The unit of time: Present and future directions

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The unit of time: Present and future directions

Sebastien Bize

To cite this version:

Sebastien Bize. The unit of time: Present and future directions. Comptes Rendus. Physique,

Académie des sciences (Paris), 2019, 20 (1-2), pp.153-168. �10.1016/j.crhy.2019.02.002�. �hal-02164954�

The unit of time: Present and future directions

L’unité de temps : directions actuelles et futures

Sébastien Bize

SYRTE,ObservatoiredeParis,UniversitéPSL,CNRS,SorbonneUniversité,LNE,61,avenuedel’Observatoire,75014 Paris,France

a r t i c l e i n f o a b s t r a c t

Articlehistory:

Availableonline26February2019

Keywords:

Atomicfountain Timescale

Opticalfrequencystandard Fundamentalphysicstest Chronometricgeodesy RedefinitionoftheSIsecond

Mots-clés : Fontaineatomique Échelledetemps Étalondefréquenceoptique Testdephysiquefondamentale Géodésiechronométrique RedéfinitiondelasecondeduSI

Some 50 years ago,physicists, and after them the entire world,started to found their timereferenceonatomicpropertiesinsteadofmotionsoftheEarththathavebeeninuse sincetheorigin.Farfrombeinganarrivalpoint,thisdecisionmarkedthebeginningofan adventurecharacterizedbyanimprovementby6ordersofmagnitudeintheuncertainty ofrealizationofatomicfrequencyandtimereferences.Ever-progressingatomicfrequency standards and timereferences derivedfrom themare key resourcesfor science andfor society. We will describe how the unit of time is realized with a fractional accuracy approaching10⁻¹⁶andhowitisdeliveredtousersviatheelaborationoftheinternational atomic time. We will describethe tremendous progress ofoptical frequency metrology overthelast20 yearsthatledtoanovelgenerationofopticalfrequencystandardswith fractionaluncertaintiesof10⁻¹⁸.Wewilldescribeworktowardapossibleredefinitionof theSIsecondbasedonsuchstandards.Wewilldescribeexistingandemergingapplications ofatomicfrequencystandardsinscience.

©^{2019Académiedessciences.PublishedbyElsevierMassonSAS.Thisisanopenaccess} articleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

r é s um é

Il y a une cinquantaine d’années, les physiciens, et après eux le monde entier, ont commencé àfonder leurréférence temporellesur lespropriétés atomiquesau lieudes mouvementsdelaTerre,quiétaientutilisésdepuisl’origine.Loind’êtreunpointd’arrivée, cette décision a marquéle début d’uneaventurecaractérisée par une amélioration par six ordres de grandeur de l’incertitude de la réalisation des références atomiques de fréquenceetdetemps.Lesétalonsdefréquenceatomiqueenconstanteprogressionetles références detempsquiendécoulentsont desressourcesessentielles pourlascienceet pourlasociété.Nousdécrironscommentl’unitédetempsestréaliséeavecuneprécision relative approchant10⁻¹⁶ etcomment elleest miseàla dispositiondesutilisateursvia l’élaborationdutempsatomiqueinternational.Nousmontreronslesprogrèsconsidérables de la métrologiedes fréquences optiquesau cours desvingt dernièresannées, qui ont conduit àunenouvelle génération d’étalonsde fréquence optiqueavecdes incertitudes relativesde10⁻¹⁸.Nousdécrironslestravauxenvued’uneéventuelleredéfinition dela

E-mailaddress:sebastien.bize@obspm.fr.

https://doi.org/10.1016/j.crhy.2019.02.002

1631-0705/©^{2019Académiedessciences.PublishedbyElsevierMassonSAS.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense} (http://creativecommons.org/licenses/by-nc-nd/4.0/).

secondeduSIbaséesurcesétalons.Nousdécrironslesapplicationsscientifiquesexistantes etémergentesdesétalonsatomiquesdefréquence.

©^{2019Académiedessciences.PublishedbyElsevierMassonSAS.Thisisanopenaccess} articleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Theunitoftime

In 1967, the 13th General Conference on Weights and Measures (CGPM) defined the SI second as “theduration of 9 192 631 770periodsoftheradiationcorrespondingtothetransitionbetweentwohyperfinelevelsofthegroundstateofthece- sium133atom”[1].Atomshavequantizedenergylevels.WithanypairofquantizedlevelsofenergyEgandEe,afrequency

ν isassociatedviaPlanck–Einstein’srelation:hν₌Ee−^Eg.Onefundamentalideabehindthedefinitionisthattheseatomic frequenciesareperfectlystableanduniversal.Observationssupportthisidea.Atomscanberegardedas“perfect”frequency standards givenby nature. The immutability of atomicfrequencies is integrated intofundamental theoriesunderpinning physics:generalrelativityandthestandardmodelofparticlephysics.

