GaAs integrated quantum photonics: Towards dense and fully-functional quantum photonic integrated circuits

4.4 MB·

by  Christof P. Dietrich

August2,2016
AbstractTherecentprogressinintegratedquantumopticshas
setthestageforthedevelopmentofanintegratedplatformfor
quantum information processing with photons, with potential
applicationsinquantumsimulation.Amongthedifferentmaterial
platformsbeinginvestigated,direct-bandgapsemiconductors
andparticularlygalliumarsenide(GaAs)offerthewidestrange
offunctionalities,includingsingle-andentangled-photongener-
ationbyradiativerecombination,low-lossrouting,electro-optic
modulationandsingle-photondetection.Thispaperreviewsthe
6
1 recentprogressinthedevelopmentofthekeybuildingblocks
0 forGaAsquantumphotonicsandtheperspectivesfortheirfull
2 integrationinafully-functionalanddenselyintegratedquantum
photoniccircuit.
g
u
A
1 GaAs integrated quantum photonics: Towards compact and

] multi-functional quantum photonic integrated circuits
l
l
a
h Christof P. Dietrich1,*, Andrea Fiore2, Mark G. Thompson3, Martin Kamp1, and Sven
-
s Ho¨fling1,4
e
m
.
t
a 1. Introduction asdesiredbyincreasingthenumberofresources(ancilla
m
photons).Inaddition,itwasproposedthatquantumlogic
- networks can be simulated by simple one-way quantum
d Quantuminformationscienceusingtheuniquefeaturesof
computationusingaparticularclassofentangledstates,so
n quantummechanics-superpositionandentanglement-can
called cluster states [5]. On a parallel line, a particularly
o greatlyenhancecomputationalefficiency,communication
c security, and measurement sensitivity. The generation of simple class of linear-optics quantum simulators, boson
[ samplingcircuits,weretheoreticallyshowntoimplement
quantumbits(qubits)andtherealizationofquantumgates
computationalproblemswhichareclassicallyintractable[6].
2 aretheprerequisitesforconductingquantuminformation
By following these approaches of only using linear opti-
v science.Theuseofphotonsasqubitshasbeenwidelycon-
6 sideredasoneoftheleadingapproachestoencode,transmit cal components, two-qubit [7] and three-qubit gates [8],
5 simple quantum algorithms [9,10] as well as boson sam-
andprocessquantuminformationbecauseoftheirlowde-
9 pling[11–14]couldalreadybeexperimentallydemonstrated.
coherence,high-speedtransmissionandcompatibilitywith
6 Earlydemonstrationsoflinear-opticsquantumprocessing
classical photonic technology [1–3]. Photonic qubits can
0 havereliedoninefficientandbulkysinglephotonsources
easily be encoded in many different degrees of freedom,
.
1 basedonspontaneousparametricdownconversion(SPDC),
e.g. polarization, path, frequency and orbital angular mo-
0 modestefficiency(atnear-infraredwavelengths)singlepho-
mentum,makingtheimplementationofqubitsusingsingle
6 ton detectors based on avalanche photodiodes (APDs) or
photonsveryattractive.However,singlephotonsaresubject
1 superconductingnanowires,andopticalcircuitswithbulk
to substantial losses. Furthermore, nonlinear interactions
:
v betweensinglephotonsareweakanddonotprovideπ cross opticalelements.However,similartointegratedelectron-
i ics,thepracticalityandscalabilityofquantuminformation
X phasemodulationinnaturalnonlinearmaterials,whichis
technologyultimatelyrequirestheintegrationofindividual
therequirementforachievingatwo-qubitgate.
r componentsonasinglechip.Integratedquantumphotonics
a In 2001, a major breakthrough known as the KLM
is emerging as a promising approach for future quantum
scheme [4] showed that scalable quantum computing is
informationscience,sinceitenablesasubstantialimprove-
possiblebyonlycombiningsingle-photonsources,linear
mentinperformanceandcomplexityofquantumphotonic
optical circuits and single-photon detectors. In this case,
circuits and provides routes to scalability by the on-chip
thenon-linearityinthedetectionreplacesadirectoptical
generation,manipulationanddetectionofquantumstates
non-linearity.Theresultingquantumgatesareprobabilistic,
of light. Major progress has been made recently towards
buttheprobabilityofsuccesscanbemadeasclosetoone
1TechnischePhysik,Universita¨tWu¨rzburg,AmHubland,97072Wu¨rzburg,Germany 2COBRAResearchInstitute,EindhovenUniversityofTech-
nology,5600MBEindhoven,TheNetherlands 3CentreforQuantumPhotonics,H.H.WillsPhysicsLaboratoryandDepartmentofElectricaland
ElectronicEngineering,UniversityofBristol,WoodlandRoad,BristolBS81UB,UnitedKingdom 4SUPA,SchoolofPhysicsandAstronomy,Univer-
sityofStAndrews,NorthHaugh,StAndrewsKY169SS,UnitedKingdom
*Correspondingauthor:e-mail:[email protected]
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2 C.P.Dietrichetal.:GaAsintegratedquantumphotonics
highlyefficientintegratedsinglephotonsources,singlepho-
tondetectorsandintegratedphotoniccircuits.
Inparticular,linearquantumphotonicintegratedcircuits
(QPICs)fortwo-photoninterference,CNOT-gatesanden-
tanglementmanipulationcouldalreadybedemonstratedon
variousplatformsandwithvariousmaterials.Theseinclude
e.g.silica-on-silicon[13,15,16],laserdirect-writingsilica
[17],galliumnitride[18],lithiumniobate[19],silicon-on-
insulator[20,21]andGaAs[22].Indiumarsenide/gallium
arsenide (InAs/GaAs) quantum dots (QDs) are routinely
embedded in photonic crystal waveguides/cavities and Figure1 Left:TransmissionelectronmicrographofanInAsQD
havebeenestablishedasrobustandefficientsingle-photon (brightarea)inaGaAsmatrix(darksurrounding)grownbyMBEin
sources[23–27].Moreover,high-efficiencysuperconduct- Stranski-Krastanovgrowthmode.Thewhitescalebarrepresents
ingnanowiresingle-photondetectorsbasedonGaAsandSi 10nm.Right:SEMimageofuncappedInGaAsQDs.
waveguideshavebeensuccessfullydemonstrated[28–31].
