|last=University of Wisconsin-Madison|title=Ultraprecise atomic clock poised for new physics discoveries|url=https://www.eurekalert.org/news-releases/943211}}</ref>}} The goal is to redefine the second when clocks become so accurate that they will not lose or gain more than a second in the [[age of the universe]].{{efn|1=One second in 13.8 billion years, the age of the universe, is an accuracy of {{val|2.3|e=-18}}.}} To do so, scientists must demonstrate the accuracy of clocks that use [[strontium]] and [[ytterbium]] and [[optical lattice]] technology. Such clocks are also called optical clocks where the energy level transitions used are in the optical regime (giving rise to even higher oscillation frequency), which thus, have much higher accuracy as compared to traditional atomic clocks.<ref>{{cite web |date=20 July 2021 |title=What Are Optical Clocks and Why Are They Important? |url=https://revolutionized.com/what-are-optical-clocks-and-why-are-they-important/ |access-date=20 July 2021 |website=Revolutionalized}}</ref>

The goal of an atomic clock with {{val|e=-16}} accuracy was first reached at the United Kingdom's [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]]'s NPL-CsF2 [[Atomic fountain|caesium fountain]] clock<ref>{{Cite web |last=Laboratory |first=National Physical |title=Accuracy of the NPL caesium fountain clock further improved |url=https://phys.org/news/2014-02-accuracy-npl-caesium-fountain-clock.html |access-date=20 February 2022 |website=phys.org |language=en}}</ref><ref>{{Cite web |title=The atomic clock with the world's best long-term accuracy is revealed after evaluation |url=https://www.eurekalert.org/news-releases/497622 |access-date=20 February 2022 |website=EurekAlert! |language=en}}</ref><ref>{{Cite web |date=23 December 2016 |title=2016 Gets Longer with Extra Second Added to New Year Countdown {{!}} Sci-News.com |url=http://www.sci-news.com/physics/2016-leap-second-04480.html |access-date=20 February 2022 |website=Breaking Science News {{!}} Sci-News.com |language=en-US}}</ref> and the United States' [[NIST-F2]].<ref name=":5">{{Cite magazine |last=Mann |first=Adam |title=How the U.S. Built the World's Most Ridiculously Accurate Atomic Clock |url=https://www.wired.com/2014/04/nist-atomic-clock/ |access-date=15 February 2022 |magazine=Wired |language=en-US |issn=1059-1028}}</ref><ref>{{Cite journal |last=robin.materese@nist.gov |date=9 April 2019 |title=Second: The Future |url=https://www.nist.gov/si-redefinition/second/second-future |journal=NIST |language=en |access-date=20 February 2022}}</ref> The increase in precision from NIST-F1 to NIST-F2 is due to [[liquid nitrogen]] cooling of the microwave interaction region; the largest source of uncertainty in NIST-F1 is the effect of [[black-body radiation]] from the warm chamber walls.<ref>{{cite journal |date=3 April 2014 |title=NIST launches a new US time standard: NIST-F2 atomic clock |url=https://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm |url-status=live |journal=NIST |publisher=nist.gov |archive-url=https://web.archive.org/web/20140406052932/http://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm |archive-date=6 April 2014 |access-date=3 April 2014}}</ref><ref name="Jefferts" />

The performance of primary and secondary frequency standards contributing to International Atomic Time (TAI) is evaluated. The evaluation reports of individual (mainly primary) clocks are [https://www.bipm.org/en/time-ftp/data published online] by the International Bureau of Weights and Measures (BIPM).

== Comparing atomic clocks ==

=== Time standards ===
{{see also|List of UTC timing centers}}
A number of national [[metrology]] laboratories maintain atomic clocks: including [[Paris Observatory]], the [[Physikalisch-Technische Bundesanstalt]] (PTB) in Germany, the National Institute of Standards and Technology [[National Institute of Standards and Technology|(NIST)]] in [[Colorado]] and [[Maryland]], USA, [[JILA]] in the [[University of Colorado Boulder]], the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]] (NPL) in the United Kingdom, and the [[All-Russian Scientific Research Institute for Physical-Engineering and Radiotechnical Metrology]]. They do this by designing and building frequency standards that produce electric oscillations at a frequency whose relationship to the transition frequency of caesium 133 is known, in order to achieve a very low uncertainty. These primary frequency standards estimate and correct various frequency shifts, including relativistic [[Doppler effect|Doppler shifts]] linked to atomic motion, the [[thermal radiation]] of the environment ([[Black body|blackbody]] shift) and several other factors. The best primary standards currently{{When|date=February 2025}} produce the SI second with an accuracy approaching an uncertainty of one part in {{val|e=16}}.

It is important to note that at this level of accuracy, the differences in the [[gravitational field]] in the device cannot be ignored. The standard is then considered in the framework of [[general relativity]] to provide a [[proper time]] at a specific point.<ref name="bipm">{{cite web |date=20 May 2019 |title=Mise en pratique for the definition of the second in the SI |url=https://www.bipm.org/documents/20126/41489667/SI-App2-second.pdf |website=Bureau International Poids et Mesures |publisher=Consultative Committee for Time and Frequency}}</ref>

The [[International Bureau of Weights and Measures]] (BIPM) provides a list of frequencies that serve as [https://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies secondary representations of the second]. This list contains the frequency values and respective standard uncertainties for the [[rubidium]] microwave transition and other optical transitions, including neutral atoms and single trapped ions. These secondary frequency standards can be as accurate as one part in {{val|e=18}}; however, the uncertainties in the list are one part in {{val|e=14}}–{{val|e=16}}. This is because the uncertainty in the central caesium standard against which the secondary standards are [[Calibration|calibrated]] is one part in {{val|e=14}}–{{val|e=16}}.

Primary frequency standards can be used to calibrate the frequency of other clocks used in national laboratories. These are usually commercial caesium clocks having very good long-term frequency stability, maintaining a frequency with a stability better than 1 part in {{val|e=14}} over a few months. The uncertainty of the primary standard frequencies is around one part in {{val|e=13}}.

[[Hydrogen]] [[maser]]s, which rely on the 1.4&nbsp;GHz hyperfine transition in atomic hydrogen, are also used in time metrology laboratories. Masers outperform any commercial caesium clock in terms of short-term frequency stability. In the past, these instruments have been used in all applications that require a steady reference across time periods of less than one day (frequency stability of about 1 part in ten{{clarify|date=August 2022}} for averaging times of a few hours). Because some active hydrogen masers have a modest but predictable frequency drift with time, they have become an important part of the BIPM's ensemble of commercial clocks that implement International Atomic Time.<ref name="bipm" />

=== Synchronization with satellites ===
The time readings of clocks operated in metrology labs operating with the BIPM need to be known very accurately. Some operations require synchronization of atomic clocks separated by great distances over thousands of kilometers. [[Satellite navigation|Global Navigational Satellite Systems]] (GNSS) provide a satisfactory solution to the problem of time transfer. Atomic clocks are used to broadcast time signals in the United States [[Global Positioning System|Global Positioning System (GPS)]], the Russian Federation's [[GLONASS|Global Navigation Satellite System (GLONASS)]], the European Union's [[Galileo (satellite navigation)|Galileo]] system and China's [[BeiDou]] system.

The signal received from one satellite in a metrology laboratory equipped with a receiver with an accurately known position allows the time difference between the local time scale and the GNSS system time to be determined with an uncertainty of a few [[nanosecond]]s when averaged over 15 minutes. Receivers allow the simultaneous reception of signals from several satellites, and make use of signals transmitted on two frequencies. As more satellites are launched and start operations, time measurements will become more accurate.

These methods of time comparison must make corrections for the effects of [[special relativity]] and [[general relativity]] of a few nanoseconds.

In June 2015, the National Physical Laboratory (NPL) in Teddington, UK; the French department of Time-Space Reference Systems at the Paris Observatory (LNE-SYRTE); the German [[Physikalisch-Technische Bundesanstalt|German National Metrology Institute (PTB) in Braunschweig]]; and Italy's Istituto Nazionale di Ricerca Metrologica (INRiM) in Turin labs started tests to improve the accuracy of satellite comparisons by a factor of 10, but still be limited to one part in {{val|1|e=16}}. These four European labs are developing and host a variety of experimental optical clocks that harness different elements in different experimental set-ups and want to compare their optical clocks against each other and check whether they agree.<ref name="Gibney 16–17">{{cite journal |last=Gibney |first=Elizabeth |date=2 June 2015 |title=Hyper-precise atomic clocks face off to redefine time – Next-generation timekeepers can only be tested against each other |journal=Nature |volume=522 |issue=7554 |pages=16–17 |bibcode=2015Natur.522...16G |doi=10.1038/522016a |pmid=26040875 |doi-access=free}}</ref>

=== International timekeeping ===
[[File:PSFS since T190.png|thumb|upright=2.6|Data points representing atomic clocks around the world that define International Atomic Time (TAI)]]
National laboratories usually operate a range of clocks. These are operated independently of one another and their measurements are sometimes combined to generate a scale that is more stable and more accurate than that of any individual contributing clock. This scale allows for time comparisons between different clocks in the laboratory. These atomic time scales are generally referred to as TA(k) for laboratory k.<ref>{{citation |title=Explanatory Supplement of BIPM Circular T |publisher=[[International Bureau of Weights and Measures]] |url=https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-date=2022-10-09 |url-status=live |date=12 July 2021 |access-date=16 June 2022}}</ref>

Coordinated Universal Time (UTC) is the result of comparing clocks in national laboratories around the world to [[International Atomic Time]] (TAI), then adding leap seconds as necessary. TAI is a weighted average of around 450 clocks in some 80 time institutions.<ref name="Time n.d.">{{cite book
|title = BIPM Annual Report on Time Activities
|url = https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|language=en
|page = 9
|publisher = International Bureau of Weights and Measures
|volume = 15
|date = 2020
|isbn = 978-92-822-2280-5
|issn = 1994-9405
|access-date = 16 June 2022
|archive-url=https://web.archive.org/web/20210814134522/https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|archive-date=14 August 2021
|url-status=live}}</ref> The relative stability of TAI is around one part in {{val|e=16}}.