Accessing the atomic frequency andtransferring its qualities to a macroscopic usable signal requires a device called atomicfrequencystandard.Thetypicalarchitectureofsuchdevice isshownandexplainedinFig.1.Theoutputfrequency

ν(t)doesnotcoincidewiththeatomicfrequency νat.Itisperturbedbynoisesandbiasesofbothtechnicalandfundamental nature.Thesenoisesandbiasesdeterminetwomainscharacteristicsofagivenatomicfrequencystandard.Noiseslimitthe uncertaintywithwhicha frequencymeasurementcanbe madewiththisstandardina givenduration.Itischaracterized by the fractionalfrequency instability σy(τ), whichisa functionof themeasurement duration τ.Biasesoffsetthe mean output frequency withrespect to the unperturbed atomicfrequency νat. Ifknown and stable, a bias can be taken into account. What reallymattersis theuncertaintyto whichbiases areknown. Thisuncertainty,often reportedinfractional terms,definestheleveltowhichthestandardactuallygivesaccesstotheunperturbedatomicfrequency.Itsummarizesthe capabilityofthestandardtorealizetheSIsecond(for¹³³Cs primarystandards),tobeusedforfundamentalphysicsandfor otherapplications.

In practice,onlywell-chosen atomictransitionsare suitableto realizestandardswithloweststability anduncertainty.

LevelsmusthavelonglifetimestoenableahighatomicqualityfactorQat (seeFig.1).Transitionmusthavelowsensitivity toexternalfields(electric,magnetic,thermalradiation,etc.).Theatomicstructuremustbecompatiblewithmethodsneeded to manipulateanddetectatoms. It isalsoessential toconsider practicalcriteriasuch asreliability,operability, possibility to generateand use theinterrogation field at the transition frequency. Giventhe state ofknowledge and technology at the time of the 13th CGPM, a frequency standard based on the ¹³³Cs ground-state hyperfine transitionwas one of the best possibilities, almost two decades after the first observation of the transition [2]. It had shown sufficient maturity and hadbeen accurately measured withrespect to the ephemeris time [3,4]. Since then, fundamental andtechnological breakthroughs inmanyareasledtomajorchangesinwaystorealizeandusehighly accurateatomicfrequencystandards.

Theiruncertaintyimprovedby6ordersofmagnitude.References[5] and[6] provideanoverviewofthesedevelopments.

In November2018, the 26th CGPMadopteda majorredefinition oftheinternationalsystemofunits.The redefinition concerns the unitsofmass,oftemperature, ofelectrical currentandofamount ofsubstance. Thenewsystemis defined by adoptingconventionalvaluesforPlanck’sconstanth,forBoltzmann’sconstant kB,fortheelementarycharge e andfor Avogadro’s constant NA,similarly to what was alreadydone since 1983 [7] withthe speed of light c to define theunit oflength.Inessence, thedefinitionofthesecond remainsunchanged. Theformofthedefinition,however,ismodifiedto resemblethoseofotherunits,i.e.“theInternationalSystemofUnits,theSI,isthesystemofunitsinwhich:theunperturbedground statehyperfinetransitionfrequencyofthecaesium133atomνCsis9 192 631 770 Hz[...]”[8].

2. Researchonhighlyaccurateatomicfrequencystandards

Section 1 above gave fundamental concepts behind atomic time andatomic frequency standards. These concepts are amazinglysimpleandhavebeenusedformorethanfivedecades.Still,theycontinuebeingatthebasisofanactivefieldof researchinthefollowingways.

Search foradvancingatomicfrequencystandardswithextremelylowuncertaintiesgoeshandinhandwithexploration ofatomicsystemsinteractingwithelectromagneticfields.Progressinatomicfrequencystandardsrevealsnewphenomena andprovides meansofinvestigatingthem. Andviceversa, progressinother areas(e.g.,laser-coolingofatoms, physics of collisionsandinteractions,quantumentanglement...)enablestheimprovementofatomicfrequencystandards.

These devices with extremely low uncertainties are tools of choice to probe the structure of space-time andto test fundamentallawsofnature.Theyprovideexperimentalinputstothequestforaunifiedtheoryofgravitationandquantum mechanics[9–11] andtothesearchfordarkmatter[12,13] andtootherapplications.

