Fritz Riehle; Lecture: June 19, 2014

Singleion clocks vs.neutralatom lattice clocks

Storageof electrically charged particles inarf trap Two dimensionaltrap Paultrap in3d Penning trap

Opticalatomic clocks based onstored ions Yb

Hyper RamseySpectroscopy Quantumlogic clock Secondary representations of the second

Otherapplications of ion traps Microwave frequency standard for deep space applications Mass spectrometry

ResearchTrainingGroup1729

Ion traps for clocks and other metrological applications

Oszillator

0

Atome, Molekle oder Ionen

Detektor

Regelungs-elektronik

0

0

S

Absorptions- signal

FehlersignaldSd

oscillator

servo electronics

absorptionsignal

errorsignal

Absorber(ions,atoms,molecules)

Principle of (optical)atomic clocks

out

Opticalclockwork:femtosecondlaser

Accuracy:How accurately agrees out with 0?

Stability:Towhatextentfluctuatesout around0?

detector

Noiseand instability

104 neutralSr atoms, =429THz, =2Hz:y(t) 51017 1/2

SingleYbion, =688THz, =3.1Hz:y(t)51015 1/26105 Csatoms, =9.2GHz, =1Hz:y(t) 41014 1/2

Measure of instability(Allan deviation):

Singleionandneutralatomopticalclocks

Electrodynamic(Paul)trap

Singleionscanbeconfinedinfieldfreecenter

Trappingtime:

Neutralatomlatticeclock

104 106 atomscanbeinterrogated HighS/N;highfrequencystability Limitedtrappingtime(seconds)

NIST(Boulder)operating ,PTB,NPL,Innsbruck,under construction

Quantumlogicclock

CourtesyofP.Schmidt(QUEST)

Singleionclock

LowS/N;limitedfrequency stability

Achievable fractional instability

Assuming: Csfountain:105 Csatoms;Tint =1sec

104 Sr atoms:Tint =0.5sec

Yb+ ion:Tint =10sec

10 1 100 10 1 102 103 10 4 10 5 106 10710 18

10 17

10 16

10 15

10 14

10 13

10 12

MonthDayHour

Yb+ ion (642THz)

104 Sratoms(429THz)

Csfountain (9.2GHz)

[sec]

AllanDe

viation

6

IonTraps

FromF.Riehle,FrequencyStandards:

BasicsandApplicationsWileyVCH(2004)

QuadrupolePotential

PaulTrap(MechanicalAnalogueModel)

From:http://nobelprize.org/nobel_prizes/physics/laureates/1989/paullecture.pdf

WolfgangPaulNobelprize 1989

Realisations oflineartrapsgeneratingaradialquadrupole potentialwithtwoadditionalringelectrodesa)orwithadditionalrodsb)foraxialconfinement.

Linearion traps

Linearion trap (Innsbruckdesign2000)

11

LinearPaulTrap

Regionsofstability

Linearstrings of ions

From :Innsbruckgroup

Traponachip

Figure23:Schematicofasurfaceelectrodeiontrap.Theiontrapelectrodesareshownatthebottomofthefigureinred(RF)andblack(DC).Ionsaretrappedattheoriginofthecoordinatesystemshown.Thesecularpotentialisplottedonalinearcolorscaleasafunctionofxandy,withbluerepresentingthelowestandredrepresentingthehighestsecularpotentialvalues.

From:Leibrandt:Integratedchipsandopticalcavitiesfortrappedionquantum information processing,ThesisMIT2009

Penning Trap

Staticelectricfield+staticmagneticfield

ringelectrode

endcap

from:evB=mv2/r

Cyclotronfrequency

from:eErad =evB

Magnetronfrequency

Oscillatorymotioninz

15

IonMotioninPenning Trap

CyclotronfrequencycMagnetronfrequencym

Oscillatorymotionz

RadioFrequency (Paul)Trap

ringelectrode

endcap

z0r0

Quantumjumpspectroscopy

Thenumberofobserveddarkphasestakenfromdatalikethatofprevioustransparencyasafunctionoftheirdurationallowsonetofitanexponentialdecayandtodeterminethelifetimeofthelonglivedstate.

