Observation of Electromagnetically Induced Transparency for a Squeezed Vacuum with the Time Domain Method

0.24 MB·English

by  M. Arikawa

Observation of electromagnetically
induced transparency for a squeezed
vacuum with the time domain method
M.Arikawa,1K.Honda,1,2D.Akamatsu,1Y.Yokoi1,
K.Akiba,1 S.Nagatsuka,1A.Furusawa,3andM.Kozuma1,2,4
8 1DepartmentofPhysics,TokyoInstituteofTechnology,
0 2-12-1O-okayama,Meguro-ku,Tokyo152-8550,Japan
0
2 2InteractiveResearchCenterofScience,TokyoInstituteofTechnology,
2-12-1O-okayama,Meguro-ku,Tokyo152-8550,Japan
n
a
3DepartmentofAppliedPhysics,SchoolofEngineering,
J
TheUniversityofTokyo,7-3-1Hongo,Bunkyo-ku,Tokyo113-8656,Japan
7
2 4CREST,JapanScienceandTechnologyAgency,1-9-9Yaesu,Chuo-ku,Tokyo103-0028,
Japan
]
h [email protected]
p
-
nt Abstract: Aprobelightinasqueezedvacuumstatewasinjectedintocold
a 87Rb atoms with an intense control light in a coherent state. A sub-MHz
u window was created due to electromagneticallyinduced transparency,and
q
the incident squeezed vacuum could pass through the cold atoms without
[
opticalloss,aswassuccessfullymonitoredusingatime-domainhomodyne

2 method.
v
1 © 2008 OpticalSocietyofAmerica
7 OCIScodes:(270.0270)Quantumoptics;(270.6570)Squeezedstates.
9
1
. Referencesandlinks
7
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1. Introduction
The coherenttransfer of quantum informationbetween light and atoms has been actively in-
vestigated, and various methods for its implementation using several phenomena, including
the Raman process [1], quantum non-demolition measurement [2], and electromagnetically
inducedtransparency(EIT)[3,4],havebeenproposedandinvestigatedexperimentally.Exper-
imentaldemonstrationofstorageandretrievalofasinglephotonstatewasfirstrealizedusing
EIT [5, 6], and this method has attracted a great deal of attention for application to various
non-classicallights[7].Thesqueezedvacuumhasbeenanimportantresourcefordeterminis-
ticintricatequantuminformationprocessing.Storingandretrievingthesqueezedvacuumstate
thusenablesustoapplysuchquantuminformationprotocolstothespatiallylocalizedatomic
ensemble.Furthermore,storageofthesqueezedvacuumimpliesatomicspinsbeingsqueezed
underthestandardquantumlimit[8],whichisusefulforprecisemeasurementssuchasmag-
netometry [9]. The storage and retrieval of light with EIT is based on ultraslow propagation
oflightbysteepdispersionwithinthetransparencywindow.Thegroupvelocityofanincident
lightpulse canbedramaticallyreducedbysimplynarrowingthetransparencywindow.Thus,
the establishmentof a techniquefordetectingthe squeezedvacuumpassed througha narrow
transparencywindowformsthefoundationforstorageandretrievalofthesqueezedvacuum.
ThefirstexperimentalconfirmationofEITwithasqueezedvacuum[10]employedtheho-
modyne detection method with a monochromaticlocal oscillator (LO), where the homodyne
detection signal was analyzed using a spectrum analyzer. Squeezing was observed when the
frequency width of the transparency window was relatively large (2.6 MHz). It is noted that
thespectrumanalyzermeasuresthepowerspectrumbymixingtheinputsignalwithanelectric
localoscillator(eLO)andfrequencyfilteringthemixeroutput(IF).Practically,atinyamount
of the eLO directlycouplesto the IF portof the mixerand this leakage is detected when the
eLOfrequencyiswithinthefilterbandwidth.Eventually,asharppeakappearsatthelowfre-
quencyregionreflectingthe’shapeofthefilter’,whichmainlylimitedthedetectableminimum
frequencyofthesqueezing.