Amongalltheseplatforms,GaAsisawell-known,ma- ideallycreatedondemandinatwo-levelsystem.Besides
ture material system for classical integrated photonics. It naturaltwo-levelsystemssuchassingleatoms,molecules
allows for the fabrication of low-loss waveguides and its ordefectcenters,alsonanometer-sizedinclusionsofalow-
highrefractiveindexenablestightconfinementoflightand gapsemiconductingmaterialincorporatedintoahigh-gap
thereforecompactdevicesandcircuits.Ithasbeenemployed matrixdeliversatwo-stateconfigurationbyformingaquasi
inGHzmodulatorsduetoitshighχ(2)nonlinearity[32].In zero-dimensional potential trap. Those energy traps are
thecontextofquantuminformationscienceapplications,the called semiconductor QDs (QDs). Single-photon sources
largeelectro-opticeffectinGaAsmakesitaverypromis- based on QDs have the huge advantage that they can be
ingcandidateforfastroutingandmanipulationofsingle- grownmonolithicallywithmonolayerprecisionundercon-
photons.Single-photonemissioninGaAscanberealizedby trolled conditions by well-established growth techniques
eitherspontaneousparametricdown-conversioninwaveg- suchasmolecularbeamepitaxy(MBE)[39–42]ormetal-
uides[33],takingadvantageofthehighχ(2),orbyintegrat- organicvaporphaseepitaxy(MOVPE)[43–45].Theunique
ingsingleQDsintonanophotonicstructures.Single-photon opticalpropertiesofsemiconductorQDshaveenabledexten-
sourcesbasedonparametricgenerationofphotonpairsand siveresearchandtremendouslyincreasedthescientificin-
heraldingmustbeoperatedatrelativelylowaveragephoton terestinrealizingphotonicQDdevices.QDsarenowadays
numbers,resultinginalowsingle-photonprobability,un- widelyusedinapplicationssuchaslight-emittingdiodesor
lesscomplexmultiplexingschemesareemployed[34].The solarcells.Regardingintegratedquantumphotonics,numer-
QD approach, facilitated by the direct bandgap of GaAs, ousproof-of-principleexperimentswerecarriedoutonQDs,
enables efficiencies close to 100% [35] and represents a includingsinglephotonemission[46],two-photoninterfer-
fundamentaladvantageofGaAsQPICswithrespecttoSi ence [47,48], polarization-entanglement [49] and strong
orLiNbO circuits. coupling[50,51],underpinningtheirpromisingapplicabil-
3
Besidessingle-photonemission,alsosingle-photonde- ityasqubitsourceinquantumcommunicationschemes.
tectorsonGaAswaveguideshavealreadybeensuccessfully The most extensively studied QD materials are InAs
demonstrated [28]. Therefore, GaAs waveguide circuits and InGaAs in GaAs matrices (see Figure 1). The huge
monolithicallyintegratedwithsingle-photonsourcesand differenceinband-gapenergiesbetweenInAs(E (2K)=
g
superconductingsingle-photondetectorsofferapromising 0.422eV)andGaAs(1.522eV)andthethree-dimensional
approach to large-scale quantum photonic integrated cir- quantum confinement makes it possible to tune the QD
cuits.Here,wereviewrecentdevelopmentsinInAs/GaAs emission in a very large spectral window - from almost
QDsingle-photonsources(Sections2-4),ridgewaveguide 850nmupto1400nm-byadjustingtheQDdimensions.In
quantumphotoniccircuits(Section5)andGaAswaveguide thefollowing,wewillhighlightachievementsinthegrowth
single-photon detectors (Section 6), and we also discuss ofQDs(Section2.1),theirpositioningondeterminedsites
thechallengeofmonolithicintegrationofindividualcom- (Section2.2)andtheiropticalproperties(Section2.3).
ponents (Section 7) towards the realization of dense and
fully-functionalquantumphotonicintegratedcircuits.Re-
centpromisingdevelopmentsinparametricgenerationof
2.1. Self-assembled quantum dots
photon pairs [33] and entangled photons [36], including
byelectricalinjection[37],havebeenreviewedrecentlyin
Ref.[38]andarethereforenotdiscussedhere. ThelatticemismatchbetweenInAsandGaAsisabout7%
givingrisetoconsiderablestrainwhenthetwomaterialsare
depositedontopofeachother.Thiscircumstanceisused
2. Semiconductor quantum dots inthemostexploitedgrowthmodeforQDs-theStranski-
Krastanovgrowthmode[52]-whichmakesuseofthefact
Integratedquantumphotonicexperimentsrelyonthegener- thatcoherent,dislocation-freeislandsformself-assembled
ation,manipulationanddetectionofsinglephotonsthatare asresultofstraincompensation.Thesizeoftheislandsis
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3
Figure2 SchematiccappingprocessofapyramidalInAsQD Figure3 Toprow:AtomicforcemicrographsfromQDsgrownby
(a)overgrownbyGaAslayerswithincreasingthicknesses(b-e). dropletepitaxybefore(left)andafterannealing(right)at400◦C.
Reprintedwithpermissionfrom[53].©2008,AIPPublishingLLC. ©IOPPublishing.Reproducedwithpermission.Allrightsreserved.
Bottomrow:Scanningtunnelmicrographsofmonolayerfluctu-
ations just after growth interruption for bottom and top QW in-
therebyextremelysensitivetotheamountofmaterialthatis
terfaces(leftandright).AdaptedwithpermissionfromRef.[70].
deposited. CopyrightedbytheAmericanPhysicalSociety.
The growth of InAs on a GaAs (100) surface ini-
tiallyresultsinathin2Dwettinglayer.Duetothelattice-
mismatch,thetwo-dimensionalgrowthmodeturnsintoa sionpropertiesofQDsaredeterminedbythestrengthofthe
three-dimensionalgrowthafterdepositionofafewmono- quantumconfinementeffectwhichcanbealteredinseveral
layersresultinginthecreationofrandomlypositionedQDs differentways.BesideschangingtheverticalheightofQDs
withapyramidalshape.Inordertopreventthedotsfrom bye.g.partialcapping,thecappinglayercompositioncan
oxidationandtoseparatethemfromthesurface(forthein- be optimized to alter the strain state and heterostructure
tegrationintophotonicnanostructures,seeSection4),they potentialintheQD,orQDscanbeannealedaftergrowth
arecommonlyovergrownbyacappinglayerofGaAscom- leadingtoaninter-diffusionofgalliumandindiumatthe
pleting the three-dimensional quantum confinement. The QD surface. The diffusion process undermines the quan-
capping changes the shape of the QDs from purely pyra- tum confinement and causes a blueshift [56–58] whereas
midal to truncated pyramidal (see Figure 2) [53]. During anInGaAscappinglayerreducesthestrainintheQDand
thecappingprocess,intermixingbetweenthecappingma- reducestheinter-diffusion,leadingtoared-shiftoftheQD
terialandtheQDsmightoccurleadingtotheformationof emission[59,60].