From:E.Peik:LaserspektroskopieangespeichertenIndiumIonen.DissertationMPQ181,MaxPlanckInstitutfrQuantenoptik,1993

Determinationof the lifetime from quantum jumps

Sidebandcooling

Absorptionspectrumofthe281.5nmtransitioninasingle198Hg+ionbefore(inset)andaftersidebandcoolingusing194nmradiation.Courtsey ofD.Wineland,withpermission

Yb+ singleionclock

E2:Chr.Tamm etal.,Phys.Rev.A89,023820(2014)

E3:N.Huntemannetal.,Phys.Rev.Lett. 108,090801(2012)

V.Yudin etal.,Phys.Rev.A82 011804(R)(2010)

E3: Insensitive to external fields E3:Extremely long natural lifetime

low instability hugelightshift

hasbeensuppressedbyHyper Ramsey Technique

Courtesy of N.Huntemann,PTB

PartialenergydiagramofYb+.Dashedlines(411nm,435nmand467nm)representtheopticaltransitionsproposedforopticalfrequencystandards.The369nmlineisusedforcoolinganddetection.

ThespectrumofthetransitionofasingleYb+ioninaPaultrapshowsbesidesthecarrierthemotionalsidebandsalongtheradial(r1andr2)andaxial(z)directions.Courtesy of Chr.Tamm.

Yb+

Currently smallest estimated uncertainty of any optical clock(comparable to Al+ NIST(8.6x1018),Sr JILA(6.4x1018))

Similarly low statistical uncertainties would require ~300hmeasuring time(could be reduced by asmaller experimentalline width;requires more stable laser)

Required:comparison of two Yb+ clocks with suchanuncertainty

Accurate measurement ofdifferentialpolarizabilityand temperature measurementinthe trap

With HyperRamseytechnique

EstimateduncertaintybudgetofPTBsYb+ clock(E3)

Courtesy of N.Huntemann

Temperatureradiationatthelocationoftheion

MeasurementwithtemperaturesensorsatacopyofthetrapandFEMbyP.BallingundM.Doleal (CMI)effec vetemperatureriseT=2(1)K

Combinationwithmeasurementofambienttemperature Frequencyshiftbythermalradiation=70.7(2.6) 1018

Courtesy of N.Huntemann

HyperRamseySpectroscopy(HRS)

Yudin etal.,Phys.Rev.A82 011804(R)(2010)Huntemannetal.,Phys.Rev.Lett. 109 213002(2012)

CompensationofthelightshiftL bydetuningS oftheclocklaserduringinterrogation

Additional pulseremoveslinearbehaviour ofLSconsiderablesuppressionoflightshift

ExperimentalinvestigationofHRS

RealtimestabilizationoffrequencyjumpSguarantees(LS)=0Huntemannetal.,Phys.Rev.Lett. 109 213002(2012)

PrincipleoftheAl+ Clock

LaserOscillator fscomb

8:52amQuantumLogicStateDetectionFrequency

Feedback

280THz=1070nm

x4

I(f)

f

Al+Ca+

quantum logic

2P3/2

2D5/2

2S1/2

397nm

729nm

866nm

854nm

I=0

2P1/2

2D3/2

40Ca+

coolingand

detection

I=5/2

clock

3P1

1S0

167nm

267.4nm

1P1

3P0logic267nm

27Al+Courtesy of P.Schmidt

Quantumlogic ion technique

a)Clock ion and logicionareintheirelectronicandmotionalgroundstates.b)Excitationoftheclockion.c)Apulsedetunedtothebluemotionalsidebandmapstheexcitationamplitudesandoftheclockionontothemotionalstatesoftheclockionand,asaresultoftheentanglement,thelogicion.

d)Apulsedetunedtotheredmotionalsidebandmapsandontheelectronicstatesofthelogicion.

Al+ clock

Al+ clock (instability and accuracy)

f(Al+)/f(Hg+)=1.052871833148990438(55)

f(Hg+)=1064721609899145.30(69)Hz.