In order to solve this problem and realize ultra-slow propagation of a squeezed vacuum,
homodynedetectionwithbichromaticLOhavingthefrequencycomponentsofn ±e wasuti-
0
lized [11],wheren ande were the carrierfrequencyof thesqueezedvacuumandthe center
0
frequencyof the spectrumanalyzer,respectively.Since this methodis sensitiveto the degen-
erate frequency component (n ), squeezing was observed within the sub-MHz transparency
0
windowandtheultra-slowpropagationofasqueezedvacuumpulsewasrealized.However,the
bichromatic homodynemethod is also sensitive to the two-mode quadraturenoise consisting
ofn ±2e ,whichareusuallypresentoutsidethetransparencywindow,sincee hastobesetto
0
a relativelyhighfrequencyto avoidthe specific peakreflectingthe ’shapeof thefilter’ ofthe
spectrumanalyzer.Thus,theobservablesqueezinglevelinevitablydecreasesinthestorageand
retrievalprocess.
Mostrecently,squeezingwassuccessfullyobservedforthelow-frequencyregionbyFourier
transform of the real-time homodyne detection signal [12, 13]. In this Letter, we report the
successfulobservationofasqueezedvacuumthathaspassedthroughasub-MHzEITwindow
usingthetimedomainmethod.Thehomodynedetectionwiththespectrumanalyzerprovides
the power noise of the quadrature amplitude. In contrast, the time domain method acquires
real-timesignalofthequadratureamplitudeandthuswecanextractfrequencyspectrumofthe
quadraturenoisebysimplyperformingFourieranalysis.Itshouldbenotedthatthepreviously
observed narrow band EIT spectrum [11] does not give us direct information about how the
squeezedvacuumisdegradedbytheEITmediumundertheslowpropagationcondition.Inthe
previousexperiment,thespectrumwasobtainedbymeasuringthesqueezinglevelforvarious
detuningofthecontrollight,whiletheslowpropagationwascarriedoutforthefixedcontrol
frequency.TheFFTanalysisenablesustoobtainthesqueezingspectrumforthefixedcontrol
frequency,whichisdirectinformationabouttheresponseofthesqueezedvacuumfortheEIT
mediumundertheconditionutilizedfortheultra-slowpropagationandstorageexperiments.
2. Experiment
Our experimental setup is shown schematically in Fig. 1. We prepared magneto-optically
trappedandlasercooled87RbatomsandemployedthemastheEITmedium.Onecycleofour
experimentwas 10ms. Each cycle consisted of the preparationof cold atoms(9 ms) and the
measurementofEIT(1ms).Duringthepreparationperiod,theRbgaswasmagneto-optically
trappedfor5.5ms,afterwhichthemagneticfieldwasturnedoff.Aftertheeddycurrentceased
(∼3ms),boththecoolingandrepumpinglightswereturnedoffanddepumpinglighttunedto
F=2→F’=2transitionwasmadeincidentonthegastopreparecoldatomsintheF=1state.
Fig.1.Schematicdiagramoftheexperimental setup.BS:beamsplitter,HBS:halfbeam
splitter,AOM:acousto-opticmodulator,PD:photodetector,PZT:piezoelectrictransducer,
Amp.:RFamplifier,Sq.Vac.:squeezedvacuum.
We first evaluated the frequency width of the EIT window with a weak probe light in a
coherentstate.Ti:Sapphirelaser1wastunedto52S ,F=1→52P ,F’=2,whichcorresponds
1/2 1/2
toaprobetransition.AweaklightfromthislaserwasmadeincidentontheOPOcavity,andthe
outputbeamwasusedasaprobelight.Notethattheprobelightwasinacoherentstatebecause
the second harmonic light in front of the OPO cavity was blocked. The proceduredescribed
above enabled us to employ a coherent state of the probe light with a spatial mode that was
identicaltothatofthesqueezedvacuumusedinthelaterexperiment.Ti:Sapphirelaser2was
tunedto52S ,F=2→52P ,F’=2andwasusedforthecontrollight.Therelativefrequency
1/2 1/2
betweentheprobeandthecontrollightswasstabilizedwithasynthesizerandAOM1usinga
feed-forwardmethod[11,15].Duringthemeasurementperiod,theprobeandthecontrollights
wereincidentonthecoldRbgaswithacrossingangleof2.5◦.Thepowerofthecontrollight
wasapproximately80m W.Thewaistsoftheprobeandthecontrollightswere150m mand550
m m,respectively.Theselightswerecircularlypolarizedinthesamedirectionbyusingquarter
waveplates (l /4). It is noted that the atomic sample prepared here was hyperfine pumped,
but unpolarized.Choosing the same circular polarizationsfor both the probe and the control
lightsallowedustokeephightransparencywhiletheZeemandegeneracyoftheatomiclevels
was concerned [5].The probe light that passed through the cold atoms was photon-counted
usingasiliconavalanchephotodiode(Perkin-Elmer:SPCM-AQR).Thetransmissionspectrum
obtained by scanning the frequency of the control light is shown in Fig. 2, where the atoms
were almost transparent around two-photon resonance, and the half width at half maximum
was approximately 300 kHz. The slight asymmetry of the signal originated from the atomic
densityvariationduringthemeasurementtimeduetothermaldiffusion.