Before TAI is published, the frequency of the result is compared with the SI second at various primary and secondary frequency standards. This requires relativistic corrections to be applied to the location of the primary standard which depend on the distance between the [[Reference ellipsoid|equal gravity potential]] and the [[Geoid|rotating geoid]] of Earth. The values of the rotating geoid and the TAI change slightly each month and are available in the [https://www.bipm.org/en/time-ftp/circular-t BIPM Circular T publication]. The TAI time-scale is deferred by a few weeks as the average of atomic clocks around the world is calculated.

TAI is not distributed in everyday timekeeping. Instead, an integer number of leap seconds are added or subtracted to correct for the Earth's rotation, producing UTC. The number of leap seconds is changed so that mean solar noon at the [[prime meridian (Greenwich)]] does not deviate from UTC noon by more than 0.9 seconds.

National metrology institutions maintain an approximation of UTC referred to as UTC(k) for laboratory k. UTC(k) is distributed by the BIPM's Consultative Committee for Time and Frequency. The offset UTC-UTC(k) is calculated every 5 days, the results are published monthly. Atomic clocks record UTC(k) to no more than 100 nanoseconds. In some countries, UTC(k) is the legal time that is distributed by radio, television, telephone, Internet, [[fiber-optic cables]], time signal transmitters, and speaking clocks. In addition, GNSS provides time information accurate to a few tens of nanoseconds or better.

=== Fiber Optics ===
In a next phase, these labs strive to transmit comparison signals in the visible spectrum through fibre-optic cables. This will allow their experimental optical clocks to be compared with an accuracy similar to the expected accuracies of the optical clocks themselves. Some of these labs have already established fibre-optic links, and tests have begun on sections between Paris and Teddington, and Paris and Braunschweig. Fibre-optic links between experimental optical clocks also exist between the American [[NIST]] lab and its partner lab [[JILA]], both in [[Boulder, Colorado]] but these span much shorter distances than the European network and are between just two labs. According to Fritz Riehle, a physicist at PTB, "Europe is in a unique position as it has a high density of the best clocks in the world".<ref name="Gibney 16–17" />

In August 2016 the French LNE-SYRTE in Paris and the German PTB in Braunschweig reported the comparison and agreement of two fully independent experimental strontium lattice optical clocks in Paris and Braunschweig at an uncertainty of {{val|5|e=-17}} via a newly established phase-coherent frequency link connecting Paris and Braunschweig, using {{convert|1415|km|mi|0|lk=on|abbr=on}} of telecom fibre-optic cable. The fractional uncertainty of the whole link was assessed to be {{val|2.5|e=-19}}, making comparisons of even more accurate clocks possible.<ref>
{{cite journal |author=Pottie |first1=Paul-Eric |last2=Grosche |first2=Gesine |date=19 August 2016 |title=A clock network for geodesy and fundamental science |journal=Nature Communications |volume=7 |pages=12443 |arxiv=1511.07735 |bibcode=2016NatCo...712443L |doi=10.1038/ncomms12443 |pmc=4980484 |pmid=27503795}}</ref><ref>{{Cite web |title=Optical fibre link opens a new era of time-frequency metrology, 19 August 2016 |url=https://syrte.obspm.fr/spip/news/article/liens-optiques-fibres-une-nouvelle-ere-de-la-metrologie-temps-frequence-s-ouvre?lang=en |url-status=live |archive-url=https://web.archive.org/web/20161114011816/https://syrte.obspm.fr/spip/news/article/liens-optiques-fibres-une-nouvelle-ere-de-la-metrologie-temps-frequence-s-ouvre?lang=en |archive-date=14 November 2016 |access-date=13 November 2016}}</ref>

In 2021, NIST compared transmission of signals from a series of experimental atomic clocks located about {{convert|1.5|km|mi|0|lk=on|abbr=on}} apart at the NIST lab, its partner lab JILA, and the University of Colorado all in Boulder, Colorado over air and fiber optic cable to a precision of {{val|8|e=-18}}.<ref>{{Cite journal |last1=Beloy |first1=Kyle |last2=Bodine |first2=Martha I. |last3=Bothwell |first3=Tobias |last4=Brewer |first4=Samuel M. |last5=Bromley |first5=Sarah L. |last6=Chen |first6=Jwo-Sy |last7=Deschênes |first7=Jean-Daniel |last8=Diddams |first8=Scott A. |last9=Fasano |first9=Robert J. |last10=Fortier |first10=Tara M. |last11=Hassan |first11=Youssef S. |date=25 March 2021 |title=Frequency ratio measurements at 18-digit accuracy using an optical clock network |url=https://www.nature.com/articles/s41586-021-03253-4 |journal=Nature |language=en |volume=591 |issue=7851 |pages=564–569 |bibcode=2021Natur.591..564B |doi=10.1038/s41586-021-03253-4 |issn=1476-4687 |pmid=33762766 |s2cid=232355391}}</ref><ref>{{Cite journal |last=sarah.henderson@nist.gov |date=24 March 2021 |title=NIST Team Compares 3 Top Atomic Clocks With Record Accuracy Over Both Fiber and Air |url=https://www.nist.gov/news-events/news/2021/03/nist-team-compares-3-top-atomic-clocks-record-accuracy-over-both-fiber-and |journal=NIST |language=en |access-date=16 February 2022}}</ref>

== Microwave atomic clocks ==

=== Caesium ===
{{main|1 = Caesium standard}}

The SI second is defined as a certain number of unperturbed ground-state [[Hyperfine structure|hyperfine transitions]] of the caesium-133 atom. Caesium standards are therefore regarded as primary time and frequency standards.

[[Caesium]] clocks include the [[NIST-F1]] clock, developed in 1999, and the [[NIST-F2]] clock, developed in 2013.<ref>{{Cite journal|last=swenson|date=29 December 1999|title=NIST-F1 Cesium Fountain Clock|url=https://www.nist.gov/news-events/news/1999/12/nist-f1-cesium-fountain-clock|access-date=19 February 2022|journal=NIST|language=en}}</ref><ref>{{Cite journal|last=mweiss|date=26 August 2009|title=NIST-F1 Cesium Fountain Atomic Clock|url=https://www.nist.gov/pml/time-and-frequency-division/time-realization/primary-standard-nist-f1|access-date=19 February 2022|journal=NIST|language=en}}</ref>

Caesium has several properties that make it a good choice for an atomic clock. Whereas a [[hydrogen]] atom moves at 1,600&nbsp;m/s at room temperature and a [[nitrogen]] atom moves at 510&nbsp;m/s, a [[caesium]] atom moves at a much slower speed of 130&nbsp;m/s due to its greater mass.<ref>{{Cite web|title=Temperature and Kinetic Energy – Answers|url=https://www.grc.nasa.gov/www/k-12/rocket/Lessons/airtempD_ans.html|access-date=19 February 2022|website=www.grc.nasa.gov}}</ref><ref name="Lombardi" /> The hyperfine frequency of caesium (~9.19&nbsp;GHz) is also higher than other elements such as rubidium (~6.8&nbsp;GHz) and hydrogen (~1.4&nbsp;GHz).<ref name="Lombardi" /> The high frequency of caesium allows for more accurate measurements. Caesium reference tubes suitable for national standards currently{{When|date=February 2025}} last about seven years and cost about US$35,000. Primary frequency and time standards like the United States Time Standard atomic clocks, NIST-F1 and NIST-F2, use far higher power.<ref name="Chip-Scale" /><ref>{{cite journal|date=3 April 2014|title=NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock|url=https://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm|url-status=live|archive-url=https://web.archive.org/web/20160819100504/http://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm|archive-date=19 August 2016|access-date=13 July 2017|journal=NIST}}</ref><ref>{{Cite web|last=University|first=Lancaster|date=11 May 2021|title=Clock Experiment Shows a Fundamental Connection Between Energy Consumption and Accuracy|url=https://scitechdaily.com/clock-experiment-shows-a-fundamental-connection-between-energy-consumption-and-accuracy/|access-date=16 February 2022|website=SciTechDaily|language=en-US}}</ref><ref>{{Cite web|last=Vleugels|first=Anouk|date=23 May 2021|title=New experiment: Clocks consuming more energy are more accurate… 'cause thermodynamics|url=https://thenextweb.com/news/clocks-consuming-more-energy-are-more-accurate-thermodynamics-experiment-syndication|access-date=16 February 2022|website=TNW {{!}} Science|language=en}}</ref>

====Block diagram====
In a [[caesium]] beam frequency reference, timing signals are derived from a high stability [[voltage-controlled crystal oscillator|voltage-controlled quartz crystal oscillator]] (VCXO) that is tunable over a narrow range. The output frequency of the VCXO (typically 5&nbsp;MHz) is multiplied by a [[frequency synthesizer]] to obtain microwaves at the frequency of the caesium atomic [[Hyperfine structure#Use in defining the SI second and meter|hyperfine transition]] (about {{val|9192.6317|u=MHz}}). The output of the frequency synthesizer is amplified and applied to a chamber containing caesium gas which absorbs the microwaves. The output current of the caesium chamber increases as absorption increases.

The remainder of the circuitry simply adjusts the running frequency of the VCXO to maximize the output current of the caesium chamber which keeps the oscillator tuned to the [[resonance]] frequency of the hyperfine transition.<ref>{{Cite web |url=http://hparchive.com/Journals/HPJ-1976-03.pdf |title=A Cesium Beam Frequency Reference for Severe Environment |access-date=24 Feb 2022  }}</ref>

=== Rubidium ===
{{main|1=Rubidium standard}}
[[File:121205-F-CX842-001.jpg|thumb|A team of United States Air Force airmen carrying a rubidium clock]]

The BIPM defines the unperturbed ground-state hyperfine transition frequency of the rubidium-87 atom, 6&nbsp;834&nbsp;682&nbsp;610.904&nbsp;312&nbsp;6&nbsp;Hz, in terms of the caesium standard frequency. Atomic clocks based on rubidium standards are therefore regarded as secondary representations of the second.

