0.54 {\mu}m resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography

0.82 MB·

by  Masayuki Okano

m
0.54 m resolution two-photon interference with
dispersion cancellation for quantum optical
coherence tomography
Masayuki Okano1,2,3, Hwan Hong Lim4, Ryo Okamoto1,2,3, Norihiko Nishizawa5, Sunao
Kurimura4, and Shigeki Takeuchi1,2,3,*
1DepartmentofElectronicScienceandEngineering,KyotoUniversity,Kyotodaigaku-katsura,Nishikyo-ku,Kyoto,
6
1 Kyoto,Japan
0 2ResearchInstituteforElectronicScience,HokkaidoUniversity,Sapporo,Hokkaido,Japan
2 3TheInstituteofScientificandIndustrialResearch,OsakaUniversity,Mihogaoka8-1,Ibaraki,Osaka,Japan

n 4NationalInstituteforMaterialsScience,1-1Namiki,Tsukuba,Ibaraki,Japan
a 5DepartmentofQuantumEngineering, NagoyaUniversity,Furo-cho,Chikusa-ku,Nagoya,Aichi,Japan
J
*[email protected]

8

]
ABSTRACT
h
p
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t Quantum information technologies harness the intrinsic nature of quantum theory to beat the limitations of the classical
n
methods for information processing and communication. Recently, the application of quantum features to metrology has
a
attractedmuch attention. Quantumopticalcoherencetomography(QOCT), whichutilizestwo-photoninterferencebetween
u
q entangled photon pairs, is a promising approach to overcome the problem with optical coherence tomography (OCT): As
[ the resolution of OCT becomes higher, degradation of the resolution due to dispersion within the medium becomes more
critical. Herewereportontherealizationof0.54m mresolutiontwo-photoninterference,whichsurpassesthecurrentrecord
1 resolution0.75 m m of low-coherenceinterferencefor OCT. In addition, the resolutionfor QOCT showed almost no change
v
againstthedispersionofa1mmthicknessofwaterinsertedintheopticalpath,whereastheresolutionforOCTdramatically
4
degrades.Forthisexperiment,ahighly-efficientchirpedquasi-phase-matchedlithiumtantalatedevicewasdevelopedusinga
3
7 novel‘nano-electrode-poling′technique.Theresultspresentedhererepresentabreakthroughfortherealizationofquantum
1 protocols, including QOCT, quantumclock synchronization, and more. Our work will open up possibilitiesfor medical and
0 biologicalapplications.
.
1
0
6
Introduction
1
:
v One of the mostdistinct featureof quantumphysicsis quantumentanglement. Entanglementattractedattention first in the
i test of nonlocality of quantum mechanics,1–3 and started to be considered as an essential resource for quantum informa-
X
tion protocols,4 including quantum key distribution,5,6 quantum teleportation,7,8 and quantum computation.9–11 Recently,
ar the application of quantum entanglement for metrology and sensing is attracting attention.12,13 One recent example is an
entanglement-enhancedmicroscope, where a photon-numberentangled state is used as probe light to enhance the sensitiv-
ity.14 Here we focuson anotherexample: an applicationof the frequencyentangledstate of photonsfor opticalcoherence
tomography(OCT).15,16
OCTbasedonlow-coherenceinterference(LCI)17hasbeenwidelyusedinvariousfields,includingmedicalapplications
suchasimagingoftheretinaandcardiovascularsystem.15,16 Figure1ashowsaschematicdiagramofOCT.Broadbandlight
fromasourceisdividedatabeamsplitter(BS).Onebeamisincidentonasampleafterpassingthroughadispersivemedium,
whiletheotherbeamisreflectedfromamirrorwithatemporaldelayt . TheOCTinterferencefringeI(t )isobtainedbythe
detectionoftheinterferedlightintensitywithvaryingdelayt (Figure1ainset). Whenthebandwidthofthesourceismade
broadertoachievehigherresolution,theresolution,farfrombeingimproved,degradesduetodispersioninthemedium.This
constitutesasevereprobleminOCT.18 Althoughdispersioneffectcanbecompensatedbyinsertinga‘phantom′,amedium
with the same dispersion, in the reference path,19 it requires a priori knowledge of both the structure and the frequency-
dependentrefractiveindexofthetargetobject.Furthermore,astheresolutionbecomeshigher,aslightdifferencebetweenthe
targetobjectandthe‘phantom′becomesacrucialproblem.