In(Ga)As QDs. This intermixing strongly affects the QD ThecontrolofthedensityofQDsiscrucialfortheper-
compositionandpotentialprofileaswellastheQDemis- formance of single photon experiments since it requires
sion. theabilitytoopticallyaddressindividualQDsbyconven-
Inrecentyears,severaltechniqueshavebeendeveloped tionalspectroscopicmethods.Severalrouteswerealready
thatfacilitatethedirectmanipulationofQDpropertiesin- demonstratedincludingthechangeofgrowthparameters
cludingtheirsize,theirsizedistribution,theirdensity,their suchasgrowthtemperature[61],III/V-ratio[62]orgrowth
shapeandemissionwavelength.TheQDsizecanbevar- interruptions[63].Oneofthemostreliablewaystocontrol
iedbychangingthecompositionofthedots[54].Thesize the density of QDs (over several orders of magnitude) is
distributionofQDsdirectlydeterminestheinhomogeneous the change of the growth rate, or by varying the amount
linewidthoftheQDensembles:largesizevariationsleadto ofdepositedmaterial(approachingthe2Dto3Dmaterial
anunwantedbroadeningoftheemission.Awaytoreduce growth transition range that can be controlled by system-
the size distribution spread would be partial capping and aticallyapplyingmaterialfluxgradients).Inthisway,den-
annealing:analmostuniformheightofQDscanbeachieved sitiesofself-assembledQDsaslowas<0.1µm−2canbe
byintroducinganannealingstepduringtheprocessofQD achieved[61,64].
capping [56]. This process is usually accompanied by a Alternatives to growing self-assembled QDs in the
blueshiftoftheQDemissionduetotheheightreduction. Stranski-Krastanov growth mode are techniques such as
Besidesthecontroloftheuniformity,thegrowthcondi- dropletepitaxy[65]orthecontrolofmonolayerfluctuations
tionscanbeusedtochangetheshapeoftheconfinement inquantumwells[66,67](seeFigure3).Dropletepitaxy
potentialandtherebytheemissionenergy.Indeed,theemis- isbasedontheaffinityofsomegroup-IIIelementstoform
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4 C.P.Dietrichetal.:GaAsintegratedquantumphotonics
dropletsonasemiconductorsurfaceandhastheadvantage
thatitdoesnotrequirealattice-mismatchbetweenthein-
volvedmaterials[68,69].Fordropletepitaxy,dropletsof
group-IIIelementsareannealedaftergrowthinanarsenic
atmosphereand,underoptimumannealingconditions,form
defect-freeQDsbysaturatingwithAs(seeFigure3top).
ComparedtotheStranski-Krastanovgrowth,QDsgrownby
dropletepitaxyarerelativelylarge.Alternatively,strain-free
QDs can be achieved by interrupting the growth of thin
quantum wells. These growth interruptions intentionally
introducemonolayerfluctuations(Figure3bottom)atthe
interfaceeffectivelycreatinganadditionalquantumconfine-
mentwithinthequantumwellplane.ThistypeofQDhasa
largerlateralextensioninthelayerplanethanQDsgrownby
theStranski-Krastanovmodeordropletepitaxy[70],lead-
ingtoalargeroscillatorstrength.Theyfurtherbenefitfrom
thefactthattheyarenotsubjecttomaterialintermixing.
Figure4 Atomicforcemicrographofsite-controlledQDswith
1µmlatticeperiodinasquarelatticegrownonamesastructure.
Thescalebarrepresents1µm.Reprintedwithpermissionfrom
2.2. Site-controlled quantum dots
[93].©2008,AIPPublishingLLC.
TheimplementationofsemiconductorQDsassourcesof
beenfoundtostronglydependontheproximitytoheteroin-
flying qubits into quantum integrated circuits requires a
terfacesandfreesurfaces,duetotheeffectoffluctuating
precise control over the relative position of the QD with
charge states [89]. For optimized growth conditions and
respect to the circuit. Small misalignment (e.g. of a QD
advancedsampledesigns,recordlinewidthvaluesaslowas
in the center of a defined PhC cavity) can lead to severe
7µeVwerereportedforrandomlyoccupiedQDsites[90]
reductionsindeviceefficiency.
andaround20µeVweredemonstratedforQDpatternswith
Adequatecontrolcanbeachievedbyeitherplacingthe
only one QD at each site [79,91] (p-shell excitation, see
circuitaroundtherandompositionofaself-assembledQD
Section3.1).Inthisregard,site-controlledQDsarecompa-
[71,72]orbypredeterminationofboththeQDandcircuit
rabletoself-assembledQDsintermsofemissionlinewidths.
location. The first approach makes a pre-characterization
Anothercrucialfeatureforphotonicapplicationsisthespec-
oftheQDdistributionnecessary,followedbyatop-down
tralwidthoftheQDensemble,whichismainlydetermined
etchingaroundachosendot.However,thisprocessistech-
bysizeandshapefluctuationsofthegrowndots.Whereas
nologicallyverychallengingandseemsincompatiblewith
self-assembledQDsexhibitinhomogeneousbroadeningin
theupscalingtolargequantumphotoniccircuits,asthede-
therangeofseveraltensofmeV,thenucleationonpredeter-
vice layout must be adapted to the QD spatial positions.
minedsitescanreducethisvaluetoonlyafewmeV[92].