Rubidium standard clocks are prized for their low cost, small size (commercial standards are as small as {{val|1.7e5|u=mm3}})<ref name="Symmetricon-CSAC" /> and short-term stability. They are used in many commercial, portable and aerospace applications. Modern rubidium standard tubes last more than ten years, and can cost as little as US$50. Some commercial applications use a rubidium standard periodically corrected by a [[global positioning system]] receiver (see [[GPS disciplined oscillator]]). This achieves excellent short-term accuracy, with long-term accuracy equal to (and traceable to) the US national time standards.<ref>{{Cite web|last=National Physical Laboratory|date=2019|title=OC18|url=http://empir.npl.co.uk/oc18/|publisher=National Physical laboratory}}</ref>

=== Hydrogen ===
{{main|1=Hydrogen maser}}
[[File:Hydrogen maser.jpg|thumb|A hydrogen maser]]

The BIPM defines the unperturbed optical transition frequency of the hydrogen-1 neutral atom, 1&nbsp;233&nbsp;030&nbsp;706&nbsp;593&nbsp;514&nbsp;Hz, in terms of the caesium standard frequency. Atomic clocks based on hydrogen standards are therefore regarded as secondary representations of the second.

Hydrogen masers have superior short-term stability compared to other standards, but lower long-term accuracy. The long-term stability of hydrogen maser standards decreases because of changes in the cavity's properties over time. The relative error of hydrogen masers is 5 × 10<sup>−16</sup> for periods of 1000 seconds. This makes hydrogen masers good for [[radio astronomy]], in particular for [[Very-long-baseline interferometry|very long baseline interferometry]].<ref name=":9" />

Hydrogen masers are used for flywheel oscillators in laser-cooled atomic frequency standards and broadcasting time signals from national standards laboratories, although they need to be corrected as they drift from the correct frequency over time. The hydrogen maser is also useful for experimental tests of the effects of [[special relativity]] and [[general relativity]] such as [[gravitational red shift]].<ref name=":9" />

== Other types of atomic clocks ==
=== Nuclear clock concept ===
{{main|Nuclear clock}}

One theoretical possibility for improving the performance of atomic clocks is to use a ''nuclear'' energy transition (between different [[nuclear isomer]]s) rather than the [[atomic electron transition]]s which current atomic clocks measure. Most nuclear transitions operate at far too high a freuency to be measured, but the exceptionally low excitation energy of {{SimpleNuclide|link=yes|Thorium|229|m}} produces "[[gamma ray]]s" in the ultraviolet frequency range. In 2003, Ekkehard Peik and Christian Tamm<ref name="Peik2003">
{{cite journal
 | first1 = E. | last1 = Peik
 | first2 = Chr. | last2 = Tamm
 | title = Nuclear laser spectroscopy of the 3.5&nbsp;eV transition in <sup>229</sup>Th
 | url = http://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_4/4.4_zeit_und_frequenz/pdf/th001.pdf
 | journal = Europhysics Letters
 | volume = 61
 | issue = 2
 | pages = 181–186
 | date = 15 January 2003
 | doi = 10.1209/epl/i2003-00210-x
 | bibcode = 2003EL.....61..181P
 | s2cid = 250818523
 | access-date = 11 September 2019
 | archive-url = https://web.archive.org/web/20131216161909/http://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_4/4.4_zeit_und_frequenz/pdf/th001.pdf
 | archive-date = 16 December 2013
 | url-status = dead
}}</ref> noted this makes a clock possible with current optical frequency-measurement techniques. In 2012, it was shown that a [[nuclear clock]] based on a single {{SimpleNuclide|Th|229|charge=3+}} ion could provide a total fractional frequency inaccuracy of {{val|1.5|e=-19}}, which was better than existing 2019 optical atomic clock technology.<ref name="Campbell2012">
{{cite journal
 | first1=C. |last1=Campbell
 | first2=A.G. |last2=Radnaev
 | first3=A.  |last3=Kuzmich
 | first4=V.A. |last4=Dzuba
 | first5=V.V. |last5=Flambaum
 | first6=A. |last6=Derevianko
 | title = A single ion nuclear clock for metrology at the 19th decimal place
 | journal = Phys. Rev. Lett.
 | volume = 108
 | issue=12
 | article-number= 120802
 | date = 2012
 | doi = 10.1103/PhysRevLett.108.120802
 | pmid=22540568
 | arxiv= 1110.2490
 | bibcode=2012PhRvL.108l0802C
 | s2cid=40863227
}}</ref> Although a precise clock remains an unrealized theoretical possibility, efforts through the 2010s to measure the transition energy<ref name="Wense2016">
{{cite journal
 | journal=[[Nature (journal)|Nature]]
 | volume=533 | issue=7601 | pages=47–51
 | date=5 May 2016
 | title = Direct detection of the <sup>229</sup>Th nuclear clock transition
 | first1=Lars | last1=von der Wense
 | first2=Benedict | last2=Seiferle
 | first3=Mustapha | last3=Laatiaoui
 | first4=Jürgen B. | last4=Neumayr
 | first5=Hans-Jörg | last5=Maier
 | first6=Hans-Friedrich | last6=Wirth
 | first7=Christoph | last7=Mokry
 | first8=Jörg | last8=Runke
 | first9=Klaus | last9=Eberhardt
 | first10=Christoph E. | last10=Düllmann
 | first11=Norbert G. | last11=Trautmann
 | first12=Peter G. | last12=Thirolf
 | doi=10.1038/nature17669
 | pmid=27147026 | arxiv=1710.11398| bibcode=2016Natur.533...47V| s2cid=205248786 }}</ref><ref name="Thielking2018">{{cite journal
 | last1=Thielking |first1=J. |last2=Okhapkin |first2=M.V. |last3=Glowacki |first3=P.
 | last4=Meier |first4=D.M. |last5=von der Wense |first5=L.  |last6=Seiferle |first6=B.
 | last7=Düllmann |first7=C.E.  |last8=Thirolf |first8=P.G.  |last9=Peik |first9=E.
 | title = Laser spectroscopic characterization of the nuclear-clock isomer <sup>229m</sup>Th
 | journal = Nature
 | volume = 556
 | issue=7701 | year = 2018
 | pages = 321–325
 | doi = 10.1038/s41586-018-0011-8
 | pmid=29670266 | arxiv=1709.05325
 | bibcode=2018Natur.556..321T
 | s2cid=4990345
}}</ref><ref name="Masuda2019">
{{cite journal
 | title = X-ray pumping of the <sup>229</sup>Th nuclear clock isomer
 | journal=[[Nature (journal)|Nature]]
 | volume=573  | issue=7773 | pages=238–242
 | date=12 September 2019
 | first1=T. |last1=Masuda
 | first2=A. |last2=Yoshimi
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 | first10=S. |last10=Kitao
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 | first12=Y. |last12= Miyamoto
 | first13=K. |last13=Okai
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 | pmid=31511686
 | arxiv=1902.04823 | bibcode=2019Natur.573..238M
 | s2cid=119083861
}}</ref><ref name="SeiferleEnergy">
{{cite journal
 | title = Energy of the <sup>229</sup>Th nuclear clock transition
 | journal=[[Nature (journal)|Nature]]
 | volume=573  | issue=7773 | pages=243–246
 | date=12 September 2019
 | first1=B. |last1=Seiferle
 | first2=L. |last2=von der Wense
 | first3=P.V.  |last3=Bilous
 | first4=I. |last4=Amersdorffer
 | first5=C. |last5=Lemell
 | first6=F. |last6=Libisch
 | first7=S. |last7=Stellmer
 | first8=T. |last8=Schumm
 | first9=C.E. |last9=Düllmann
 | first10=A. |last10=Pálffy
 | first11=P.G. |last11=Thirolf
 | doi=10.1038/s41586-019-1533-4
 | arxiv=1905.06308 | pmid=31511684 | bibcode=2019Natur.573..243S
 | s2cid=155090121
}}</ref> culminated in the 2024 measurement of the optical frequency with sufficient accuracy ({{val|2020407384335|2|u=kHz}} = {{val|2.020407384335|(2)|e=15|u=Hz}}<ref name="Thirolf2024">
{{cite news
 |title=Shedding Light on the Thorium-229 Nuclear Clock Isomer
 |first=Peter |last=Thirolf
 |date=April 29, 2024
 |journal=[[Physics (magazine)|Physics]] |volume=17 |article-number=71
 |doi=10.1103/Physics.17.71
 |url=https://physics.aps.org/articles/v17/71
}}</ref><ref name="Tiedau2024">
{{cite journal
 |title=Laser Excitation of the Th-229 Nucleus
 |first1=J. |last1=Tiedau  |first2=M. V. |last2=Okhapkin  |first3=K. |last3=Zhang
 |first4=J. |last4=Thielking  |first5=G. |last5=Zitzer  |first6=E. |last6=Peik
 |first7=F. |last7=Schaden  |first8=T. |last8=Pronebner  |first9=I. |last9=Morawetz
 |first10=L. |last10=Toscani De Col |first11=F. |last11=Schneider  |first12=A. |last12=Leitner
 |first13=M. |last13=Pressler  |first14=G.A. |last14=Kazakov  |first15=K. |last15=Beeks
 |first16=T. |last16=Sikorsky  |first17=T. |last17=Schumm
 |display-authors=6
 |journal=[[Physical Review Letters]] |volume=132
 |date=29 April 2024
 |issue=18 |article-number=182501 |doi=10.1103/PhysRevLett.132.182501
 |pmid=38759160 |bibcode=2024PhRvL.132r2501T |url=https://www.tuwien.at/fileadmin/Assets/tu-wien/News/2024/Thorium_Preprint.pdf
 |quote=The nuclear resonance for the Th<sup>4+</sup> ions in Th:CaF<sub>2</sub> is measured at the wavelength {{val|148.3821|(5)|u=nm}}, frequency {{val|2020.409|(7)|u=THz}}, and the fluorescence lifetime in the crystal is {{val|630|(15)|u=s}}, corresponding to an isomer half-life of {{val|1740|(50)|u=s}} for a nucleus isolated in vacuum.
}}</ref><ref>
{{cite journal
 |title=Laser excitation of the <sup>229</sup>Th nuclear isomeric transition in a solid-state host
 |first1=R. |last1=Elwell  |first2=Christian |last2=Schneider  |first3=Justin |last3=Jeet
 |first4=J. E. S. |last4=Terhune  |first5=H. W. T. |last5=Morgan  |first6=A. N. |last6=Alexandrova
 |first7=Hoang Bao |last7=Tran Tan  |first8=Andrei |last8=Derevianko  |first9=Eric R. |last9=Hudson
 |journal=[[Physical Review Letters]] |date=2 July 2024
 |volume=133 |issue=1 |article-number=013201
 |doi=10.1103/PhysRevLett.133.013201
 |pmid=39042795 |arxiv=2404.12311
 |quote=a narrow, laser-linewidth-limited spectral feature at {{val|148.38219|(4)|errend=<sub>stat</sub>(20)<sub>sys</sub>|u=nm}} ({{val|2020407.3|(5)|errend=<sub>stat</sub>(30)<sub>sys</sub>|u=GHz}}) that decays with a lifetime of {{val|568|(13)|errend=<sub>stat</sub>(20)<sub>sys</sub>|u=s}}. This feature is assigned to the excitation of the <sup>229</sup>Th nuclear isomeric state, whose energy is found to be {{val|8.355733|(2)|errend=<sub>stat</sub>(10)</sys>|u=eV}} in <sup>229</sup>Th:LiSrAlF<sub>6</sub>.
}}</ref><ref name="Zhang2024">
{{cite journal
 |title=Frequency ratio of the <sup>229m</sup>Th nuclear isomeric transition and the <sup>87</sup>Sr atomic clock
 |first1=Chuankun |last1=Zhang  |first2=Tian |last2=Ooi  |first3=Jacob S. |last3=Higgins
 |first4=Jack F. |last4=Doyle  |first5=Lars |last5=von der Wense  |first6=Kjeld |last6=Beeks
 |first7=Adrian |last7=Leitner  |first8=Georgy |last8=Kazakov  |first9=Peng |last9=Li
 |first10=Peter G. |last10=Thirolf  |first11=Thorsten |last11=Schumm  |first12=Jun |last12=Ye |author-link12=Jun Ye
 |journal=[[Nature (journal)|Nature]] |volume=633 |issue=8028 |pages=63–70
 |date=4 September 2024
 |doi=10.1038/s41586-024-07839-6
 |pmid=39232152 |arxiv=2406.18719
 |bibcode=2024Natur.633...63Z |quote=The transition frequency between the {{math|1=''I'' = 5/2}} ground state and the {{math|1=''I'' = 3/2}} excited state is determined as: {{math|1=
''𝜈''<sub>Th</sub> = {{sfrac|1|6}} (''𝜈''<sub>a</sub> + 2''𝜈''<sub>b</sub> + 2''𝜈''<sub>c</sub> + ''𝜈''<sub>d</sub>) = {{val|2020407384335|(2)|u=kHz}}}}.
}}</ref>) that an experimental optical nuclear clock can now be constructed.<ref>{{cite news
 |title=A nuclear clock prototype hints at ultraprecise timekeeping
 |first=Emily |last=Conover |author-link=Emily Conover 
 |date=4 September 2024
 |journal=[[ScienceNews]]
 |url=https://www.sciencenews.org/article/nuclear-clock-ultraprecise-timekeeping
}}</ref>