As an alternative method, quantum optical coherence tomography (QOCT)20–24 based on the two-photon interference
(TPI) of frequency-entangled photon pairs25 has been proposed20 (Figure 1b). Broadband entangled photon pairs can be
generated via a spontaneous parametric down-conversion process from a nonlinear crystal. Signal photons reflected at a
samplethroughadispersivemediumandidlerphotonswithatemporaldelayt ,interferequantummechanicallyataBS,and
coincidencedetectioneventsarecountedattwosinglephotondetectors.TheQOCTinterferencedipC(t ),whichissocalled
Hong-Ou-Mandel(HOM)dip,25isobtainedbythecoincidencecountratewithvaryingdelayt (Figure1binset). Duetothe
frequencycorrelationofentangledphotonpairs, theresolutionofQOCT(thewidthoftheHOM dip)doesnotchangeeven
withgroupvelocitydispersion(GVD)inthemedium.26,27 This‘dispersioncancellation′ ofTPIwasfirstdemonstratedwith
19m mresolution21andveryrecentlywith3m mresolution,wheretheGVDeffectbecomessignificant.28
Inthiswork,we report0.54 m mresolutionTPIwithdispersioncancellationforultra-highresolutionQOCT.Forhighly
efficientgenerationofultra-broadband(166THz,l =660-1040nm)frequency-entangledphotonpairs,wedevelopeda1st-
orderchirpedquasi-phase-matched(QPM)29lithiumtantalate30deviceusingthenanofabricationtechnologyforfineelectrode
patterns. Thedevicewaspumpedusinganarrowband(∼100kHz)pumplasertoensurethedispersioncancellationofTPI.28
Wealsoconstructedstableinterferometersetupwithhybridultra-broadbanddetectionsystems(HUBDeS)operatedatroom
temperature. Inaddition,dispersioncancellationinTPIwasdemonstratedagainsta1mmthicknessofwaterinsertedinthe
opticalpath. AlmostnodegradationinresolutionwasobservedforTPI(from0.54m mto0.56 m m),whichisincontrastto
thesignificantdegradationinLCIresolution(from1.5m mto7.8m m). The0.54m mresolutioninair,whichcorrespondsto
theresolutionof0.40m minwater,isthebestamongthepreviouslyachievedLCIresolution0.75m m31forOCTandalsoTPI
resolutionsforQOCT,includingthat(0.85m m23)wheredispersioncancellationwasnotverified.
Results
The 1st-orderQPM devicewasdevelopedusinga ‘nano-electrode-poling′technique. Notethattheconversionefficiencyof
the 1st-order QPM32 is supposed to be almost one order magnitude (9 times) larger than that of the 3rd-order QPM;22,23
however,itisimpossibletorealizeusingconventionalphotolithographytechniques.Forhigh-powerultravioletpumping,Mg-
doped stoichiometriclithium tantalate (Mg:SLT)30,33 was selected because it has a short absorptionedge around270 nm34
and high thermal conductivity.35,36 Furthermore, Mg:SLT is free from visible-light-inducednonlinear infrared absorption,
which is observedin Mg:LiNbO .37 The new device fabrication process that was employedis shown in Figure 2a. A 500
3
m m thick Mg:SLT wafer doped with 1.0 mol% Mg was used to suppress photorefractive damage and a 100 nm thick Al
film was evaporatedonto the wafer surface. A nanoscaleresist pattern was definedusing electronbeam lithography(EBL)
and then transferred to an Al pattern by dry etching on the surface of the Mg:SLT wafer. EBL free from the diffraction
limit of light provides over 10 times higher accuracy than photolithography, but special care is required to avoid charge-
up in the ferroelectric Mg:SLT substrate. The width of the Al electrode was 400 nm and the duty ratio of the period was
approximately10%totheperiodassumingreasonablesidewiseexpansion(scanningelectronmicroscopy(SEM)imagesare
showninFigure2b). Anelectricfieldof2kV/mmwasthenappliedinthevacuumchambertoachieveahighelectricfield
contrastbysuppressionofthesurfacescreeningchargeforprecisecontrolofthedomaindutyratio. Domainsidewisemotion
was successfully controlledover6,000domainsalongthe 20 mm devicelength with a 6.7%chirpedpoling periodvarying
from3.12to3.34m m(opticalmicroscopyimagesareshowninFigure2c). AlthougheachEBLscanningareaislimitedtoa
widthof200m m(≪20mmdevicelength),theextremelyaccuratetranslationstageenablesa20nmconnectionerror,which
resultsinalowphaseslipbetweenscannedareas. Thefluctuationinthedomaindutyratio(typically0.65)waslessthan10%
totheperiod(Figure2c),whichsuggestsuniformconversionefficiencyalongtheentirespectralrange.