T.Rosenbandetal,Science319(2008),1808 1812

31

Influence of special relativity

1905"ZurElektrodynamikbewegterKrper"

Principleofrelativity:LawsofPhysicsarethesameinallinertialsystems

c=const:Thespeedoflighthasineachinertialsystem(invacuum)thesamevalue(c=299792458m/s).

t:Timeintervalinaninertialsystem,movingw/rtoasecondonewithvelocityv.t:Timeintervalasobservedfromthesecondinertialsystem.

Spaceandtimearenolongerabsolute!

Timedilation:movedclocksslowdown

Al+ quantum logic clock relativistic tests (I)

C.W.ChouandD.B.HumeandT.Rosenband andD.J.Wineland:OpticalClocksandRelativity;Science329 (2010)1630 1633

Relativistic timedilation

Theory of GeneralRelativity

Largemass(sun,earth)

Theoryofgeneralrelativity(1915)frominertialsystemsofspecialrelativitytoacceleratedsystems

Equivalenceprinciple:Gravitationandaccelerationareequivalent

Result:Gravitationmodifiesspace(curvature)andslowsdowntime

Curvatureofspace

Matter(density,pressure,..)

Fundamentalconstants

Metric tensords2=g (x)dx dx

metric tensor inasuitable coordinate system (x) = (x0, x1, x2 x3)

Metrictensorforanonrotatinggeocentriccoordinatesystem:

with U=UEarth +UTide:Newtonian gravitational potential

Near Earths surface the approximation holdsU~ghwith g~9.81m/s2and h:height/ ~gh/c2~1.1. 1016 h

C.W.ChouandD.B.HumeandT.Rosenband andD.J.Wineland:OpticalClocksandRelativity;Science329 (2010)1630 1633

Al+ quantum logic clock relativistic tests (II)

h =33cm

Relativistic timevariation inagravitational potential

Inthefutureanewdefinitionforthesecondwillberequired.

Opticalclocksvs.Csclocks Status2014

PrimaryCsclocksOpticalfrequencies (relativeto Cs)Estimated uncertainties of optical standards

year

fractio

naluncertainty

Adoption as such secondary representations would help with detailedevaluation of reproducibility of these standards at the highest level

Such systems could be used to realise the second, provided their accuracy was close to that of caesium

Optical and other micowave standards were expected to demonstratereproducibility and stability approaching that of primary caesium

Their uncertainty could obviously be no better than the caesiumuncertainty

This activity was likely to significantly aid the process of evaluation of different standards in preparation for a possible future redefinition of the second

In2001CCTFhas established aworking group,that developed the concept,procedures and recommendations (now CCL CCTFWGFS).

Secondary representations of the second

Criteria for asecondary representation

2)Thisuncertaintyshouldbenolargerthanaboutafactorof10oftheprimarystandardsofthatdatethatserveasthebestrealisationsofthesecond.

1)TheSIvalueoftheunperturbedfrequencyofaquantumtransitionsuitableasasecondaryrepresentationofthesecondmusthaveanuncertaintythatisevaluated anddocumentedsoastomeettherequirementsadoptedfortheprimaryfrequencystandardforuseinTAI.

Secondary Representations of the Second

System Studied at Value / Hz Relative uncertainty

27Al+ NIST, PTB 1 121 015 393 207 857.3 1.9 x 10-15

199Hg+ NIST 1 064 721 609 899 145.3 1.9 x 10-15

171Yb+ (E2) PTB, NPL 688 358 979 309 307.1 3 x 10-15

171Yb+ (E3) PTB, NPL 642 121 496 772 645.6 1.3 x 10-1588Sr+ NPL, NRC 444 779 044 095 485.3 4.0 x 10-1587Sr PTB, SYRTE,

U. Tokyo, JILA, NIMJ, NPL,

429 228 004 229 873.4 1 x 10-15

171Yb NIST, 518 295 836 590 865.0 2.7 x 10-1587Rb SYRTE, NPL,

6 834 682 610. 904 312 1.3 x 10-15

Theseoptical clocks can be used alternatively to the Csclock,butcan never have anuncertainty better than the Csclock.

(CIPM2012)

Application 1:Deep SpaceAtomic Clock

Microwave IonTrap(199Hg+)

IntheJetPropulsionLaboratoryultrastablefrequencystandards[basedonlineartrapswithtypically106to107 199Hg+ ionspumpedbya202Hgrf dischargelampandcooledwithHebuffergastonearroomtemperature.