Although neutral {{SimpleNuclide|Th|229|m}} atoms decay in microseconds by [[internal conversion]],<ref name="Seiferle2017">
{{cite journal
 | last1=Seiferle |first1=Benedict  |last2=von der Wense |first2=Lars  |last3=Thirolf |first3=Peter G.
 | title = Lifetime measurement of the <sup>229</sup>Th nuclear isomer  
 | journal = [[Physical Review Letters]]
 | year = 2017 | volume = 118 | issue = 4 | article-number = 042501
 | doi = 10.1103/PhysRevLett.118.042501
 | pmid = 28186791 | arxiv = 1801.05205 | bibcode = 2017PhRvL.118d2501S | s2cid = 37518294
 | quote = A half-life of {{val|7|1|u=us}} has been measured
}}</ref> this pathway is energetically prohibited in {{SimpleNuclide|Th|229|m|charge=+}} ions, as the second and higher [[ionization energy]] is greater than the nuclear excitation energy, giving {{SimpleNuclide|Th|229|m|charge=+}} ions a long half-life on the order of {{val|e=3|u=s}}.{{r|Tiedau2024}} It is the large ratio between transition frequency and isomer lifetime which gives the clock a high [[quality factor]].{{r|Campbell2012}}

A nuclear energy transition offers the following potential advantages:<ref>
{{cite conference
 |title=Concepts and Prospects for a Thorium-229 Nuclear Clock
 |first=Ekkehard  |last=Peik
 |conference=EMMI Workshop: The <sup>229m</sup>Th Nuclear Isomer Clock
 |location=Darmstadt
 |date=25–27 September 2012
 |url=https://indico.gsi.de/event/1797/contribution/4/material/slides/0.pdf
 |access-date=2 December 2019
 |archive-date=10 October 2021
 |archive-url=https://web.archive.org/web/20211010004300/https://indico.gsi.de/event/1797/contributions/4786/attachments/3908/4827/E_Peik-Thorium-Workshop-GSI-_2012.pdf
 |url-status=live
}}</ref>
# Higher frequency. All other things being equal, a higher-frequency transition offers greater stability for simple statistical reasons (fluctuations are averaged over more cycles).
# Insensitivity to environmental effects. Due to its small size and the shielding effect of the surrounding electrons, an atomic nucleus is much less sensitive to ambient electromagnetic fields than is an electron in an orbital.
# Greater number of atoms. Because of the aforementioned insensitivity to ambient fields, it is not necessary to have the clock atoms well-separated in a dilute gas. Current measurements take advantage of the [[Mössbauer effect]] and place the thorium ions in a solid, which allows billions of atoms to be interrogated.

== Potential for redefining the second ==
In 2022, the best realisation of the second is done with caesium primary standard clocks such as IT-CsF2, NIST-F2, NPL-CsF2, PTB-CSF2, SU–CsFO2 or SYRTE-FO2. These clocks work by laser-cooling a cloud of caesium atoms to a microkelvin in a magneto-optic trap. These cold atoms are then launched vertically by laser light. The atoms then undergo Ramsey excitation in a microwave cavity. The fraction of excited atoms are then detected by [[laser]] beams. These clocks have {{val|5|e=-16}} systematic uncertainty, which is equivalent to 50 picoseconds per day. A system of several fountains worldwide contributes to International Atomic Time. These caesium clocks also underpin optical frequency measurements.

The advantage of optical clocks can be explained by the statement that the instability <math>\sigma\propto \frac{\Delta f}{f} \frac{1}{S/N}</math>, where <math>\sigma</math> is the instability, f is the frequency, and ''S''/''N'' is the signal-to-noise ratio. This leads to the equation <math>\sigma(\tau)=\frac{1}{2 \pi f \sqrt{N T_{int} \tau}}</math>.

Optical clocks are based on forbidden optical transitions in ions or atoms. They have frequencies around {{val|e=15|u=Hz}}, with a natural linewidth <math>\Delta f</math> of typically 1&nbsp;Hz, so the Q-factor is about {{val|e=15}}, or even higher. They have better stabilities than microwave clocks, which means that they can facilitate evaluation of lower uncertainties. They also have better time resolution, which means the clock "ticks" faster.<ref>{{Cite journal|last=National Physical Laboratory|date=2011|title=When should we change the definition of the second?|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=369|issue=1953|pages=4109–4130|doi=10.1098/rsta.2011.0237|pmid=21930568|bibcode=2011RSPTA.369.4109G|s2cid=6896025}}</ref> Optical clocks use either a single ion, or an [[optical lattice]] with {{val|e=4}}–{{val|e=6}} atoms.

=== Rydberg constant ===
A definition based on the [[Rydberg constant]] would involve fixing the value to a certain value: <math>R_{\infty}=\frac{m_e e^4}{8 \varepsilon_0^2 h ^3 c}=\frac{m_e c \alpha^2}{2h}</math>. The Rydberg constant describes the energy levels in a hydrogen atom with the nonrelativistic approximation <math>E_n \approx -\frac{R_{\infty} c h}{n^2}</math>.

The only viable way to fix the Rydberg constant involves trapping and cooling hydrogen. Unfortunately, this is difficult because it is very light and the atoms move very fast, causing Doppler shifts. The radiation needed to cool the hydrogen —{{val|121.5|u=nm}}— is also difficult. Another hurdle involves improving the uncertainty in [[quantum electrodynamics]]/QED calculations.<ref name=":10">{{Cite journal|last=Gill|first=Patrick|date=28 October 2011|title=When should we change the definition of the second?|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=369|issue=1953|pages=4109–4130|doi=10.1098/rsta.2011.0237|pmid=21930568|bibcode=2011RSPTA.369.4109G|s2cid=6896025}}</ref>

In the Report of the 25th meeting of the [[Consultative Committee for Units]] (2021),<ref>{{Cite web |title=Consultative Committee for Units (CCU) Report of the 25th meeting (21-23 September 2021) to the International Committee for Weights and Measures |url=https://www.bipm.org/documents/20126/68201438/CCU25.pdf/ab1be833-d656-ae2e-36fa-feb04948ed4c}}</ref> 3 options were considered for the redefinition of the second sometime around 2026, 2030, or 2034. The first redefinition approach considered was a definition based on a single atomic reference transition. The second redefinition approach considered was a definition based on a collection of frequencies. The third redefinition approach considered was a definition based on fixing the numerical value of a fundamental constant, such as making the Rydberg constant the basis for the definition. The committee concluded there was no feasible way to redefine the second with the third option, since no physical constant is known to enough digits currently to enable realizing the second with a constant.