Fig.2. Transmissionspectrumofthecoherentprobelightasafunctionofthetwo-photon
detuning.Trace(A)indicatestransmissionspectrumwhentheprobelightwasincidenton
the cold atoms with the control light. Trace (B) shows the spectrum without the control
light.
We next observed the EIT spectrum for the squeezed vacuum, which passed through the
cold atoms under the EIT condition. We generated the squeezed vacuum resonant on the Rb
D line using a sub-threshold optical parametric oscillator (OPO) with a periodically poled
1
KTiOPO crystal[14].Injecting85mWofthesecond-harmoniclightfromthedoublerintothe
4
OPO cavity, the squeezed vacuum was generatedand was incidenton the cold atoms during
themeasurementperiod.TherelativephasebetweenthesqueezedvacuumandtheLOhadto
befixedinordertoselectivelymonitoranti-squeezingandsqueezing.Westabilizedtherelative
phase with the help of the weak coherent state of light, which was used as the probe in the
aboveclassicalEITexperiment.Wehereinafterrefertothislightthelockingbeam.Therelative
phasebetweenthelockingbeamandthesecondharmoniclightwasstabilizedusingaclassical
parametric amplification signal and piezo transducer PZT1. The relative phase between the
locking beam and the LO was also stabilized using the homodynedetector signaland PZT2.
Eventually,therelativephasebetweenthesqueezedvacuumandtheLOwaslockedtoq =p /2
or0duringthecoldatompreparationperiod.ThefeedbackvoltagestoPZTswereheldinthe
measurementperiodandtheweaklockingbeamwasturnedoffwithAOM2andAOM3,sothat
wecouldmeasureanti-squeezingorsqueezinginthemeasurementperiod[13,16].
Duringthe measurementperiod,we importedsignalsfromthe homodynedetectorintothe
high-speed digital oscilloscope and performed Fourier transform of the obtained real-time
waveforms, where the signal sampling rate was 5 × 107 samples/sec. Vertical resolution of
thedigitaloscilloscopewas8bitsandthusthedynamicrangeforthepowermeasurementwas
almost50dB.Inordertominimizetheattributionoftheclassicalnoisestothehomodynesig-
nal,weadjustedthepowerbalancebetweenthetwoLObeamsasmuchaspossible.Weapplied
classicalpowermodulationtotheLOandminimizedthemodulationsignalfromthebalanced
homodyne detector by changing the reflectivity of the half beam splitter, which was carried
outbyadjustingtheangleofthesplitter.Eventuallywecouldachieve−58dBofsuppression
for the classical modulation. Figure 3(a) indicates the frequency spectrum of the quadrature
noise for the squeezed vacuum, where trace (A) indicates the shot noise and traces (B) and
(C)indicatethequadraturenoiseswithoutthecoldatoms.Here,therelativephasesweresetto
q =p /2and0,respectively.Eachdatawasaveragedover1,000times.ThesharppeaksinFig.
3(a)originatedfromtheelectriccircuitnoisesofthehomodynedetectorandthustheycouldnot
be eliminated by balancingthe laser intensities. The quadraturenoise was approximatelyflat
overthefrequencyrangeshowninFig.3(a)becausethespectrumwidthoftheOPO(15MHz)
wasmuchbroaderthanthemeasurementfrequencyrange(1.5MHz).Traces(D)and(E)indi-
catethemeasuredquadraturenoiseofthesqueezedvacuumpassedthroughthecoldatomswith
the controllight, where the relative phase was set to q =p /2 and 0, respectively.Both anti-
squeezingandsqueezingwereobservedwithinthesub-MHznarrowfrequencyregion,which
correspondstothetransparencywindowcausedbyEIT.