Ontheappliedside,atomicfrequencystandardsarekeytomajorapplicationsofutmostimportanceinmodern science andsociety.ThepracticalrealizationoftheunitoftimeoftheSIsystemisoneofthem,inparticularviatheelaborationof theinternationalatomictimeandoftheuniversalcoordinatetime(TAI/UTC).Anotherexampleisglobalnavigationsatellite

Fig. 1.Ontheleft:architectureofhighlyaccurateatomicfrequencystandards.Anoscillatorgeneratesamacroscopic,practicallyusableelectromagnetic signal.Afractionofthissignalissplittoprobetheatomictransitionchosenasareference.Theresponseoftheatomicsampleisdetectedtodetermine theprobabilityofexcitingthetransition.Thisinformationisusedtostabilizethefrequencyoftheoscillatortothespectroscopicsignal.Ontheright:

representativespectroscopicsignal.KeyfeaturesofthissignalaretheatomicqualityfactorQat=νat/νandthenoiseinthemeasurementofthetransition probabilityσδP.Thefrequencyν(t)oftheusablesignaldoesnotcoincideexactlywiththeunperturbedatomicfrequencyνat:ν(t)=νat×(1+ε+y(t)), whereεisafractionalfrequencyoffsetandy(t)representsfractionalfrequencyfluctuations.

systems(GNSS)such asGPS, GALILEO,etc.In turn,theserealizations arekey fortelecommunications, transports,finance, digitaleconomy,etc.

Search forultra-low uncertainties in atomicfrequencystandards isa steadydriver forinnovation inmultiple techno- logical areas such as lasers, low-noise electronics,ultra-stable oscillators. Also, it creates knowledge necessary to define trade-offs between performance and other requirements for industrial frequency standards or spaceclocks. This knowl- edgeisoftenapplicable notonlytonovelfrequencystandards,butalsotoother typesofatom-basedinstrumentslike,for example,accelerometersandgyrometersbasedonmatter–waveinterferometryormagnetometers.

Progress in reducing the uncertainty ofatomic frequencystandards leads to novel applications.For instance,because of its much lower uncertainty, the newgeneration of optical frequencystandards enableschronometric geodesy, i.e.the determinationofdifferencesinterrestrialgravitationalpotentialviathemeasurementofEinstein’sgravitationalredshift.

3. Primaryfrequencystandardsbasedonatomicfountains

Thefirstgenerationof¹³³Csprimaryfrequencystandards,whichledtotheadoptionoftheatomictime,wasbasedon thethermalatomicbeamtechnologyandtheseparatedoscillatoryfieldsmethod[14,15].Thedevelopmentoflasercooling ofatomsinthe 1980s [16–18] enablesasecond generationcalledatomicfountains[19–21]. Atomicsampleslaser-cooled totemperaturesnear1μ^{K enable atomicqualityfactorshigherthan1010,a factor100timeshigherthaninatomicbeam} standards.Fig.2displaysaschematicofanatomicfountain.Whenanultra-lownoisemicrowavesourceisusedtointerro- gatetheatomictransition,thequantumprojectionnoiselimitisreached[22].Thislimitisthefundamentallimitsetbythe quantummeasurementprocessforunentangledparticles.Thisyieldsshort-termfractionalfrequencyinstabilitiesaslowas 1.6×^{10−14at1 s[23].Nowadays, theaccuracyofthebestatomicfountainsranges between1 and3 partsin1016.This} istheresultofrefiningmodels oftheinterrogationanddetectionprocesses,andofstringentlytestingthesemodels with experiments.Such experiments typically requiremanyfrequency measurements withstatisticaluncertainties near10⁻¹⁶, whichisreached,intheverybestcase,afterseveralfulldaysofmeasurement.Inotherwords,fountainshavereachedthe situationwherethestabilityimposesapracticallimittostudyingsystematicshiftsandimprovingtheaccuracy.Exampleof effectswhosemodeling improvedsignificantlyincludestheeffectsofphasegradientsintheinterrogationmicrowavecavity [24,25],theeffectsofcoldcollisions[26–28],theeffectsofcollisionswithbackgroundgases[29,30],andtheeffectsofthe microwavefieldonexternalatomicmotion(“microwavelensing”)[31–33].Theimplementationoffountainswithcryogenic interrogationenvironmentenabledanewdirectmeasurementoftheeffectsofthermalradiationshift(“blackbodyradiation shift”) [34–37].Recently, a completeaccuracy budgetwas published forcontinuous fountainatthelevel of1.99×¹⁰⁻¹⁵ [38].Moredetailsonatomicfountainscanbefound,forinstance,in[39],[23] and[40].