=== Requirements ===
A redefinition must include improved optical clock reliability. TAI must be contributed to by optical clocks before the BIPM affirms a redefinition. A consistent method of sending signals, such as [[Optical fiber|fiber-optics]], must be developed before the second is redefined.<ref name=":10" />

=== Secondary representations of the second ===
Representations of the second other than the SI cesium standard are motivated by the increasing accuracy of other atomic clocks. In particular the high frequencies and small linewidths of optical clocks promise significantly improved signal-to-noise ratio and instability. Further secondary representations would aid in the preparation of a future redefinition of the second<ref name=":11">{{cite web |author=Riehle |first=Fritz |title=On Secondary Representations of the Second |url=http://www.ursi.org/Proceedings/ProcGA08/papers/A01p2.pdf |url-status=dead |archive-url=https://web.archive.org/web/20150623002643/http://www.ursi.org/Proceedings/ProcGA08/papers/A01p2.pdf |archive-date=23 June 2015 |access-date=22 June 2015 |website=Physikalisch-Technische Bundesanstalt, Division Optics}}</ref>

A list of frequencies recommended for secondary representations of the second is maintained by the International Bureau of Weights and Measures (BIPM) since 2006 and is [https://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies-second available online]. The list contains the frequency values and the respective standard uncertainties for the rubidium microwave transition and for several optical transitions. These secondary frequency standards are accurate at the level of {{10^|-18}}; however, the uncertainties provided in the list are in the range {{10^|-14}} – {{10^|-15}} since they are limited by the linking to the caesium primary standard that currently (2018) defines the second.<ref name="bipm" />

{| class="wikitable"
! Type
! Working frequency ([[Hz]])
! Relative [[Allan deviation]]<br />(typical clocks)
! Reference
|-
| [[Isotopes of caesium|<sup>133</sup>Cs]]
| {{val|9.192631770|e=9}} [[Second#International second|&nbsp;by definition]]
| {{val|e=-13}}
| <ref>
 {{cite book |title=SI Brochure |date=2014 |publisher=[[BIPM]] |chapter=Unit of time (second) |access-date=23 June 2015 |chapter-url=http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html |archive-url=https://web.archive.org/web/20111119081900/http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html |archive-date=19 November 2011 |url-status=live |orig-year=2006}}</ref>
|-
| [[Isotopes of rubidium|<sup>87</sup>Rb]]
| {{val|6.834682610904324|e=9}}
| {{val|e=-12}}
| <ref>{{Cite web |title=<sup>87</sup>Rubidium BIPM document |url=http://www.bipm.org/utils/common/pdf/mep/SRS_87Rb_6834.pdf |url-status=live |archive-url=https://web.archive.org/web/20150923224650/http://www.bipm.org/utils/common/pdf/mep/SRS_87Rb_6834.pdf |archive-date=23 September 2015 |access-date=22 June 2015}}</ref>
|-
| [[Isotopes of hydrogen|<sup>1</sup>H]]
| {{val|1.4204057517667|e=9}}
| {{val|e=-15}}
| <ref>
 {{cite journal |last1=Essen |first1=L |author-link1=Louis Essen |last2=Donaldson |first2=R W |last3=Hope |first3=E G |last4=Bangham |first4=M J |date=July 1973 |title=Hydrogen Maser Work at the National Physical Laboratory |journal=Metrologia |volume=9 |issue=3 |pages=128–137 |bibcode=1973Metro...9..128E |doi=10.1088/0026-1394/9/3/004 |s2cid=250828528}}</ref><ref>
 {{cite journal |last1=Dupays |first1=Arnaud |last2=Beswick |first2=Alberto |last3=Lepetit |first3=Bruno |last4=Rizzo |first4=Carlo |date=August 2003 |title=Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen |url=https://hal.archives-ouvertes.fr/file/index/docid/561/filename/hfspra.pdf |url-status=live |journal=Physical Review A |volume=68 |issue=5 |arxiv=quant-ph/0308136 |bibcode=2003PhRvA..68e2503D |doi=10.1103/PhysRevA.68.052503 |s2cid=3957861 |archive-url=https://web.archive.org/web/20190114100511/https://hal.archives-ouvertes.fr/file/index/docid/561/filename/hfspra.pdf |archive-date=14 January 2019 |access-date=26 September 2016 |article-number=052503}}</ref>
|-
| Optical clock ([[Isotopes of strontium|<sup>87</sup>Sr]])
| {{val|4.292280042298734|e=14}}
| {{val|e=-17}}
| <ref>{{Cite web |title=<sup>87</sup>Strontium BIPM document |url=http://www.bipm.org/utils/common/pdf/mep/87Sr_429THz_2013.pdf |url-status=live |archive-url=https://web.archive.org/web/20160304113120/http://www.bipm.org/utils/common/pdf/mep/87Sr_429THz_2013.pdf |archive-date=4 March 2016 |access-date=25 June 2015}}</ref>
|-
| Optical clock ([[Isotopes of aluminum|<sup>27</sup>Al<sup>+</sup>]])
| {{val|1.12101539320785916|e=15}}
| {{val|e=-18}}
| <ref>{{cite web |title=<sup>27</sup>Aluminum ion BIPM document |url=https://www.bipm.org/documents/20126/69375069/27Al+_1121THz_2021.pdf/af023aa2-90d2-74eb-14bf-842141bf288e |url-status=live |archive-url=https://web.archive.org/web/20220802111533/https://www.bipm.org/documents/20126/69375069/27Al+_1121THz_2021.pdf/af023aa2-90d2-74eb-14bf-842141bf288e |archive-date=2022-08-02 |accessdate=2022-12-09}}</ref><ref>{{cite journal |last1=Brewer |first1=S. |last2=Chen |first2=J.-S. |last3=Hankin |first3=A. |last4=Clements |first4=E. |date=15 July 2019 |title=<sup>27</sup>Al<sup>+</sup> Quantum-Logic Clock with a Systematic Uncertainty below 10<sup>−18</sup> |url=https://doi.org/10.1103/PhysRevLett.123.033201 |journal=Physical Review Letters |volume=123 |issue=3 |arxiv=1902.07694 |bibcode=2019PhRvL.123c3201B |doi=10.1103/PhysRevLett.123.033201 |pmid=31386450 |s2cid=119075546 |article-number=033201}}</ref>
|-
| Optical clock ([[Isotopes of ytterbium|<sup>171</sup>Yb<sup>+</sup>]], 642 THz)
| {{val|6.4212149677264512|e=14}}
| {{val|e=-18}}
| <ref>{{cite web |title=<sup>171</sup>Ytterbium 171 ion (642 THz) BIPM document |url=https://www.bipm.org/documents/20126/69375142/171Yb+_642THz_2021.pdf/a22c77ad-0c15-e054-ee6c-b7114a23a7a3 |url-status=live |archive-url=https://web.archive.org/web/20220802111530/https://www.bipm.org/documents/20126/69375142/171Yb+_642THz_2021.pdf/a22c77ad-0c15-e054-ee6c-b7114a23a7a3 |archive-date=2022-08-02 |accessdate=2022-12-09}}</ref><ref>{{cite journal |last1=Huntemann |first1=N. |last2=Sanner |first2=C. |last3=Lipphardt |first3=B. |last4=Tamm |first4=Chr. |date=8 February 2016 |title=Single-Ion Atomic Clock with 3×10<sup>−18</sup> Systematic Uncertainty |url=https://doi.org/10.1103/PhysRevLett.116.063001 |journal=Physical Review Letters |volume=116 |issue=6 |arxiv=1602.03908 |bibcode=2016PhRvL.116f3001H |doi=10.1103/PhysRevLett.116.063001 |pmid=26918984 |s2cid=19870627 |article-number=063001}}</ref>
|-
| Optical clock ([[Isotopes of ytterbium|<sup>171</sup>Yb<sup>+</sup>]], 688 THz)
| {{val|6.8835897930930824|e=14}}
| {{val|e=-16}}
| <ref>{{cite web |title=<sup>171</sup>Ytterbium 171 ion (688 THz) BIPM document |url=https://www.bipm.org/documents/20126/69375151/171Yb+_688THz_2021.pdf/6ffc6ec4-76a5-d043-ba4c-af680662fc29 |url-status=live |archive-url=https://web.archive.org/web/20220802112424/https://www.bipm.org/documents/20126/69375151/171Yb+_688THz_2021.pdf/6ffc6ec4-76a5-d043-ba4c-af680662fc29 |archive-date=2022-08-02 |accessdate=2022-12-09}}</ref><ref>{{cite journal |last1=Leute |first1=J. |last2=Huntemann |first2=N. |last3=Lipphardt |first3=B. |last4=Tamm |first4=Christian |date=3 February 2016 |title=Frequency Comparison of <sup>171</sup>Yb<sup>+</sup> Ion Optical Clocks at PTB and NPL via GPS PPP |url=https://doi.org/10.1109/TUFFC.2016.2524988 |journal=IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |volume=63 |issue=7 |pages=981–985 |arxiv=1507.04754 |doi=10.1109/TUFFC.2016.2524988 |pmid=26863657 |s2cid=20466105}}</ref>
|}