TheexperimentalsetupfortheTPIisshowninFigure3a(DetailsaregiveninMethods).ThechirpedQPMMg:SLTdevice
is setina temperaturecontrolledmetalholder(Figure3a upperinset). ThetemperatureT iscontrolledbya thermoelectric
coolerwithanaccuracyof0.1K.Wehavefoundthatinultra-highresolutionregimethelinewidthofapumplaserdegradesthe
dispersiontolerance.28 Toensurethedispersiontolerance,weusedanarrowbandpumplaser(∼100kHz)withawavelength
of 401 nm. The pump beam is focused to a diameter of 80 m m with a lens; this diameter is sufficiently smaller than the
cross-section of the device (500 m m (vertical)× 800 m m (horizontal)),and then cut by filters after the device. Collinearly
emittedphotonshadultra-broadbandwidthwithadevicetemperatureT =351KasshowninFigure3b. Thespectrumspans
from 660 nm with a sharp rise. We think that the offset in the shorter wavelengthregion(≤ 650 nm) is stray fluorescence
fromthedevice.Consideringthefrequencycorrelationwiththecenterwavelengthof802nm,thespectrumshouldspanupto
1040nmwithabandwidthof166THz. Thelowintensityinthelongerwavelengthregion(≥950nm)maybeduetothelow
couplingefficiencyto the opticalfiber for the spectrometerwe used. Figure3c showsnon-collinearlyemitted photonpairs
(signalphotonsandidlerphotons)withanemissionangleof1.5degreesrelativetothepumpbeamwithadevicetemperature
T =353K.Withthedetectioneventofasignalphotonasatrigger,thecoincidencecountrateoftheidlerphotonswastypically
5%(5×105Hz)thatofthesinglephotoncountrate(∼1×107Hz). Signalandidlerphotonscoupledtofibercouplers(FCs)
aretransferredtotheTPIinterferometerthroughpolarization-maintainingfibers. Thedelayt isdeterminedbythephysical
positionoftheFC.ThecoincidencecountrateC(t )isobtainedbytwoHUBDeSs,whichconsistofaSiavalanchephotodiode
(APD)withadetectionbandwidthspanningfrom400to1060nmandanInGaAsAPDwithabandwidthspanningfrom950to
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1150nm. FortheLCIexperiments,weusedsignalphotonsasalow-coherencelightsourcewiththeexactlysamebandwidth
ofthesourceforTPIandtheHUBDeS1fordetection(Figure3alowerinset). Forthecheckofthedispersioneffect,a1mm
thicknessofwaterenclosedbytwothinglasscoverplatesisinsertedintheopticalpathsofbothTPIandLCIinterferometers.
NotethataccordingtotheconventionaldefinitionforOCT,16 theinterferogramsbelowareexpressedinunitsofthe‘delay′
ct /2, where c is the speed of light, consideringthe physicaldisplacementof the delay mirrorsin OCT and QOCT systems
(Figure1).
TheexperimentalresultsareshowninFigure4. First,theLCIsignalwasobtainedasplottedbythereddotsinFigure4a.