The⁸⁷Rbground-statehyperfinetransitionisalsousedtorealize atomicfountainfrequencystandards.LNE–SYRTEde- velopeda dualfountainusingRb andCs, whichtruly realizes twostate-of-the-art microwavestandardsina single setup [41,42]. The Rb partof thisfountainhas an uncertaintyof 3.2×^{10−16 similar to the one ofthe best cesium fountains.}

Thisdualfountainenableshighlyaccuratecomparisonsofthe⁸⁷Rband¹³³Cshyperfinefrequencies.Thesecomparisonsfind manyapplications (see sections 6and7 below). Inparticular, they led to theadoption ofthis transitionasa secondary representationoftheSIsecond[42,43].

Agreement betweenfountains is well testedby means ofspecific remote comparisons by satellite methods [44] and recently by optical links between LNE–SYRTE and PTB [45]. Also, the elaboration of TAI provides a vehicle to compare fountainfrequencystandards(seesection4below).

Fig. 2.Ontheleft:Schematicofanatomicfountainfrequencystandard.Acloudofcoldatomsiscapturedatthecrossingof3pairsofcounter-propagating laserbeams.Itislaunchedupwardsatatypicalspeedof4 m s⁻¹andwithtemperatureof∼¹μ^{K.Duringtheballisticflight,atomsare}state-selected withafirstmicrowaveinteractionandapushlaserbeam.Then,theypassupwardanddownwardthroughamicrowavecavitywheretheyinteractwith thesignalfromtheinterrogationoscillator.Theycontinuefallingthroughtwolaserbeamsheetsinthedetectionregion.Ontheright:Top:Energylevelsof 133Csshowingtheground-statehyperfinetransitiondefiningtheSIsecond.Inred,transitionsusedforlaser-coolinganddetection.Bottom:Spectroscopy ofthecesiumhyperfinetransitioninanatomicfountainshowingRamseyfringeswithawidth<1 Hz andanatomicqualityfactorQatof10¹⁰.Eachpoint isasinglemeasurementofthetransitionprobabilityatarateof∼^{1 persecondwithatypicalnoise}σδP∼²×^10−4.

4. ElaborationofTAI:accuracyofatomicfountainsdeliveredtousers

One essentialoutcomeoftime andfrequencymetrologyistheconstruction oftheinternationalatomictime (TAI)and oftheuniversalcoordinatetime(UTC).Itisworth notingherethatthe26th CGPMadoptedaresolutiononthedefinition of time scales [8], whichcorrects forthe lack so farof a self-containeddefinition ofTAI. We remind that a meaningful definition and realization of a time scale valid globally in the vicinity of the Earth requires the framework of general relativity,inparticulartoproperlyaccountforEinstein’sgravitationalredshift,whichisabout10⁻¹⁶ permeterofelevation at the surface of theEarth. Adescription of theelaboration ofTAI by the BIPM canbe found,for example,in [46] and referencestherein.Bymeansofsatellite-basedcomparisons,datafromabout450continuouslyoperatedcommercialclocks areusedtocomputethefreeatomictimescale(EAL).Thelargenumberofdevicesandlocationsensurethepermanenceof EAL. Datafromamuchsmallernumberofprimaryandsecondaryfrequencystandards(about20)inanevenmorelimited number of institutes are used to calibrate the frequency ofEAL against the ¹³³Cs hyperfine transition, according to the definitionofthe second,andtosteerEALtorealizeTAI.UTC isderivedfromTAIby insertingleap secondsthat maintain agreement withthe universal time (UT1) andthe observed rotationof theEarth. The result ofthisprocess is published by theBIPM in its monthlyCircular T [47]. Thisinformation, inturn, isused by national metrologyinstitutes andother participantstosteertheirlocalphysicalrepresentationofUTC,fromwhichdisseminationsinsocietystartbyvariousmeans.

Circular T andcalculationsdoneattheBIPMalsoyieldanestimationoftheperformanceofTAIandprovideavehicleto compare frequencystandardsworldwide.Differences betweenfrequencystandardsobserved bythismeans areconsistent withuncertainties[48,49].Theaccuracytowhichthescaleintervalisdeterminedwithrespectto¹³³Cshyperfinetransition now reaches2×^{10−16 [46].Inother words,the}performance offrequencystandardsistransferred tothetime scaleand thereby tousers.The2×^{10−16fractional frequency}uncertaintytranslatesintoanerroroflessthan10 ns afteroneyear.