Twenty-first century experimental atomic clocks that provide non-caesium-based secondary representations of the second are becoming so precise that they are likely to be used as extremely sensitive detectors for other things besides measuring frequency and time. For example, the frequency of atomic clocks is altered slightly by gravity, magnetic fields, electrical fields, force, motion, temperature and other phenomena. The experimental clocks tend to continue to improve, and leadership in performance has shifted back and forth between various types of experimental clocks.<ref>{{Cite web |date=September 2001 |title=StackPath |url=https://www.laserfocusworld.com/test-measurement/research/article/16556429/alloptical-atomic-clock-may-be-worlds-most-precise |access-date=11 February 2022 |website=www.laserfocusworld.com}}</ref><ref>{{Cite web |last=Ahmed |first=Issam |title=What the world's most accurate clock can tell us about Earth and the cosmos |url=https://phys.org/news/2021-09-world-accurate-clock-earth-cosmos.html |access-date=11 February 2022 |website=phys.org |language=en}}</ref><ref name="news.mit.edu">{{Cite web |date=16 December 2020 |title=New type of atomic clock keeps time even more precisely |url=https://news.mit.edu/2020/atomic-clock-time-precise-1216 |access-date=11 February 2022 |website=MIT News {{!}} Massachusetts Institute of Technology |language=en}}</ref><ref>{{Cite web |last=Woodward |first=Aylin |date=5 October 2017 |title=The most precise atomic clock ever made is a cube of quantum gas |url=https://www.newscientist.com/article/2149568-the-most-precise-atomic-clock-ever-made-is-a-cube-of-quantum-gas/ |access-date=11 February 2022 |website=New Scientist |language=en-US}}</ref>

== Applications ==
[[File:How an atomic clock works, and its use in the global positioning system (GPS).webm|thumb|Atomic clocks and their usage in GPS, by [[Bill Hammack]]]]
The development of atomic clocks has led to many scientific and technological advances such as precise global and regional [[satellite navigation|navigation satellite systems]], and applications in the [[Internet]], which depend critically on frequency and time standards. Atomic clocks are installed at sites of [[time signal]] radio transmitters.<ref>{{Cite journal|last1=Ren|first1=Wei|last2=Li|first2=Tang|last3=Qu|first3=Qiuzhi|last4=Wang|first4=Bin|last5=Li|first5=Lin|last6=Lü|first6=Desheng|last7=Chen|first7=Weibiao|last8=Liu|first8=Liang|date=18 December 2020|title=Development of a space cold atom clock|url=https://doi.org/10.1093/nsr/nwaa215|journal=National Science Review|volume=7|issue=12|pages=1828–1836|doi=10.1093/nsr/nwaa215|issn=2095-5138|pmc=8288775|pmid=34691520}}</ref> They are used at some long-wave and medium-wave broadcasting stations to deliver a very precise carrier frequency.<ref>{{Cite journal|last=andrew.novick@nist.gov|date=11 February 2010|title=Help with WWVB Radio Controlled Clocks|url=https://www.nist.gov/pml/time-and-frequency-division/time-distribution/radio-station-wwvb/help-wwvb-radio-controlled|access-date=15 February 2022|journal=NIST|language=en}}</ref> Atomic clocks are used in many scientific disciplines, such as for long-baseline [[interferometry]] in [[radioastronomy|radio astronomy]].<ref>
{{cite book
 |page=266
 |last1=McCarthy |first1=D. D.
 |last2=Seidelmann |first2=P. K.
 |author-link1=Dennis McCarthy (scientist)
 |year=2009
 |title=TIME—From Earth Rotation to Atomic Physics
 |location=Weinheim
 |publisher=Wiley-VCH
 |isbn=978-3-527-40780-4
}}</ref>

=== Global navigation satellite systems ===
The [[Global Positioning System]] (GPS) operated by the [[United States Space Force]] provides very accurate timing and frequency signals. A GPS receiver works by measuring the relative time delay of signals from a minimum of four, but usually more, GPS satellites, each of which has at least two onboard caesium and as many as two rubidium atomic clocks. The relative times are mathematically transformed into three absolute spatial coordinates and one absolute time coordinate.<ref name="gps.gov">{{cite web|url=http://www.gps.gov/systems/gps |title=Global Positioning System |publisher=Gps.gov |access-date=26 June 2010 |url-status=dead |archive-url=https://web.archive.org/web/20100730173245/http://www.gps.gov/systems/gps |archive-date=30 July 2010 }}</ref> GPS Time (GPST) is a continuous time scale and theoretically accurate to about 14 [[nanosecond]]s.<ref>{{cite journal |author=Allan |first=David W. |year=1997 |title=The Science of Timekeeping |url=http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf |url-status=live |journal=Application Note |publisher=Hewlett Packard |issue=1289 |archive-url=https://web.archive.org/web/20121025234726/http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf |archive-date=25 October 2012}}</ref> However, most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds.<ref>{{cite journal |last1=Dana |first1=Peter H. |last2=Penro |first2=Bruce M. |date=July–August 1990 |title=The Role of GPS in Precise Time and Frequency Dissemination |url=http://www.pdana.com/PHDWWW_files/gpsrole.pdf |url-status=live |journal=GPSworld |archive-url=https://web.archive.org/web/20121215031941/http://www.pdana.com/PHDWWW_files/gpsrole.pdf |archive-date=15 December 2012 |access-date=27 April 2014}}</ref><ref>{{cite web|url=http://www.atomic-clock.galleon.eu.com/support/gps-time-accuracy.html|title=GPS time accurate to 100 nanoseconds|publisher=Galleon|access-date=12 October 2012|archive-date=14 May 2012|archive-url=https://web.archive.org/web/20120514001920/http://www.atomic-clock.galleon.eu.com/support/gps-time-accuracy.html|url-status=live}}</ref>

GPST is related to but differs from TAI (International Atomic Time) and UTC (Coordinated Universal Time). GPST remains at a constant offset from TAI (TAI – GPST = 19 seconds) and like TAI does not implement [[leap seconds]]. Periodic corrections are performed to the on-board clocks in the satellites to keep them synchronized with ground clocks.<ref>{{cite web|url=https://confluence.qps.nl/display/KBE/UTC+to+GPS+Time+Correction|title=UTC to GPS Time Correction|website=qps.nl|access-date=4 October 2015|archive-date=21 March 2017|archive-url=https://web.archive.org/web/20170321094832/https://confluence.qps.nl/display/KBE/UTC+to+GPS+Time+Correction|url-status=live}}</ref><ref>{{cite web|title=NAVSTAR GPS User Equipment Introduction|url=http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf|access-date=4 October 2015|archive-date=21 October 2013|archive-url=https://web.archive.org/web/20131021060507/http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf|url-status=live}} Section 1.2.2</ref> The GPS navigation message includes the difference between GPST and UTC. As of July 2015, GPST is 17 seconds ahead of UTC because of the leap second added to UTC on 30 June 2015.<ref>{{Cite web |url=http://www.navcen.uscg.gov/?pageName=currentNanus&format=txt |title=NOTICE ADVISORY TO NAVSTAR USERS (NANU) |date=May 2017 |access-date=4 October 2015 |archive-date=28 May 2017 |archive-url=https://web.archive.org/web/20170528232614/https://www.navcen.uscg.gov/?pageName=currentNanus&format=txt |url-status=dead }}</ref><ref>{{cite web|url=https://gps.afspc.af.mil/gps/archive/2012/nanus/2012034.nnu |title=Notice Advisory to Navstar Users (NANU) 2012034 |date=30 May 2012 |access-date=2 July 2012 |publisher=GPS Operations Center |url-status=dead |archive-url=https://web.archive.org/web/20130408111458/https://gps.afspc.af.mil/gps/archive/2012/nanus/2012034.nnu |archive-date=8 April 2013 }}</ref> Receivers subtract this offset from GPS Time to calculate UTC.

The [[GLONASS|GLObal NAvigation Satellite System]] (GLONASS) operated by the [[Russian Aerospace Defence Forces]] provides an alternative to the Global Positioning System (GPS) system and is the second navigational system in operation with global coverage and of comparable precision. GLONASS Time (GLONASST) is generated by the GLONASS Central Synchroniser and is typically better than 1,000 nanoseconds.<ref>{{cite web|url=http://www.navipedia.net/index.php/Time_References_in_GNSS|title=Time References in GNSS|website=navipedia.net|access-date=2 October 2015|archive-date=2 June 2018|archive-url=https://web.archive.org/web/20180602120535/http://www.navipedia.net/index.php/Time_References_in_GNSS|url-status=live}}</ref> Unlike GPS, the GLONASS time scale implements leap seconds, like UTC.<ref>{{Cite web |url=http://www.spacecorp.ru/upload/iblock/1c4/cgs-aaixymyt%205.1%20ENG%20v%202014.02.18w.pdf |title=GLONASS Interface Control Document, Navigation radiosignal In bands L1, L2 (ICD L1, L2 GLONASS), Russian Institute of Space Device Engineering, Edition 5.1, 2008 |access-date=2 October 2015 |archive-date=14 April 2016 |archive-url=https://web.archive.org/web/20160414062343/http://www.spacecorp.ru/upload/iblock/1c4/cgs-aaixymyt%205.1%20ENG%20v%202014.02.18w.pdf |url-status=live }}</ref>

[[File:ESA Galileo Passive Hydrogen Maser.jpg|thumb|upright=1.2|Space Passive Hydrogen Maser used in ESA Galileo satellites as a master clock for an onboard timing system]]