Thefullwidthathalfmaximum(FWHM)oftheinterferencefringeis1.5m m,whichisslightlylargerthantheFWHMof1.1
m mfortheoreticalcalculation(bluelineinFigure4a)assumingarectangularspectralshapewitha166THzbandwidth. We
thinkthatthisdegradationisinducedbytheGVD:WhenthethicknessesoftheglassofBSintheopticalpathsoftheprobe
beamandthereferencebeam(Figure3alowerinset)aredifferent,thedegradationoccursbytheGVDoftheglass. Wehave
foundthatthedifferenceoftheFWHMscanbeexplainedwhenweassumethatthedifferenceofthethicknessesoftheglass
isjust150m m.
Figure4bshowstheLCIsignalwhena1mmthicknessofwaterisinsertedintheopticalpath. DuetotheGVDofthe1
mmthicknessofwater,38 theinterferencefringebecomesmuchbroader. TheFWHMofthefringeis7.8m m,whichismore
than5timeslargerthanthatwithoutthe1mmthicknessofwatersample. TheseresultsillustratehowGVDeffectbecomes
crucialinultra-highresolutionregime.
ThemainresultsofthispaperareshowninFigures. 4cand4d. Figure4cshowstheTPIsignalwithoutthewatersample.
TheFWHMoftheobservedHOMdipis0.54±0.05m m,whichsurpasses0.75m mofLCI31forOCTusingabroadbandlaser
lightwithacenterwavelengthof725nm,whichisthecurrentbestrecordresolutionasfarasweknow.Theresolutionof0.54
m minaircorrespondstotheresolutionof0.40m minwaterorbiologicaltissue. Thetheoreticalcurve(bluelineinFigure4c)
assumingtheobservedspectrumofthesignalphotons(Figure3c)fitswellwiththeexperimentaldata. Notethatforthesame
bandwidthofthephotonsourcewith arectangularshapedspectrum,theFWHM oftheTPIisa halfoftheLCI,28 whichis
alsoanadvantageofQOCTespeciallywhenthebandwidthoftheopticalwindowislimited.
Finally,experimentaldemonstrationofthedispersioncancellationofanultra-highresolutionTPIforQOCTisshownin
Figure4d. TheHOMdipisalmostunchangedfromFigure4cevenwhena1mmthicknessofwaterisinsertedintheoptical
path, which is in striking contrastto the case of LCI (Figures. 4a and 4b). The FWHM of the HOM dip is 0.56±0.04m m
and the difference between the FWHMs with and without the 1 mm thickness of water is 0.02 m m, which is smaller than
the margins of errors. The theoretical curve (blue line in Figure 4d) calculated taking the higher-orderdispersion of the 1
mmthicknessofwater38 intoaccountfitsalsowellwiththeexperimentaldata. NotethattheasymmetricityoftheHOMdip
observedintheexperimentaldataisduetothehigherodd-orderdispersion,28,39whichcanbealsoobservedinthetheoretical
curve. Our theoreticalcalculation suggeststhat the resolutionwill be still kept0.60 m m even when a thicknessof water is
increasedto3mm.Forthickermedium,‘phantom′canalsobeusedtocompensatethedispersioneffectforQOCT,similarto
OCT.IncaseofQOCT,thethicknessofthephantomdoesnothavetobeexactlythesamewiththemediumduetotheinherit
dispersion cancellationby frequencyentanglementdemonstratedhere. In case of OCT, on the other hand, the thicknessor
theGVDofthephantomhastobeexactlythesamewiththemediumaswediscussedonFigure4a,whichistechnicallyvery
difficult. ThedetailofthetheoreticalestimationofFWHMsandthecalculationaregiveninMethods.