The growth of QDs on predetermined sites provides ac-
curate alignment (see Figure 4) of single photon sources
with respect to photonic circuits [73] and facilitates high
yielddevicefabrication.Severalstrategiesweredeveloped 2.3. Optical properties of quantum dots
inthepasttopreciselypositionQDsonasemiconductor
platform[74].Thisincludese.g.thedepositionofoptically MostcommonbarrierandQDmaterialcombinations,in-
activeQDsonanopticallyinactivestresslayer[75].Amore cludingtheextensivelyinvestigatedcombinationofInAs
commonstrategyisthepre-patterningofthesemiconductor QDsinGaAsbarriers,formatype-Iheterostructureresult-
surface by e.g. drilling holes into it [76–83]. This can be inginstrongquantumconfinementforbothelectronsand
achieved by a combination of electron beam lithography holes. In good approximation, it can be assumed that the
andionetching,byatomicforcenano-lithography[84],by QDbehavesasatwo-levelsystem,wherethelowest-energy
nanoimprint lithography [85] or by local oxidation nano- electronicexcitation(heavy-holeexciton,X)involvesone
lithography[86].Duringsubsequentregrowththeadatoms electronintheconductionbandandoneholeinthevalence
preferentiallynucleateatthepatternedsitesandformQDs. bandwithstrongheavy-holecharacter(notethatbyapply-
ThisprocesscanprovideanaccuracyoftheQDposition ingelasticstresstoinitiallyunstrainedQDstheexcitonic
ofabout±50nmwhichinmanycasesissufficientforthe groundstatecanalsohavelight-holecharacter[94]).Higher
application in photonic circuits [87]. Similar results can occupiedstatessuchasbiexcitonsortrionsaredetunedin
beobtainedbygrowingsite-controlledQDsusingmasked energy due to Coulomb interactions. The degeneracy of
surfaces[88]. the QD valence band is usually lifted by the asymmetric
In experiments and applications exploiting multipho- shape of the confinement potential and by strain causing
toninterference(seesection3.3),QDemissionlinewidths anon-vanishingenergysplittingbetweenheavyandlight
are an important figure of merit and should ideally reach holelevelsontheorderofseveraltensofmeV.Fortypical
transform-limitedvalues.Inthisregard,thelinewidthhas self-assembledQDsthesplittingissolargethatthetransi-
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5
excitons (X), biexcitons (XX) as well as trions (X−, X+)
canbeseeninFig.5.
Biexcitonsareparticularlyinterestingsincetheyposses
a net projection of the angular momentum of 0 and are
thereforenotsubjecttoexchangeinteractions.Ifthefine-
structure splitting is suppressed, this leads to the decay
intotwobrightexcitonswithoppositecircularpolarization.
This decay scheme has extensively been investigated for
thecreationofpolarization-entangledphotonpairsinQDs
systems[49,102–104].Fortheentanglement,thetwodecay
paths σ+ →σ− and σ− →σ+ (with σ being the pho-
XX X XX X
ton polarization state) need to be indistinguishable. This
Figure5 Non-resonantphotoluminescencespectrumofaGaAs is typically not the case due to finite fine structure split-
QDshowingexciton(X),biexciton(XX)andtrion(X−,X+)tran- tings.Therefore,inQDsystemswithfinestructuresplittings
sitions. The upper panel schematically depictsthe QD charge smallerthantheexcitonlinewidths(asforQDsgrownon
configurationforeachtransition.Adaptedwithpermissionfrom GaAs(111)layers[105]),entangledphotonpairscandeter-
Ref.[95].CopyrightedbytheAmericanPhysicalSociety. ministicallybecreated[106].Othertechniquessuchasther-
malannealing[107],theapplicationofelectricfields[108],
tionbetweenconductionbandandlight-holevalenceband strain[109],aswellastheshapingoftheconfinementpo-
caneasilybeneglectedmakingthesystematruetwo-level tential[104]arealsoabletoreducetheFSSandproduce
system. entangledphotonpairs.
ThetotalangularmomentumJofheavy-holeexcitons
isasumofheavy-holeangularmomentumandelectronspin
allowingfourdifferenttransitionconfigurationshavingan 3. Quantum dots as single photon sources
angularmomentumalongthegrowthdirection:J =±1
z,1
andJ =±2.TheJ configurationsaretermedbrightex-
z,2 z,1 On-chipsingle-photonsourcescanberealizedbyexploit-
citonstatesastheycoupletotheopticalfieldandtherefore
ingtheradiativerecombinationfromanexcitonicstateofa
preferentiallydecaythroughradiativerecombinationchan-
singleQD[46].SingleQDshavebeenwidelyinvestigated
nels.Incontrast,configurationswithtotalangularmomen-
assingle-photonandentangled-photonsources(see[110]
tumJ aretermeddarkexcitonstatesanddecaythrough
z,2 forareview).Ascomparedtosingle-photonsourcesbased
non-radiativerecombinationchannels.Duetothecloseprox-
onparametricdown-conversionandheralding,QD-based
imity of both electrons and holes in semiconductor QDs,
sourcespresenttheadvantageofdeterministic,on-demand
exchangeinteractionsofelectron-holepairsareenhanced
singlephotonemission,mucheasierfilteringofthepump
and cause an energetic splitting between dark and bright
duetothelowerpowersneeded(tensofnWlevel)andthe
states as well as the formation of mixed dark and mixed
possibilityofpumpingfromthetop-thisisparticularlyrel-
brightstates.Brightanddarkexcitondecaybi-exponentially
evantinthecontextofquantumphotonicintegratedcircuits
caused by radiative and non-radiative recombination as
asitreducesthecouplingofpumplightintothechip.
wellasspinflipprocesses(turningbrightstatesintodark
states,andviceversa,undercreationorannihilationofLA
phonons)[96,97].
3.1. First- and second-order coherence
Whilethepurestatesarecircularlypolarized,theymix
asaconsequenceofexchangeinteractionsandofthepref-
In general, quantum emitters can be classified regarding
erentialQDelongationalongthein-plane[110]-direction
their coherence properties and photon statistics. The de-
forgrowthonGaAs(100)substrates,givingrisetomixed
greeoffirst-ordercoherenceisquantifiedbythefield-field
stateswithlinearpolarizationplanesparalleltothe[110]-
and[110]-crystaldirection[98,99].Thoselinearlypolarized correlationfunctiong(1)andthedegreeofsecond-orderco-
transitionscandirectlyberecordedinluminescenceexperi- herenceisdescribedbytheintensity-intensitycorrelation
ments[100].Theirenergeticseparationistheso-calledfine functiong(2).g(1) ofaquantumemitterisusuallyprobed
structuresplitting(FSS).Darkstateshavetypicalfinestruc- in optical interferometers where the optical beam is split
ture splittings in the order of 1µeV [101] whereas bright intotwoarmsandjoinedagainafterintroducingavariable
statescanhaveFSSuptoseveralhundredsofµeV[98](few timedelayτ intooneofthearms.Thelightproducedby
tofewtensofµeVaremorecommonlyobserved). an ideal single-quantum emitter with a lifetime T1 is de-
(cid:12) (cid:12)
Besidesbrightanddarkexcitonstates,alsostateswith scribedby(cid:12)g(1)(τ)(cid:12)whichdecaysexponentiallywithatime
(cid:12) (cid:12)
higheroccupationsuchastrions(i.e.chargedexcitons,X−
constantT =2T -correspondingtoasingle-photonpulse
orX+)orbiexcitons(XX)occur.OwingtoCoulombinterac- 2 1
withnophasejumps.However,realquantumemitterssuch
tionsbetweenconfinedcarriers,thesestateshaverecombina-
asexcitonsinQDsareimperfectsystemsandshowfaster
tionenergiesdifferentfromtheexcitontransitionsallowing (cid:12) (cid:12)
thespectralfilteringofindividualexcitonictransitions.A decaysof(cid:12)(cid:12)g(1)(τ)(cid:12)(cid:12)causedbydephasingmechanismssuch
typical QD spectrum showing the radiative transitions of asphononinteractions.Dephasingreducesthecoherence
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6 C.P.Dietrichetal.:GaAsintegratedquantumphotonics
Figure 6 Non-resonant, quasi-resonant and resonant excita-
tionscheme:high-energyparticles(dottedcircles)decaythrough
phonon-interactionsintotheQDgroundstate(solidcircles).The
verticalarrowsindicatetheenergynecessaryforeachprocess.