The [[Galileo (satellite navigation)|Galileo]] [[Satellite navigation#Global satellite navigation systems|Global Navigation Satellite System]] is operated by the [[European GNSS Agency]] and [[European Space Agency]]. Galileo started offering global Early Operational Capability (EOC) on 15 December 2016, providing the third, and first non-military operated, global navigation satellite system.<ref name="operational">{{cite web|url=http://www.esa.int/Our_Activities/Navigation/Galileo_begins_serving_the_globe|title=Galileo begins serving the globe|publisher=European Space Agency|access-date=15 December 2016|archive-date=13 September 2019|archive-url=https://web.archive.org/web/20190913073120/http://www.esa.int/Our_Activities/Navigation/Galileo_begins_serving_the_globe|url-status=live}}</ref><ref name="European Commission"/> Galileo System Time (GST) is a continuous time scale which is generated on the ground at the Galileo Control Centre in Fucino, Italy, by the Precise Timing Facility, based on averages of different atomic clocks and maintained by the Galileo Central Segment and synchronised with TAI with a nominal offset below 50 nanoseconds.<ref>{{Cite web |url=http://www.gsc-europa.eu/system/files/galileo_documents/OS_SIS_OSD_Web.pdf |title=European GNSS (Galileo) Open Service Signal-In-Space Operational Status Definition, Issue 1.0, September 2015 |access-date=3 October 2015 |archive-date=9 January 2017 |archive-url=https://web.archive.org/web/20170109163657/https://www.gsc-europa.eu/system/files/galileo_documents/OS_SIS_OSD_Web.pdf |url-status=dead }}</ref><ref>{{Cite web |url=http://www.unoosa.org/pdf/icg/2009/icg-4/45d.pdf |title=1 The Definition and Implementation of Galileo System Time (GST). ICG-4 WG-D on GNSS time scales. Jérôme Delporte. CNES – French Space Agency. |access-date=5 October 2015 |archive-date=6 November 2016 |archive-url=https://web.archive.org/web/20161106184619/http://www.unoosa.org/pdf/icg/2009/icg-4/45d.pdf |url-status=live }}</ref><ref name="Galileo's clocks">{{cite web|url=http://www.esa.int/Our_Activities/Navigation/Galileo/Galileo_s_clocks|title=Galileo's clocks|publisher=European Space Agency|access-date=16 January 2017|archive-date=29 August 2019|archive-url=https://web.archive.org/web/20190829183314/http://www.esa.int/Our_Activities/Navigation/Galileo/Galileo_s_clocks|url-status=live}}</ref><ref name="European Commission">{{cite news|title=Galileo's contribution to the MEOSAR system|url=http://ec.europa.eu/growth/sectors/space/galileo/sar/meosar-contribution/index_en.htm|access-date=30 December 2015|publisher=European Commission|archive-date=9 July 2016|archive-url=https://web.archive.org/web/20160709033428/http://ec.europa.eu/growth/sectors/space/galileo/sar/meosar-contribution/index_en.htm|url-status=live}}</ref> According to the European GNSS Agency, Galileo offers 30 nanoseconds timing accuracy.<ref name="Timing accuracy">{{cite web|url=https://www.gsa.europa.eu/galileo/services/initial-services|title=Galileo Goes Live|publisher=European GNSS Agency|date=15 December 2016|access-date=1 February 2017|archive-date=15 January 2021|archive-url=https://web.archive.org/web/20210115130957/http://www.gsa.europa.eu/galileo/services/initial-services|url-status=live}}</ref>

The March 2018 Quarterly Performance Report by the European GNSS Service Centre reported the UTC Time Dissemination Service Accuracy was ≤&nbsp;7.6 nanoseconds, computed by accumulating samples over the previous 12 months, and exceeding the ≤&nbsp;30 ns target.<ref name="Timing accuracy2">{{cite web|url=https://www.gsc-europa.eu/system/files/galileo_documents/Galileo-IS-OS-Quarterly-Performance_Report-Q4-2017.pdf|title=Galileo Initial Services – Open Service – Quarterly Performance Report Oct–Nov–Dec 2017|publisher=European GNSS Service Centre|date=28 March 2018|access-date=28 March 2017|archive-date=26 August 2019|archive-url=https://web.archive.org/web/20190826181137/https://www.gsc-europa.eu/system/files/galileo_documents/Galileo-IS-OS-Quarterly-Performance_Report-Q4-2017.pdf|url-status=live}}</ref><ref>{{Cite web |url=https://www.gsc-europa.eu/electronic-library/performance-reports |title=Galileo Open Service and Search and Rescue – Quarterly Performance Reports, containing measured performance statistics |access-date=3 March 2019 |archive-date=26 August 2019 |archive-url=https://web.archive.org/web/20190826170704/https://www.gsc-europa.eu/electronic-library/performance-reports |url-status=dead }}</ref> Each Galileo satellite has two passive hydrogen maser and two [[Rubidium standard|rubidium]] atomic clocks for onboard timing.<ref>{{cite news|url=https://safran-navigation-timing.com/product/imaser-3000/|title=Passive Hydrogen Maser (PHM)|newspaper=Safran - Navigation & Timing|access-date=30 January 2017|archive-date=6 March 2019|archive-url=https://web.archive.org/web/20190306111752/https://safran-navigation-timing.com/product/imaser-3000/|url-status=live}}</ref><ref>{{cite web|url=https://safran-navigation-timing.com/solution/atomic-clocks-and-oscillators/|title=Rb Atomic Frequency Standard (RAFS)|website=safran-navigation-timing.com|access-date=30 January 2017|archive-date=6 November 2018|archive-url=https://web.archive.org/web/20181106205737/https://safran-navigation-timing.com/solution/atomic-clocks-and-oscillators/|url-status=live}}</ref>

The Galileo navigation message includes the differences between GST, UTC and GPST, to promote interoperability.<ref>{{Cite web |url=http://www.unoosa.org/pdf/icg/2012/Timescale-GALILEO.pdf |title=GNSS Timescale Description |access-date=5 October 2015 |archive-date=28 October 2020 |archive-url=https://web.archive.org/web/20201028210310/http://www.unoosa.org/pdf/icg/2012/Timescale-GALILEO.pdf |url-status=live }}</ref><ref>{{cite web|url=http://www.insidegnss.com/node/3560|title=ESA Adds System Time Offset to Galileo Navigation Message|website=insidegnss.com|access-date=5 October 2015|archive-date=28 March 2018|archive-url=https://web.archive.org/web/20180328231238/http://www.insidegnss.com/node/3560|url-status=dead}}</ref> In the summer of 2021, the European Union settled on a passive hydrogen maser for the second generation of Galileo satellites, starting in 2023, with an expected lifetime of 12 years per satellite. The masers are about 2 feet long with a weight of 40 pounds.<ref>{{Cite news|last=Belcher|first=David|date=1 November 2021|title=Trying to Get Somewhere? An Atomic Clock May Be Helping.|language=en-US|work=The New York Times|url=https://www.nytimes.com/2021/11/01/fashion/watches-leonardo-galileo-atomic-clock.html|access-date=15 February 2022|issn=0362-4331}}</ref>

The [[BeiDou Navigation Satellite System#Global system (BeiDou Navigation Satellite System or BeiDou-2)|BeiDou-2/BeiDou-3]] satellite navigation system is operated by the [[China National Space Administration]]. BeiDou Time (BDT) is a continuous time scale starting at 1 January 2006 at 0:00:00 UTC and is synchronised with UTC within 100 ns.<ref>[http://interact.beidou.gov.cn/interact/download.service?attachment=2013/12/26/20131226b8a6182fa73a4ab3a5f107f762283712.pdf China Satellite Navigation Office, Version 2.0, December 2013]{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{Cite web |url=http://www.unoosa.org/pdf/icg/2010/ICG5/wgD/05.pdf |title=Definition and Realization of the System Time of COMPASS/BeiDou Navigation Satellite System, Chunhao Han, Beijing Global Information Center,(BGIC), Beijing, China |access-date=5 October 2015 |archive-date=29 October 2020 |archive-url=https://web.archive.org/web/20201029001034/http://www.unoosa.org/pdf/icg/2010/ICG5/wgD/05.pdf |url-status=live }}</ref> BeiDou became operational in China in December 2011, with 10 satellites in use,<ref name="op_china">{{cite news|url=https://www.bbc.co.uk/news/technology-16337648|title=China GPS rival Beidou starts offering navigation data|publisher=BBC|date=27 December 2011|access-date=22 June 2018|archive-date=3 February 2012|archive-url=https://web.archive.org/web/20120203001904/http://www.bbc.co.uk/news/technology-16337648|url-status=live}}</ref> and began offering services to customers in the [[Asia-Pacific]] region in December 2012.<ref name=CustomersDec2012>{{cite web|url=https://www.bbc.co.uk/news/technology-20852150|title=China's Beidou GPS-substitute opens to public in Asia|publisher=BBC|date=27 December 2012|access-date=27 December 2012|archive-date=27 December 2012|archive-url=https://web.archive.org/web/20121227182347/http://www.bbc.co.uk/news/technology-20852150|url-status=live}}</ref> On 27 December 2018 the BeiDou Navigation Satellite System started to provide global services with a reported timing accuracy of 20 ns.<ref>{{Cite web|url=https://www.livemint.com/Technology/9rkTgLBMCHVottY3rP636J/Chinas-BeiDou-navigation-satellite-rival-to-US-GPS-starts.html|title=China's BeiDou navigation satellite, rival to US GPS, starts global services|last=Varma|first=K. J. M.|date=27 December 2018|website=livemint.com|language=en|access-date=27 December 2018|archive-date=27 December 2018|archive-url=https://web.archive.org/web/20181227230231/https://www.livemint.com/Technology/9rkTgLBMCHVottY3rP636J/Chinas-BeiDou-navigation-satellite-rival-to-US-GPS-starts.html|url-status=live}}</ref> The final, 35th, BeiDou-3 satellite for global coverage was launched into orbit on 23 June 2020.<ref>{{cite news |title=China puts final satellite for Beidou network into orbit – state media |url=https://uk.reuters.com/article/us-space-exploration-china-satellite/china-puts-final-satellite-for-beidou-network-into-orbit-state-media-idUKKBN23U08P |access-date=23 June 2020 |work=Reuters |date=23 June 2020 |language=en |archive-date=28 October 2020 |archive-url=https://web.archive.org/web/20201028212332/https://uk.reuters.com/article/us-space-exploration-china-satellite/china-puts-final-satellite-for-beidou-network-into-orbit-state-media-idUKKBN23U08P |url-status=dead }}</ref>