In a previous experiment [11], the squeezing and the anti-squeezing signals alternatively
appearedwhenthefrequencyofthecontrollightwassweptwithinanarrowtransparencywin-
dow,whichwasdueto atomsaddingan additionalphaseshiftto thesqueezedvacuum.Such
acomplicatedstructuredidnotappearinthepresentexperimentasaresultofthecancellation
ofthedispersioneffect.Notethatinthecurrentexperiment,thefrequencyofthecontrollight
wasnotswept,butratherwasfixed,andthusthesidebandsconstructingthesqueezedvacuum
alwayshavetheoppositesignoftheadditionalphaseshifts.Thetwomodequadratureoperator
isdefinedas
Xˆ(n ,q )=aˆn0+n exp(−iq )+aˆn†0−n exp(iq ), (1)
wherethesidebandfrequenciesaren ±n [17].Nowweconsiderthesituationwheretheop-
0
positesignofthephaseshifts±f areaddedtothetwosidebands,i.e.,
Xˆ(n ,q ,f )=aˆn0+n exp(−iq )exp(if )+aˆn†0−n exp(iq )exp(−i(−f )). (2)
Thequadraturenoiseisgivenby
h|D Xˆ(n ,q ,f )|2i=h(Xˆ(n ,q ,f )−hXˆ(n ,q ,f )i)(Xˆ†(n ,q ,f )−hXˆ†(n ,q ,f )i)i
Sym
= 1hXˆ(n ,q ,f )Xˆ†(n ,q ,f )+Xˆ†(n ,q ,f )Xˆ(n ,q ,f )i−hXˆ(n ,q ,f )ihXˆ†(n ,q ,f )i
2
= 1hXˆ(n ,q )Xˆ†(n ,q )+Xˆ†(n ,q )Xˆ(n ,q )i−hXˆ(n ,q )ihXˆ†(n ,q )i
2
=h|D Xˆ(n ,q )|2i (3)
Fig.3.(a)Quadraturenoiseoftheprobelightinthesqueezedstate.Trace(A)indicatesthe
shotnoise.Traces(B)and(C)showthequadraturenoisesoftheprobelightwithoutcold
atoms,wheretherelativephasewereq =p /2and0,respectively.Traces(D)and(E)show
thequadraturenoiseswhentheprobelightwasincidentonthecoldatomswiththecontrol
light,wheretherelativephasewereq =p /2and0,respectively.(b)Thenumericallysim-
ulatednoisespectrumforthesqueezed vacuumpassedthroughthecoldatomsunder the
EITcondition.Trace(A)indicatestheshotnoise.Traces(B)and(C)showthequadrature
noisesforq =p /2and0,respectively.
where
hAˆBˆi =hAˆBˆ+BˆAˆi/2. (4)
Sym
Namely,additionalphasef doesnotaffectthepowernoiseofthequadratureamplitude.
Figure3(b)showsthenumericalsimulationofthequadraturenoisesofthesqueezedvacuum
thatpassedthroughthecoldatomsundertheEITcondition,where,forthesakeofsimplicity,
we assumedtheincidentsqueezedvacuumexperiencedtheopticallosscorrespondingtoFig.
2andtheincidentanti-squeezingandsqueezinglevelswereconstantinallfrequencyregions.
The absorption loss is represented by the model using a beam splitter whose transmittance
T(n )isdependentonthefrequencyofthelight.Thequadraturenoiseofthesqueezedvacuum
experiencedabsorptionlossisgivenby
1
h|D Xˆ(n ,q )|2i= {T(n )(cosh2r−cos2q sinh2r)+(1−T(n ))}, (5)
4
whereristhesqueezingparameter.Weusetheaverageofthetransmissionofthecoherentprobe
lightpassingthroughtheatomswiththecontrollightwhosedetuningwas±n ,whichisshown
in Fig. 2, as T(n ). The numerical simulation is in good agreement with the experimentally
obtainednoisespectrum.
3. Conclusion
In conclusion, we have succeeded in observing the EIT spectrum of the squeezed vacuum,
wherebothsqueezingandanti-squeezingweremonitoredwithinsub-MHztransparencywin-
dow.Theobservationofsqueezingforsuchalow-frequencyregionisanessentialstep inthe
realizationofthestorageandretrievalofthesqueezedvacuum.
Acknowledgment
Theauthorswouldlike tothankN. Takeiforengagingin numeroushelpfuldiscussions.Two
of the authors (D. A. and K. A.) were supported by the Japan Society for the Promotion of
Science.ThisstudywassupportedbyaGrant-in-AidforScientificResearch(B)andthe21st
CenturyCOEProgramatTokyoTech,”Nanometer-ScaleQuantumPhysics”bytheMEXT.