Conclusion
Inconclusion,wehaveachieved0.54m mresolutionTPIwithdispersioncancellationforultra-highresolutionQOCT,which
surpassesthecurrentrecordresolution0.75m mofLCIforOCT.Wedevelopeda1st-orderchirpedQPMMg:SLTdeviceusing
a‘nano-electrode-poling′techniquewithEBLforultra-broadbandentangledphotonpairgeneration(166THz,l =660-1040
nm). A6.7%chirpedpolingperiodvaryingfrom3.12to3.34m mwasfabricatedinover6,000domainsalonga20mmlong
device. WeconstructedstableinterferometerswithHUBDeSsthatconsistofcommerciallyavailablesinglephotondetectors
operatedatroomtemperature.Inaddition,dispersioncancellationwasdemonstratedinTPIagainsta1mmthicknessofwater
insertedintheopticalpath.AlmostnodegradationinresolutionwasobservedinTPI(from0.54m mto0.56m m),whereasthe
LCIresolutionwassignificantlydegraded(from1.5m mto7.8m m). Theseresultswillopenthedoortoultra-highresolution
QOCT imaging with depth resolution less than half a micrometer. Such ultra-high resolution QOCT will be beneficial for
manydifferentareas,forexample,followingupthechangeoftheretinalthicknesswiththeultra-highresolutionwillgreatly
help the early detection of glaucoma.40 For this end, the increase in the flux of entangled photonsis very important. The
flux of 0.3 m W has already been realized using bulk QPM devices.41–43 Further increase in flux up to tens of m W can be
expected using slab or ridge type waveguide structures.44,45 A promising direction may be an OCT/QOCT hybrid system
whereOCTisusedforaquickwide-rangescanandQOCTisusedwhenultra-highresolution/highprecisionobservationis
required.Wealsonotethattheultra-highresolutionTPIwithdispersioncancellationdemonstratedhereisusefulforquantum
protocols,includingnotonlyQOCTbutalsoquantumclocksynchronization,46time-frequencyentanglementmeasurement47
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andmultimodefrequencyentanglement.48
Methods
Detailsofexperimentalsetup
Thepumplasersystemconsistsofasingle-frequencycontinuouswaveTi:sapphirelaser(MBR-110,Coherent)excitedbya
diode-pumpedsolid state laser (VerdiG-10, Coherent)and a resonantfrequencydoublingunit(MBD-200, Coherent). The
output of the Ti:sapphire laser (wavelength: 802 nm; linewidth: approximately 100 kHz) is frequencydoubled by second-
harmonicgeneration. Itisusedasthepumpbeamwithapowerof100mW.Thisnarrowlinewidth(∼100kHz)ensuresthe
dispersion tolerance of TPI in ultra-high resolution regime.28 We treated the narrowbandpump beam as a monochromatic
pumpfornumericalcalculationsbasedonthetheory.28,39 Thefocusedpumpbeamatthechirpedquasi-phase-matcheddevice
hasaconfocalparameter(i.e.,twicetheRayleighlength)of18mm.
Forthemeasurementsoffrequencyspectra,generatedentangledphotonsfromthedevicearecoupledtothethepolarization-
maintainingfiberandsenttoa300-mmspectrometerwitha150-grooves/mmgratingblazedat800nm(SP-2358,Princeton
Instruments)andachargecoupleddevice(CCD)camera(Pixis:100BRX,PrincetonInstruments).Thetransmissionefficiency
ofthespectrometerandthequantumefficiencyoftheCCDcamerawerecalibratedinFigures3band3c.
Each of HUBDeS shown in Figure 3a consists of a Si APD (SPCM-AQRH-14, Perkin Elmer) and an InGaAs APD
(id401, idQuantique). The coincidencecount rateC between two HUBDeSs is obtained by the sum of coincidence counts
betweentwoAPDsasC=C +C +C +C ,whereforexampleC isthe
Si-1/Si-2 Si-1/InGaAs-2 Si-2/InGaAs-1 InGaAs-1/InGaAs-2 Si-1/InGaAs-2
coincidencecountratebetweenSiAPD1inHUBDeS1andInGaAsAPD2inHUBDeS2. Thecoincidencetimewindowof
thecoincidencecounter(id800,idQuantique)was2ns.