This improvementbya factorof10since 2000isthe resultof thecommitmentofa fewmetrologyinstitutesto provide

Fig. 3.LocalrealizationsofUTCusingatomicfountaindata.TheplotshowstimedifferencesUTC–UTC(k)asafunctionoftheModifiedJulianDate(MJD) forUTC(USNO),UTC(PTB)andUTC(OP).Dataareshownbetween29October2012and8November2018.

regular calibrations of TAI. Nowadays, aboutfour orfive calibrations by fountains are typically available each month,as canbeseeninsection 3ofCircular T[47].Overthelast15years,LNE–SYRTEmade40%ofallworldwidecalibrationswith fountains.TheadoptionofsecondaryrepresentationsoftheSIsecond(see[43] andsection7below)ledtothepossibilityto calibrateTAIwithotheratomictransitionsthanthe¹³³Cshyperfinetransition.Thiswasdoneforthefirsttimewiththe⁸⁷Rb hyperfinetransitionbyLNE–SYRTE,whichprovidedcloseto100calibrationsbythismean[42].LNE–SYRTEalsopioneered providing calibrations based onan optical transition. This was done withthe ⁸⁷Sr¹S₀–³P₀ transition at698 nm. Regular calibrations ofTAI by optical frequencystandardsare an importantprerequisite for apossible redefinition ofthe second basedonoptical transition(s)[50].The transferoflong-termstability andaccuracyofprimary frequencystandardstoTAI enableshighly accurate SI-traceablefrequencymeasurements without alocalprimary frequency[51,52] and fundamental physicstests[53,54].

Progress in the reliabilityof atomicfountains made itpossible for a few institutesto steer their local realizationsof UTC withfountain data[55–57]. Local realizationofUTC by institutek isdenoted UTC(k). Fig. 3shows time differences betweensuchtimescalesandUTC.Theyarerealizedusinghydrogenmaserswhosefrequencyiscalibratedandsteeredwith atomic fountains,andfor the long term, with thetime difference UTC(k)–UTC provided every month inCircular T. They typicallydeviatefromUTCandfromeachothersbynomorethanafewnanoseconds.Itisworthnotinganothersignificant evolutionintimekeeping,namelytherapidrealizationofUTCbytheBIPM[58]. UTCrimplementsfasterexchangeofdata thanCircular TdoesbetweenparticipatinglaboratoriesandtheBIPM.Itimprovestheleveltowhichagivenlaboratorycan verifythesynchronizationofitsUTC(k)toUTC.Thisisofparticularinterestandsignificanceforlaboratorieswhereresources allocatedtothelocaltimescalearelimited(i.e.toafewcommercialCsbeamstandards).

5. Anewgenerationofopticalatomicfrequencystandards

Opticalfrequencymetrologyisadvancing athighpace, inparticularsincethe introductionofopticalfrequencycombs [59,60].Optical frequencystandardsrefer to atomicstandardsrelying on transitionswhosefrequency corresponds tothe opticaldomainoftheelectromagneticspectrum.Theirfrequencyisby10⁴to10⁵higherthanthe¹³³Cshyperfinefrequency and their potential atomic quality factor can exceed 10¹⁶ instead of 10¹⁰ for atomic fountain standards. To date, both neutralatomsandionsarestudied withtheaimtoobtain thelowestpossible uncertainties.Fig. 4explainstheprinciple ofoperation ofthesetwotypes ofstandards.Optical frequencystandardsachieve fractionalfrequency uncertaintiesclose to 10⁻¹⁸ [61–68].Forexample,reference[61] reports anuncertaintyof 1.4×^{10−18 foran 171Yboptical latticestandard.}

References[64] and[62] reportuncertaintiesof2.1×^10−18and4.8×^10−18,respectively,for⁸⁷Sropticallatticestandards.

Reference[63] reportsanuncertaintyof3.2×^{10−18fora171Yb+ionstandard.Manyphysicaleffectshadtobeunderstood} and controlled at an even lower level individually. Some notable ones are frequency shifts due to black-body radiation [64–71] andtoelectricfields[72],shiftsinducedbythelatticelight[73,74],shiftsinducedbyinteractions[75],light-shifts inducedbyprobelight[76].Thislistofexamplesmustnotbeconsideredascompleteeitherintermsofeffectsorinterms ofreferences.Comparisonsbetweenopticalfrequencystandardsusingthesametransitionwereperformedwithimproving uncertainties [65,77–80], down to below10⁻¹⁸ for the mostrecent work [61]. A recentand morecomplete account on opticalfrequencystandardscanbefoundin[81].Fig.5showsarecentmeasurementofthestabilityofa⁸⁷Sropticallattice frequencystandardfromLNE–SYRTE.