Figure7 CalculatedabsorptionspectraofanInAsQDatdiffer-
timeoftheQDresultingin1/T =1/2T +1/T∗(withT∗
2 1 2 2 enttemperatures.Atlowtemperatures,aclearasymmetricbroad-
beingthepuredephasingtime)andincreasesitslinewidth.
eningofthezero-phononline(ZPL)causedbyexciton-phonon-
Dephasingprocessesaredetrimentalinquantumphotonic
interactionswithlongitudinalacousticphononsisvisible.Inset:
applicationsastheymakephotonsemittedfromdifferent
CalculatedbroadeningoftheZPLcomparedwithexperimental
sources distinguishable and reduce the visibility in two-
results from [111]. Reprinted with permission from Ref. [112].
photoninterferenceexperiments. CopyrightedbytheAmericanPhysicalSociety.
The occurrence of dephasing is strongly related to
theexcitationschemeusedfortheexperiment.Nowadays,
threemaindifferentschemesaredistinguished:off-resonant,
quasi-resonant(p-shellexcitation)andresonantpumping
(s-shell excitation), see Figure 6 for the different energy
configurations (less common excitation schemes omitted
here include wetting layer excitation or excitation above
shellresonanttoanLOphononreplica).Theexcitationofa
QDwellaboveitsgroundstateorresonantwithanexcited
state(e.g. p-shell)resultsintherelaxationofcarriersinto
the ground state by generation of phonons [111]. In gen-
eral,QDsalwaysemitandabsorbphononsthroughinelastic
processes.Especially,LAphononsarewellknownsources
fordephasingandcauseanasymmetricbroadeningofthe
QDtransition(asvisibleinthecalculatedabsorptionspec-
trumshowninFigure7)[112–116].TheinteractionofQD
excitonswithphononscaneitherbesuppressedbyperform-
ingtheexperimentatverylowtemperaturesorbyadapting
resonants-shellexcitation(seeSection3.2).Wenotethat
off-resonantandquasi-resonantexcitationalsoproducea
certaintimejitterinthegenerationofsinglephotonevents,
reducingtheindistinguishability[117,118,121].Another
dephasingprocessisinducedbytherandomdistributionof
Figure 8 (a) Typical spectrum of InAs/GaAs QDs measured
chargecarriersinsideaQDandchangesintheelectronic
throughanaperturewith100nmwidth.(b)Temporalevolution
configurationaroundtheQD.Chargeandspinfluctuations
of(a)showingspectralwanderingofalmostallQDtransitions.
resultinapersistentchangeoftheexcitonicgroundstate ReprintedwithpermissionfromRef.[127].Copyrightedbythe
inducingspectralwanderingoftheQDemission(seeFigure AmericanPhysicalSociety.
8).ThisleadstoaneffectiveincreaseoftheQDlinewidth
and a decrease of the QD coherence time [122]. Charge
producesalossofindistinguishabilityinthesamewayas
fluctuations can be suppressed drastically by employing
puredephasing,andmustbesuppressed[125,126].
resonantpumpingandaddingaweakauxiliarycontinuous
Photonstatisticscanbeprobedbymeasuringthesecond-
wavereferencebeamtotheexcitationbeamoftheQD[123].
Spectralwanderingistypicallymuchslowerthantheradia- ordercorrelationfunctiong(2)(τ)thatgivestheprobability
tivedecayofexcitonsanditseffectcaninsomecasesbe ofdetectingtwophotoneventswithtimedelayτ between
circumventedbypumpingtheQDwithashortpulsetwice them.Inthisregard,theg(2)(0)value(atzerotimedelay)is
atshorttimeintervalstoobtaintwophotonswithverysim- particularlyimportantsinceitmeasurestheprobabilitythat
ilar energies [124]. However, when interference between twophotonsaredetectedatthesametime.Experimentally,
photonsfromdifferentQDsisrequired,spectralwandering g(2)(τ) is routinely determined in a Hanbury Brown and
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7
Twiss(HBT)setupthatconsistsofa50:50beamsplitterand
twonominallyequalsingle-photondetectorswithatempo-
ralresolutionmuchbetterthanτ.Whereasforacoherent
andthermallightsourceg(2)(0)approaches1and2,respec-
tively,aperfectsinglephotonsourcegivesg(2)(0)=0since
theprobabilityofdetectingtwophotonseventsatthesame
timeisthenzero.
Thephotonstatisticsofrealsingle-photonsourcesare
strongly affected by non-idealities such as multi-photon
emissionfrommulti-excitonstates,collectionoftheemis-
sionofotherQDs,re-pumpingoftheemitteraftertheemis-
sionofthefirstphoton,etc.,andthereforeproducenon-zero
coincidences [115,116]. Resonant, pulsed excitation can
lead to g(2)(0) values very close to zero [124,128,129].