Analysisofinterferencesignals
ForLCIexperimentaldata(plottedbyreddotsinFigures4aand4b),aFWHMofinterferencefringeisdeterminedbythefull
widthatthemiddlebetweenabaselineandapeakheight.Thebaselineistheaverageofthewholeinterferencefringealong
thedelay.Thepeakheightiscalculatedusingthesmallestorlargestdatapoint.IntheoreticalcalculationsforLCI(bluelines
inFigures4aand4b),wecalculatedbasedonthetheory28assumingarectangularspectralshapewithacenterwavelengthof
802nmandabandwidthof166THzforthelightsource. Inthecasewitha1mmthicknessofwaterinsertedintheoptical
path,weassumedthe2nd-orderdispersionandthe3rd-orderdispersionofthewater.38 ForTPIexperimentaldata(reddotsin
Figures4cand4d),aFWHMofinterferencedipisdeterminedbytheFWHMofaGaussianfittingcurve(blackdashedlines
inFigures4cand4d).TheGaussianfitusesthewholerangeofthedipalongthedelayandassumestheexperimentalvisibility.
The experimentalvisibilities of dips with and without the water dispersion are 0.67±0.05and 0.73±0.04, respectively. In
theoreticalcalculationsfor TPI (blue lines in Figures 4c and 4d), we assumed the observedspectrumof the signal photons
(Figure3c),experimentalcoincidencecountrateandexperimentalvisibilities. WealsoassumedtheGVDandthe3rd-order
dispersionofthewater38forthecasewiththe1mmthicknessofwaterinserted.
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Acknowledgements
The authors thank Shoichi Sakakihara (ISIR, Osaka Univ.) for water sample preparation, Toru Hirohata and Masamichi
Yamanishi(HamamatsuPhotonics)forlendingultra-broadbandphotomultipliertubesforus,YuEtoandAkiraTanaka(Osaka
Univ.)forhelpfuldiscussions.ThisworkwassupportedinpartbytheJapanScienceandTechnologyAgencyCRESTproject
(JST-CREST), the Quantum Cybernetics project of the Japan Society for the Promotion of Science (JSPS), the Funding
Program for World-Leading Innovative R&D on Science and Technology Program of JSPS (FIRST), Grant in-Aids from
JSPS;theProjectforDevelopingInnovationSystemsoftheMinistryofEducation,Culture,Sports,Science,andTechnology
(MEXT),theNetworkJointResearchCenterforAdvancedMaterialsandDevices,theResearchFoundationforOpto-Science
andTechnology,andtheGlobalCOEprogramme.
Author contributions statement
Experiments,measurementsanddata analysiswereperformedbyM.O.withassistance ofR.O. andS.T.Devicefabrication
was carriedoutbyH.H.L.andS.K. Allauthorsdiscussedtheresultsandcommentedonthemanuscriptatallstages. M.O.,
S.K.andS.T.wrotethemanuscript.TheprojectwassupervisedbyN.N.,S.K.andS.T.
Additional information
Competingfinancialinterests
Theauthorsdeclarenocompetingfinancialinterests.
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detectorwithvaryingdelayt (inset). BSisabeamsplitter. (b),SchematicdiagramofQOCT.C(t )isthecoincidencecount
ratecountedattwosinglephotondetectorswithvaryingdelayt (inset).
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device. Mg:SLTisMg-dopedstoichiometriclithiumtantalate. (b),Scanningelectronmicroscopyimages(upperandlower)
ofthe400nmwideAlelectrodesfabricatedforthepolingperiodof3.2m m. (c),OpticalMicroscopyimagesofperiodically
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Figure3. Experimentalsetup. (a),TPIandLCIinterferometerswithhybridultra-broadbanddetectionsystems(HUBDeS).
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avalanchephotodiode(APD)andanInGaAsAPD.ThelowerinsetshowstheLCIinterferometer.A1mmthicknessofwater
canbeinsertedintheopticalpathinTPIandLCIinterferometers.BS,beamsplitter;FC,fibercoupler;PMF,
polarization-maintainingfiber;Mg:SLT,Mg-dopedstoichiometriclithiumtantalate. (b),Frequencyspectrumofcollinearly
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(reddots)andthetheoreticalcurves(blueline)areplottedinunitsofthedelay.Theintegrationtimewas1secondperpoint.
(c,d),TPIdipsobtainedintheTPIinterferometer.Thedipswithout(c)andwith(d)the1mmthicknessofwater. The
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plottedinunitsofthedelay.Theintegrationtimewas10secondsperpoint.Theredlinesconnectingthedatapointsarea
guidetotheeye(a–d).
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