==== Experimental space clock ====
In April 2015, NASA announced that it planned to deploy a [[Deep Space Atomic Clock]] (DSAC), a miniaturized, ultra-precise mercury-ion atomic clock, into outer space. NASA said that the DSAC would be much more stable than other navigational clocks.<ref name="NASA-20150427">{{cite web|last=Landau|first=Elizabeth|date=27 April 2015|title=Deep Space Atomic Clock|url=http://www.jpl.nasa.gov/news/news.php?feature=4567|url-status=live|archive-url=https://web.archive.org/web/20151210213448/http://www.jpl.nasa.gov/news/news.php?feature=4567|archive-date=10 December 2015|access-date=29 April 2015|website=[[NASA]]}}</ref> The clock was successfully launched on 25 June 2019,<ref>{{Cite web|last=Northon|first=Karen|date=25 June 2019|title=NASA Technology Missions Launch on SpaceX Falcon Heavy|url=http://www.nasa.gov/press-release/nasa-technology-missions-launch-on-spacex-falcon-heavy|access-date=20 February 2022|website=NASA}}</ref> activated on 23 August 2019<ref>{{Cite web |title=NASA Activates Deep Space Atomic Clock|url=https://www.jpl.nasa.gov/news/nasa-activates-deep-space-atomic-clock|access-date=20 February 2022|publisher=NASA Jet Propulsion Laboratory (JPL)|language=en-US}}</ref> and deactivated two years later on 18 September 2021.<ref>{{Cite web|last=Hartono|first=Naomi|date=1 October 2021|title=Working Overtime: NASA's Deep Space Atomic Clock Completes Mission|url=http://www.nasa.gov/feature/jpl/working-overtime-nasa-s-deep-space-atomic-clock-completes-mission|access-date=20 February 2022|website=NASA}}</ref>

==== Military usage ====
In 2022, [[DARPA]] announced a drive to upgrade to the U.S. military timekeeping systems for greater precision over time when sensors do not have access to GPS satellites, with a plan to reach precision of 1 part in {{val|e=12}}. The Robust Optical Clock Network will balance usability and accuracy as it is developed over 4 years.<ref>{{Cite web|date=1 February 2022|title=DARPA Aims for More Accurate Atomic Clock to Replace GPS|url=https://www.thedefensepost.com/2022/02/01/darpa-new-atomic-clock/|access-date=15 February 2022|website=The Defense Post|language=en-US}}</ref><ref>{{Cite web|date=21 January 2022|title=DARPA to launch programme for creating optical atomic clocks|url=https://www.airforce-technology.com/news/darpa-optical-clocks/|access-date=15 February 2022|website=Airforce Technology|language=en-US}}</ref>

=== Time signal radio transmitters ===
{{main|Radio clock}}
A [[radio clock]] is a clock that automatically synchronizes itself by means of radio time signals received by a [[radio receiver]]. Some manufacturers may label radio clocks as atomic clocks,<ref name="TSRF">Michael A. Lombardi, [http://tf.nist.gov/general/pdf/2429.pdf "How Accurate is a Radio Controlled Clock?"], {{Webarchive|url=https://web.archive.org/web/20210107194406/https://tf.nist.gov/general/pdf/2429.pdf|date=7 January 2021}}, National Institute of Standards and Technology, 2010.</ref> because the radio signals they receive originate from atomic clocks. Normal low-cost consumer-grade receivers that rely on the amplitude-modulated time signals have a practical accuracy uncertainty of ± 0.1 second. This is sufficient for many consumer applications.<ref name=TSRF/> Instrument grade time receivers provide higher accuracy. Radio clocks incur a propagation delay of approximately 1&nbsp;[[millisecond|ms]] for every 300 kilometres (186&nbsp;mi) of distance from the [[radio transmitter]]. Many governments operate transmitters for timekeeping purposes.<ref>{{Cite web|last=lombardi|date=24 September 2009|title=Radio Station WWV|url=https://www.nist.gov/pml/time-and-frequency-division/time-distribution/radio-station-wwv|access-date=16 February 2022|website=NIST|language=en}}</ref>

=== General relativity ===
[[General relativity]] predicts that clocks tick slower deeper in a gravitational field, and this [[gravitational redshift]] effect has been well documented. Atomic clocks are effective at testing general relativity on ever smaller scales. A project to observe twelve atomic clocks from 11 November 1999 to October 2014 resulted in a further demonstration that Einstein's theory of general relativity is accurate at small scales.<ref>{{Cite magazine|last=Chen|first=Sophia|title=These Physicists Watched a Clock Tick for 14 Years Straight|language=en-US|magazine=Wired|url=https://www.wired.com/story/these-physicists-watched-a-clock-tick-for-14-years-straight/|access-date=15 February 2022|issn=1059-1028}}</ref>

In 2021 a team of scientists at [[JILA]] measured the difference in the passage of time due to [[gravitational redshift]] between two layers of atoms separated by one millimeter using a strontium optical clock cooled to 100 nanokelvins with a precision of {{val|7.6|e=-21}} seconds.<ref>{{Cite journal|last1=Bothwell|first1=Tobias|last2=Kennedy|first2=Colin J.|last3=Aeppli|first3=Alexander|last4=Kedar|first4=Dhruv|last5=Robinson|first5=John M.|last6=Oelker|first6=Eric|last7=Staron|first7=Alexander|last8=Ye|first8=Jun|title=Resolving the gravitational redshift across a millimetre-scale atomic sample|journal=Nature|year=2022|volume=602|issue=7897|pages=420–424|doi=10.1038/s41586-021-04349-7|pmid=35173346|arxiv=2109.12238|bibcode=2022Natur.602..420B|s2cid=237940816}}</ref> Given its quantum nature and the fact that time is a relativistic quantity, atomic clocks can be used to see how time is influenced by general relativity and [[quantum mechanics]] at the same time.<ref name=":7">{{Cite web|last=sarah.henderson@nist.gov|date=16 February 2022|title=JILA Atomic Clocks Measure Einstein's General Relativity at Millimeter Scale|url=https://www.nist.gov/news-events/news/2022/02/jila-atomic-clocks-measure-einsteins-general-relativity-millimeter-scale|access-date=17 February 2022|website=NIST|language=en}}</ref><ref>{{Cite web|date=25 October 2021|title=An Ultra-Precise Clock Shows How to Link the Quantum World With Gravity|url=https://www.quantamagazine.org/an-atomic-clock-promises-link-between-quantum-world-and-gravity-20211025/|access-date=16 February 2022|website=Quanta Magazine|language=en}}</ref>

=== Financial systems ===
Atomic clocks keep accurate records of transactions between buyers and sellers to the millisecond or better, particularly in [[high-frequency trading]].<ref>{{Cite web|last=mark.esser@nist.gov|date=18 June 2020|title=Keeping Time at NIST|url=https://www.nist.gov/blogs/taking-measure/keeping-time-nist|access-date=16 February 2022|website=NIST|language=en}}</ref><ref>{{Cite web|title=TimeChainZ – Regulatory Reporting For High-Frequency Trading|url=https://www.chainzy.com/case-studies/timechainz-regulatory-reporting-for-high-frequency-trading/|access-date=16 February 2022|website=www.chainzy.com}}</ref> Accurate timekeeping is needed to prevent illegal trading ahead of time, in addition to ensuring fairness to traders on the other side of the globe. In 2018, the then current system known as [[Network Time Protocol|NTP]] is only accurate to a millisecond.<ref>{{Cite conference|last1=Geng|first1=Yilong|last2=Liu|first2=Shiyu|last3=Yin|first3=Zi|last4=Naik|first4=Ashish|last5=Prabhakar|first5=Balaji|last6=Rosenblum|first6=Mendel|last7=Vahdat|first7=Amin|date=2018|title=Exploiting a Natural Network Effect for Scalable, Fine-grained Clock Synchronization| url=https://www.usenix.org/conference/nsdi18/presentation/geng |language=en |pages=81–94 |isbn=978-1-939133-01-4 |conference=15th USENIX Symposium on Networked Systems Design and Implementation}}</ref>

=== Transportable Optical Clocks ===
Many of the most accurate optical clocks are big and only available in large metrology labs. Thus they are not readily useful for space-limited factories or other industrial environments that could use an atomic clock for GPS accuracy. 

Researchers have designed a strontium optical lattice clock that can be moved around in an air-conditioned car trailer.  They achieved a relative uncertainty of {{val|7.4|e=-17}} compared to a stationary one.<ref>{{Cite journal |last1=Koller |first1=S. B. |last2=Grotti |first2=J. |last3=Vogt |first3=St. |last4=Al-Masoudi |first4=A. |last5=Dörscher |first5=S. |last6=Häfner |first6=S. |last7=Sterr |first7=U. |last8=Lisdat |first8=Ch. |date=13 February 2017 |title=Transportable Optical Lattice Clock with {{val|7|e=-17}} Uncertainty |url=https://link.aps.org/doi/10.1103/PhysRevLett.118.073601 |journal=Physical Review Letters |language=en |volume=118 |issue=7 |pages=073601 |arxiv=1609.06183 |doi=10.1103/PhysRevLett.118.073601 |issn=0031-9007 |pmid=28256845 |s2cid=40822816}}</ref>

== Manufacturers ==
Manufacturers of atomic clocks in use for keeping track of [[Coordinated Universal Time|UTC]] includes [[Microchip Technology|Microchip]], [[T4Science]], [[Anritsu]], [[Microsemi]] and [[HP Inc.|HP]].<ref>{{Cite web |title=BIPM Time Dept database |url=https://webtai.bipm.org/database/clocklab.html |access-date=2025-02-20 |website=[[International Bureau of Weights and Measures]]}}</ref>

== See also ==
{{Portal|Electronics}}
{{Div col|colwidth=22em}}
* [[Caesium standard]]
* [[Clock drift]]
* [[Dick effect]]
* [[List of atomic clocks]]
* [[Network Time Protocol]]
* [[Optical clock]]
* [[Primary Atomic Reference Clock in Space]]
* [[Pulsar clock]]
* [[Speaking clock]]
* [[Time metrology]]
* [[Time transfer]]
{{div col end}}

== Explanatory notes ==
{{notelist}}

== References ==
{{Reflist}}

{{Time Topics}}
{{Electric clock technology}} 
{{Time measurement and standards}}
{{Machines}}
{{Authority control}}

{{DEFAULTSORT:Atomic Clock}}
[[Category:Atomic clocks| ]]
[[Category:Resonance]]
[[Category:Electronic test equipment]]
[[Category:Metrology]]
[[Category:Time measurement systems]]