Pumping by adiabatic rapid passage using chirped laser
Figure9 Left:Excitation-dependentPLspectraofaresonantly-
pulses can further suppress multi-photon emission [130]. pumpedsingleQD.EΩ=h¯Ωdenotestheenergeticsplittingbe-
Evenwiththesehighlysophisticatedexcitationanddetec-
tweenzero-phononlineanditsfirstMollowsideband.Topright:
tion schemes, multi-photon emission in QD systems can EvolutionofQDtransitionsinthe”dressed”picture.Bottomright:
neverbeturnedoffcompletely.Inthisregard,themeasured Thedeterminedsidebandsplittingh¯Ωvs.squarerootoftheexcita-
g(2)(0)valuecanbeseenasameasureofthequalityofthe tionpowershowingalineardependence.Adaptedwithpermission
single-photonsource[128,129]. fromRef.[117].CopyrightedbytheAmericanPhysicalSociety.
populationversusexcitationpulsearea(so-calledRabios-
3.2. Resonance fluorescence
cillations [143,144]). In this way, the creation of single
Asmentionedabove,resonants-shellexcitationcircumvents photonscandrasticallybeincreasedbyapplyingpulseareas
severaldephasingprocesses,suchasthecreationofhigh- matchingthemaximumQDpopulation(π-pulses).
energy carriers or the interaction with phonons, leading IntheMollowtripletregime,mostofthelightisscat-
to a considerable increase of the coherence time of QDs teredincoherentlyowingtothesaturationoftheQDs.Re-
[131].However,themonochromaticpumpingofatwo-level ducingthestrengthofthedrivingfieldchangesthescattering
systematresonanceoffersmanymoreadvantagesincluding propertiesofQDs[123].Intheso-calledHeitlerregime(at
thecoherentgeneration[117,132–135],manipulation[134, verylowexcitationpowers)theQDbehaveslikeapassive
136–138]andcharacterization[139]oftheexcitonicstates. scatterer and incident photons are scattered almost fully
Ingeneral,thespectralandtemporalpropertiesofpho- coherently[141].Asaconsequence,thespectrumofcoher-
tonsscatteredbyatwo-levelsystemaredeterminedbythe entlyscatteredphotonsisonlydeterminedbythespectral
laserdetuningfromtheexcitonicresonance.Theelectric- characteristicsoftheexcitationsource[145].Inthisway,
dipoleinteractionisresponsibleforacouplingoftheexci- QDs linewidths as low as 0.03µeV have been observed
tonicstatestothedrivingfieldandturnsthetwolevelsof already.ThoseQDsareinthe”subnaturallinewidth”[146]
theexcitoninto”dressedstates”[140].Thedressed-state or”ultracoherence”regime[147].Theapplicationofpulsed
pictureallowsfourradiativetransitionsofwhichtwoarede- excitationschemesincombinationwiththeweakcoherent
generateandtwoarespectrallydisplacedbytheRabienergy scatteringregimesenablespureQDspectroscopyintheab-
E (seeFigure9topright).Thisresultsintheemergence sence of almost all dephasing mechanism and, with that,
Ω
ofthreeemissionlines,theso-calledMollowtriplet[141], facilitates the deterministic generation of single photons.
withthecentrallinehavingthehighestintensity(Figure9 However,thelowphotongenerationratesareadisadvan-
left).TheRabienergyscaleswiththeexcitationdensityof tage. At moderate excitation powers, coherent scattering
thedrivingfield(asshowninFigure9bottomright).This andtheMollowtripletcanalsocoexistwhentheresonantly
enablesadirectcontrolofthesidebandtransitions.Byin- drivendotisthermalizedwiththephononbath[148].
troducingasecondlaserbeaminresonancewithoneofthe Experimentally, the observation of resonance fluores-
sidebandtransitions(preferablythelowerenergysideband), cenceischallenging.Sophisticatedresonantelectricalinjec-
the Mollow triplet turns into a multitude of peaks under tionispossible[149]buttechnologicallyverychallenging.
suppressionofthemainpeak(duetodeconstructiveinterfer- Morecommonopticalpumpingschemessufferfromprob-
ence).InthesemultiplydressedQDstatesalsophenomena lemsrelatedtotheseparationoftheexcitonicemissionfrom
likethemulti-photonACStarkeffectcanbepresentthat thescatteredlaserlightrequiringelaboratedsampledesigns
havepreviouslyonlybeenobservedinatomicphysics[142]. oradvancedexcitationanddetectionschemes.Asimpleway
Whereas the above mentioned phenomena can be ob- ofperformingopticallypumpedresonancefluorescenceex-
servedbyusingcontinuouslaserirradiation,pulsedresonant perimentsistheuseofplanarwaveguides[132,150,151].
drivingofatwo-levelsystem(withultra-shortpulses)fur- Thelaserlightiscoupledtothewaveguidemodeexcitingthe
ther facilitates the external control of the QD population QDswhichemitperpendiculartothesampleplane.Another
as a consequence of the oscillatory behavior of the QD approachtothepumpsuppressionisthecross-polarization
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8 C.P.Dietrichetal.:GaAsintegratedquantumphotonics
pulsestemporallyseparatedbya2nsdelay[47].Avariable
mirrorabletocompensateforthedelaytimewasplacedat
oneofthebeamsplitteroutputs,afixedmirroratanother
output. In this way, five different scenarios were created
ofphotonsimpingingonthedetectorsofwhichonlyone
createsatemporaloverlapofbothphotonsshowingadip
inthecorrelationfunction.Sofar,two-photoninterference
couldbedemonstratedforverydifferentsystemsincluding
dissimilar(betweenaQDandaPoissonianlaser[160],a
parametric down-conversion source [161] or a frequency
comb [162]) and similar single photon sources (between
differentQDs)[137,163].Inmostcases,indistinguishabil-
ity has been demonstrated between QDs of two different
and spatially separate samples [48,125,126], but in the
perspectiveofquantumphotonicintegratedcircuitsitisof
specialimportancetodemonstratetwo-photoninterference
Figure10 (a)Second-ordercorrelationfunctiong(2)(τ)fortwo between single photon sources on the same semiconduc-
QDsonthesamechipseparatedby40µm.(b)Two-photoninter- torchip(Figure10).ThishasbeenachievedfortwoQDs
ferenceofthetwoQDsfrom(a).Thegreyline(IRF)in(a)displays on the same substrate with only 40µm distance between
theinstrumentresponsefunction.Adaptedwithpermissionfrom
them[156].Theexperimentaldifficultyhereistofindtwo
Ref.[156].CopyrightedbytheAmericanPhysicalSociety.
QDswithinthefieldofviewthathavealmostidenticalemis-
sion energies, linewidths and polarization. A much more
techniquethatrequiresahighextinctionratebetweenboth practicalapproachisthetuningoftheexcitonicQDtransi-
polarizations[134].Ingeneral,thedetectionofresonance tionsbychangingthepropertiesexternally,e.g.byapplying
fluorescence is always aggravated by scattering at imper- anelectricfield.Seesection4.3forareviewabouttuning
fections.Thiscircumstancebecomesevenmoredelicatein mechanisms.
photonicnanostructuressuchasridgewaveguides[152,153]
andphotoniccrystals[154,155].(Pulsed)resonancefluores-
cencehassofarnotbeenobservedinwaveguide-coupled 4. Purcell-enhanced single-photon emission
photoniccrystalcavities.