Microwave IonTrap(199Hg+)for deep space applications

InanextendedlineartrapionsaretransferredbetweentwoconfinementregionsoneforproductionanddetectionoftheionsandoneforRamseyexcitation.ThecontributionofthefractionalsecondorderDopplershiftwasestimatedtobe4 1013.

2.29cmx26cmx23cm;17,5kg;44W

From:https://directory.eoportal.org/web/eoportal/satellitemissions/d/dsac

https://directory.eoportal.org/web/eoportal/satellite

Microwave IonTrap(199Hg+)for deep space applications

Application 2:LinearPaulTrapas Mass Filter

From:http://nobelprize.org/nobel_prizes/physics/laureates/1989/paullecture.pdf

LinearPaulTrapasMassFilter

Resolvingpowerm/m=6500

From:http://nobelprize.org/nobel_prizes/physics/laureates/1989/paullecture.pdf

IonTrapMass Spectrometry inSpace

PtolemyInstrumentandtheRosettaSpaceMission

J.F.J.Todd,S.J.Barberetal.J.MassSpectrom. 2007;42;110

Cometsaresmallbodiesthatorbitthesuninoursolarsystem

Cometscompriseofrock,dustandice Nucleusissmallerthan50km,thetail(coma,

etc.)canbeverylarge upto150millionkm(largerthanthesun)

Cometsareusuallyverydarkobjects:onlyfew%ofmassreflectlight

Cometsconsistofmaterialformedattheformationoftheearth(+otherplanets)frozenintime(4600millionyearsago)

CometHaleBopp(03/21/97)

RosettaMission LaunchedMar2004onAriane 5G+inKourou,French

Guyana DesignedtomeetupwithcometChuryumov

Gerasimenko (67P)in2014 3000kglaunched(100kglander,165kgscientific

instruments) Flybyseveralothercometsuntilthelanding Fullyautomaticlanding Totalcost:$970980million

2004

2005

02/2007

11/2007

05/2014

PtolemyInstrumentonRosettaLander

Mass Spectrometer of Ptolemy

Measure2H,13C,15N,17Oand18Orelativetospecifiedreference

http://ptolemy.open.ac.uk/frames.htm

http://ptolemy.open.ac.uk/frames.htm

KATRIN:KarlsruheTritiumNeutrinoExperiment(75mlong)

Application 3:Mass spectrometer for neutrino restmasshttp://depts.washington.edu/uwptms/pics/dp7neutrino.png

Fritz Riehle; Lecture: June 19, 2014

Singleion clocks vs.neutralatom lattice clocks

Storageof electrically charged particles inarf trap Two dimensionaltrap Paultrap in3d Penning trap

Opticalatomic clocks based onstored ions Yb

Hyper RamseySpectroscopy Quantumlogic clock Secondary representations of the second

Otherapplications of ion traps Microwave frequency standard for deep space applications Mass spectrometry

ResearchTrainingGroup1729

Ion traps for clocks and other metrological applications

Foliennummer 1Principle of (optical) atomic clocksFoliennummer 3 Single ion and neutral atom optical clocksFoliennummer 5Foliennummer 6Foliennummer 7Foliennummer 8Foliennummer 9Foliennummer 10Foliennummer 11Foliennummer 12Foliennummer 13Foliennummer 14Foliennummer 15Foliennummer 16Foliennummer 17Foliennummer 18Foliennummer 19 Yb+ single ion clockYb+Foliennummer 22Foliennummer 23Foliennummer 24Foliennummer 25Foliennummer 26Principle of the Al+ ClockQuantum logic ion techniqueAl+ clockAl+ clock (instability and accuracy)Foliennummer 31Al+ quantum logic clock - relativistic tests (I)Foliennummer 33Foliennummer 34Foliennummer 35Foliennummer 36Foliennummer 37Criteria for a secondary representationFoliennummer 39Foliennummer 40Foliennummer 41Foliennummer 42Foliennummer 43Foliennummer 44Foliennummer 45Foliennummer 46Foliennummer 47Foliennummer 48Foliennummer 49Application 3: Mass spectrometer for neutrino rest massFoliennummer 51