Intrinsicdephasingprocesses(e.g.phononscattering)and
extrinsicspectralfluctuations,relatedtovaryingchargeen-
vironment in the vicinity of the QD, typically limit the
3.3. Two-photon interference
coherencetimeofsingleQDstoT ≈100−200ps,while
2
thenaturalexcitonlifetimesarelimitedtoT >400ps.The
WhentwosinglephotonswiththesameFourier-transform 1
exploitationoftwo-photoninterferenceinphotonicquan-
limitedspectrum,temporalprofileandpolarizationfromtwo
tum information processing (QIP) requires the reduction
spatiallyseparatesourcespropagatewithalinearnetwork,
ofthelifetimesinordertoachieveT ≈2T .Thiscanbe
onecannotdistinguishwhichofthetwophotonsstemsfrom 2 1
achievedemployingcavityquantumelectrodynamiceffects
oneortheothersource,i.e.theyareindistinguishable[157].
innanophotonicstructuresthatallowtheprecisetailoring
Duetotheinterferenceoftheprobabilityamplitudes,two
oftheelectromagneticfieldsurroundingofthedot.Inthis
indistinguishablephotonsimpingingonthetwoinputsof
way, the rate of radiative recombination from the embed-
abalancedbeamsplitter(50:50)willalwaysexittogether
dedemittercanbecontrolledviathePurcelleffect[164]in
(so-calledphoton-bunching).Theexperimentaldemonstra-
e.g.a cavity. Theenhancementfactor ofthespontaneous
tion of photon-bunching was first achieved by Hong, Ou
emissionrateisherebydeterminedbythespatialandspec-
andMandelin1987[158]andisoneofthemainprerequi-
tralmatchingbetweenemitterandcavitymode,thequality
sitesforquantuminformationsciencebeingthebasisfor
factorQandthemodevolumeV ofthecavitymodeinthe
e.g.KLMquantumgates[15]andbosonsampling[6].This
photonicnanostructure[165].Inparticular,foraspectrally
so-calledtwo-photoninterferenceisusuallymeasuredusing
narrow source in resonance with a broader optical mode,
a Michelson interferometer consisting of a beam splitter,
thePurcell-enhancementisproportionaltotheQ/V ratio
twodistinctopticalpathsandtwosingle-photondetectors
(badcavityregime).Inordertoapproachanalmostperfect
atthetwooutputsofthesplitter(anequivalentconfigura-
cavity-emitterinterfacebyincreasingthelight-matterinter-
tionbasedonaMach-Zehnderinterferometercanalsobe
action,photonicnanostructuresneedtoprovideveryhigh
used).Atemporaldisplacementbetweenbothinputscanbe
qualityfactorsandlowmodevolumes.
introducedeitherbychangingthepositionofthebeamsplit-
ter[158]orbyintroducingavariabledelaylineintooneof
thephotonpaths[159]formakingthephotonsgraduallydis- 4.1. Cavities
tinguishable.ForsinglephotonsfromsemiconductorQDs,
two-photoninterferencewasfirstdemonstratedforphotons Typical examples of photonic nanostructures include mi-
from the same source by exciting the QD with two short crodisks,micropillars,nanobeams,photoniccrystalslabs
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9
Figure11 OverviewoverdifferentGaAs-basedcavitytypesprovidingthree-dimensionalphotonicconfinement:(a)microdisks[166],
(b)micropillars,(c)nanobeams[166],(d)PhCslabsand(e)three-dimensionalphotoniccrystals.TherespectiverecordopticalQ-factors
forGaAs-basedphotonicnanocavitiesembeddingQDsaregivenatthebottomofeachimagetogetherwithestimatedmodevolumes.
(b)AdaptedwithpermissionfromRef.[50].CopyrightedbytheAmericanPhysicalSociety.(d,e)AdaptedbypermissionfromMacmillan
PublishersLtd:Sci.Rep.[167],©2013,andNat.Photon.[168],©2011.
and3Dphotoniccrystals(seeFigure11foranoverview). latticewhereasthelatterismostcommonlypreferredasit
Allstructuresprovideaneffectivethree-dimensionalpho- providesalargerphotonicbandgap[172].
tonic confinement based on the possibility to manipulate PhC cavities are formed by displacing neighboring
andcontrollightpropagationbyintroducinginterfaceswith holes (H0 cavity [173]) or leaving out a single (H1 cav-
veryhighrefractiveindexcontrast.Obviously,thebestindex ity[174,175])orseveralairholes,therebyformingadefect
contrastforGaAs-baseddevicesisgivenfortheinterface inthephotoniccrystalbandgap.Intheprospectofsingle-
betweenGaAs(withn=3.5)andair(n=1). photonemission,L3cavities(threemissingholesinaline)
aremostpromisingastheysupportpolarizedsinglemodes
Inmicrodisks,lightisconfinedbytotalinternalreflec-
withawidespectralmargin[176].ThehighestQ-factors
tion(TIR)attheGaAs/airboundaryandpropagateswithin
forGaAsweresofarreportedforpassiveL3cavitiesina
the disk cross section in the vicinity of the disk rim. The
triangularlatticewithreducedholeradius[177]andshifted
so-calledwhispering-gallerymodespossessveryhighqual-
nextneighborpositions[178]withexperimentalvaluesup
ityfactorsofuptoQ=100,000[169]butsufferfromthe
to700,000[179,180](calculatedQ-valuesexceed1×106
relativelylargemodevolumes.EvenhigherQ-factorscan
for optimised L3 designs [181]). Active structures (with
be observed in micropillar resonators (Q can be as high
embedded QDs) show quality factors up to Q = 35,000
as250,000[170])whereBraggmirrors(alternatingpairs
(25,000) and mode volumesV/(λ/n)3 =0.9(0.4) for L3
of dielectric materials with high index contrast and λ/4-
(H1) cavities [182]. Note that the difference between Q-
thicknessforconstructiveinterference)belowandontop
valueswithandwithoutQDsmayberelatedtothedifferent
ofthecavityregionconfinephotonsinthepillareffectively.
wavelength range of operation (typically around 900nm
Depending on the pillar diameters mode volumes as low
withQDs,thereforeinthespectralregionofband-tailab-
as 2.3(λ/n)3 [171] can be achieved. However, while mi-
sorption in GaAs) or to residual non-resonant absorption
cropillarswithembeddedQDsareidealvertical-emitting
bytheQDs.Comparableresultshavebeenobtainedusing
single-photonsources,theydonotmatchtherequirements
one-dimensionalPhCsinnanobeams[166,183].
ofquantumphotonicintegratedcircuitsthatinvolvein-plane
Three-dimensional PhCs, for example based on the
photonroutingandprocessing.Inthisregard,photoniccrys-
woodpile structure [168] (see Figure 11), may, in princi-
tals slabs embody the perfect compromise by facilitating
ple,offerhigherqualityfactorsduetosuppressedleakage
highqualityfactors,lowmodevolumesandin-planecon-
intheverticaldirectionandadditionallyprovidebettercon-
trol.TheyarebasedonBraggscatteringinperiodicphotonic
trol of the QD spontaneous emission. However, they are
structures which are most commonly realized by drilling
technologicallymuchmorechallengingtofabricate.
airholesinalattice-geometryintoamembraneofsemicon-
ductormaterial.In-planeconfinementisthenachievedby
thephotonicbandgapintroducedbytheholesetchedinto 4.2 Photon collection and routing in waveguides
themembrane,whileout-of-planeconfinementfullyrelies
on total internal reflection at the membrane-air interface. Quantumphotonicintegratedcircuitsaretwo-dimensional
Photoniccrystalscanbefabricatedinsquareortriangular arrangementsofdifferentfunctionalitiesononesemicon-
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10 C.P.Dietrichetal.:GaAsintegratedquantumphotonics
Figure13 Left:BandstructureofaStark-tunabledeviceconsist-
ingofInAsQDsgrownwithinGaAsquantumwellsandAlGaAs
superlattices. Right: Field-dependence of two QDs (Dot1 and
DotA)aswellasthecavitymode.Reprintedwithpermissionfrom
MacmillanPublishersLtd:Nat.Photon.[48],©2010.
Figure12 Left:Calculatedbandstructure(insidefirstBrillouin
zone)forTE-modesofaninfinitePhCwaveguide.Theblacklines
indicate y-polarized modes, the gray lines indicate x-polarized 4.2. Tuning Quantum Dot and Cavity Mode
modes.Right:ScanningelectronmicroscopeimageofthePhC
waveguide.Thescalebarrepresents1µm.Reprintedwithper-
Inaperfectcavity-emitterinterface,bothQDtransitionand
missionfrom[25].©2011,AIPPublishingLLC.
cavitymodehavethesameenergyformaximumPurcellen-
hancement.However,inrealphotonicnanostructureswith
embedded QDs it is most likely that both resonances are
slightly detuned from each other as result of growth and
ductor chip that allow the generation, manipulation and processingimperfections.Thiscircumstancemakesexter-
detectionofsinglephotons.Thisrequiresefficientphoton nal tuning mechanisms indispensable. The simplest way
collectionfromsinglephotonsources,interconnectionsbe- of tuning the QD excitonic emission with respect to the
tweentheindividualfunctionalitiesaswellaslow-losstrans- cavity mode is by changing the sample temperature in a
portoflightwithinthecircuitfromthestationaryqubitto temperature-variablecryostat[23,51,189],bylaserirradi-
themanipulationanddetectionsites.Waveguides(suchas ationorbyimplementingheatpadsclosetothephotonic
PhCwaveguides[23,25–27,184]orridgewaveguides,see crystal[190,191].Allthesemechanismswillaffecttheelec-
Section 5) perfectly meet these requirements as they effi- tronicbandstructure,therefractiveindexofthedeviceand
ciently collect photons emitted by the QDs (even in the thelateralexpansionofthecavity.Thetwolatterchanges
absence of a cavity) and transport them via propagating onlyslightlyaffectthespectralpositionofthecavitymode,
modes.PhCwaveguideshavethehugeadvantageofatight whilethebandgapchangestronglytunestheQDenergy.Ex-
mode confinement paving the way for a high density of perimentallymorechallengingareotherpost-growthtuning
componentsononechip.Onthedownside,theysufferfrom mechanismssuchastheapplicationofexternalmagnetic
opticallossesandmechanicalinstabilities. fields[192]orstrain[193,194].Amoreintegratedapproach
is the implementation of electrical contacts into the pho-
One way of efficiently collecting photons in a single tonic nanostructures and shifting the QD transitions via
guidedmodeistheuseofaPhCwaveguide[185–187](e.g. Stark tuning by applying an electric field across the QD
”W1”waveguide,basedonamissingrowofholesinatri- layer[27,48,195–200].Additionalheterostructurebarriers
angularlatticeofholespatternedinasemiconductorslab). (seeFigure13)aroundtheQDsuppresscarriertunneling
TheradiativebandgapcreatedbythePhCsuppressesthe out of the dot enabling a tuning range of several tens of
emissionintoin-planemodesotherthantheintendedmode meV[48].
(seeFigure12),resultinginalarge(β =80−90%)sponta- Whereasasingleexcitoncaneasilybetunedintoreso-
neousemissioncouplingfactor(definedasthefractionof nancewithacavitymodeusingtheStarkeffect,moreelab-
spontaneousemissioncoupledtothedesiredmode).This oratedintegrationschemessuchastheinterferenceoftwo
istrueevenintheabsenceofastrongPurcelleffect.The indistinguishablesinglephotonsfromtwoQDsintwosepa-
β-factor can be even higher in case the QD is spectrally ratephotonicsurroundingsrequiretheabilitytocontrolboth
closetothebottomofthedispersioncurve.Thentheemis- theQDandcavityfrequenciesindependentfromeachother
sionintotheguidedmodeisenhancedduetoadecreased sothatdifferentQDandcavitylinescanbeallbroughtto
groupvelocity,furtherincreasingβ.Efficientfunnelingof resonance[201].Inthisregard,Starktuningonlyaffectsthe
the emission of single QDs into a PhC waveguide mode QDexcitonenergyanddoesnotshiftthecavityresonance.
hasbeenobservedexperimentallyforQDsemittinginthe TheseparatetuningofPhCcavityresonancesisachalleng-
900nm[26]rangebutalsoforthetelecommunicationrange ingtask,especiallyatthelowtemperaturesofinterest.Sev-
around 1300nm [27]. In this context, β-factors as high eralmethodsforcavitytuninghavebeenproposed,includ-
as 0.98 [24,35] and Purcell enhancements of up to F = ingtheuseofphotosensitivematerials[202],wet-chemical
p
2.7[188]werealreadyreported. etching [203], nano-oxidation techniques [204–207], the
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