Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid adiabatic passage

1.2 MB·

by  Timo Kaldewey

Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid
adiabatic passage
Timo Kaldewey,1 Sebastian Lu¨ker,2 Andreas V. Kuhlmann,1,3 Sascha R. Valentin,4 Arne
Ludwig,4 Andreas D. Wieck,4 Doris E. Reiter,2 Tilmann Kuhn,2 and Richard J. Warburton1
1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
2Institut fu¨r Festko¨rpertheorie, Universita¨t Mu¨nster,
7 Wilhelm-Klemm-Strasse 10, D-48149 Mu¨nster, Germany
1 3IBM Research-Zurich, S¨aumerstrasse 4, 8803 Ru¨schlikon, Switzerland
0 4Lehrstuhl fu¨r Angewandte Festko¨rperphysik, Ruhr-Universit¨at Bochum, D-44780 Bochum, Germany
2 (Dated: March 20, 2017)

r
A biexciton in a semiconductor quantum dot is a source of polarization-entangled photons with
a
M highpotentialforimplementationinscalablesystems. Severalapproachesfornon-resonant,resonant
and quasi-resonant biexciton preparation exist, but all have their own disadvantages, for instance
low fidelity, timing jitter, incoherence or sensitivity to experimental parameters. We demonstrate
6
1 a coherent and robust techniqueto generate a biexciton in an InGaAs quantum dot with a fidelity
close to one. The main concept is the application of rapid adiabatic passage to the ground state-
] exciton-biexciton system. We reinforce our experimental results with simulations which include a
l microscopic coupling to phonons.
l
a
h
- Entangled photon pairs are a powerful resource, es- preparation results in a timing jitter. In some cases,
s
e pecially for quantum teleportation and quantum key charge carrier relaxation times can reach values of up
m
distribution protocols. Spontaneous parametric down- to a nanosecond [23].
. conversion in non-linear optics is a source of entangled We presentherea coherenttechnique to createa biex-
t
a photon pairs [1], but success is not guaranteed – the citon with high probability, low jitter and weak depen-
m
emission is a probabilistic process – and the error rate dence on the excitation and system parameters. The
- is high. In contrast,semiconductor quantum dots (QDs) technique is based on rapid adiabatic passage (RAP).
d
n are bright, on-demand sources of both single photons [2] RAP allowsthe robustcreationof anexciton[24–26] via
o and entangled photon pairs and hence have enormous aprocessrequiringtwo-levels. RAPisappliedheretothe
c potential in quantum computing and quantum cryptog- groundstate-exciton-biexcitonsystem, 0 X0 2X0 ,
[ raphy [3]. a three-level system [12, 15], and allow| si−bi|exciit−o|n crei-

2 A biexciton in a QD is the starting point for a two ation without significant exciton creation. In the imple-
v photon cascade: when perfectly prepared, biexciton de- mentation here, we use the full bandwidth of ultra-short
1
cayleadstothesubsequentemissionoftwophotons,Fig. 130fs pulses allowing us to access spectrally both the
7
1(f). In a QD without a significant fine structure split- ground state-exciton and exciton-biexction transitions
3
1 ting (FSS), the two photons are polarization-entangled withinonelaserpulse. Thebroadbandwidthpulseshave
0 [4]. The majority of InGaAs QDs show a FSS due to the advantage over the narrow bandwidth pulses sug-
. a reduced symmetry [5–7]. However, sophisticated tech- gested in [12] of enhanced robustness owing to stronger
1
0 niques were developed to compensate for the FSS with avoided crossings and a decoupling of phonons even for
7 strain[8], electric [9] or magnetic fields [10, 11] and with negative chirped pulses. We describe this process theo-
1 special growth conditions [7]. retically and demonstrate excellent agreement with the
:
v Severalapproachesforbiexcitonpreparationhavebeen experimentalresults. Moreover,weanalyzetheinfluence
i proposed[12–15]anddemonstrated[4,16–20]. Resonant of phonons on the preparationprotocol. For RAP-based
X
two-photon schemes involving Rabi rotations [4, 17, 18] exciton creation, the influence of phonons depends sen-
r
a are sensitive to fluctuations in both laser power and QD sitively on the sign of the chirp [26–28]. We find also
optical frequency. They are likely to suffer from an im- in RAP-based biexciton creation that we can choose the
perfectbiexcitonpreparationresultinginundesiredexci- chirpsuchthatthephononsareunimportantatlowtem-
ton photons unrelated to the cascade process. perature.
A more robust scheme using phonon-assisted excita- We study self-assembled InGaAs QDs at a tempera-
tion wasreportedby severalgroupsrecently [18–22]. An ture of 4.2K. The QDs are grown by molecular beam
impressivelyhighbiexcitonoccupationofup to 95%was epitaxy and embedded in an n-i-p or n-i-Schottky struc-
demonstratedusingthisquasi-resonantscheme[20]. But ture, Fig. 1(a) (with more details in the supplementary
the strength here is also a weakness. The scheme relies information (SI) [29]). The bias voltage allows control
on the coupling to the phonon bath in the semiconduc- over the QD charge via Coulomb blockade; and within a
tor environment: it is an inherently incoherent process. charging plateau, control over the optical resonance fre-
Also, a dependence on relaxation processes in the state quency via the DC Stark shift, Fig. 1(d). The biexciton
2
(a) V top- (d) tointroducechirp[29]. Wecontrolpreciselythesignand
n-contact SIL g contact 937 1323 70k
n-dopectdusa DnpbupnB-appceceRionklr nlg-bact aatlotarcincrytiteeearrct InAs QD Wavelength (nm) 999933448901 X1+ 2XX00 1111333322112098Energy (meV) 2345600000kkkkkRFSignal (Hz) mracahbatiorigoupnnticttiuonhedeffiienstoceeiften-tnushtipets,ycuwhipseirsptrtoer[fe2e|t9αrc]|h.toe=Tdthhu0eep.7FS0tWIop[Hs∆229Mt]F.=oorf1t5mhpeosrpecuodlvseeetradiniulgs-
s X1-
super lattice 942 1316 10k The electronic structure in QDs is in generalcomplex.
wafer -0.75 -0.50 -0.25 0.00 0.25 0.50 For example in II-VI semiconductor colloidal QDs the
(b) 5M (e) Gate Voltage (V) electronicstructureofmultiexcitoncomplexeswasstud-
al (Hz) 34MM fmolidrrinogr lens blazed grating iHedow[3ev2e]ra,nidn stehveerIaIIl-VbiesxecmitiocnonsdtautcetsorwQerDesidsetnutdiifieeddh[3er3e].,
n
g
F Si 2M mirror 1 mirror 3 only the s-shells are populated such that the system can
1-XR 1M mirror 2 be describedby four states,namely the groundstate 0 ,
00.010.1 1 10 100 the two bright exciton states X0 and a single bi|exi-
ExcitationPower (nW) unpcuhlisrpeed cphuirlpseed citon 2X0 , Fig. 2(a). The p-s|heHll/sVaire energetically far
(c) (f)
400k Γ=1.96µeV remov|ed evien when using the full bandwidth of the ul-
al (Hz)300k 35pW 2X0 2X0photon trafast laser pulses. The energy of the biexciton state
RF Sign120000kk X0 Xem0pishsoiotonn |o2fXth0ieinse¯huωtr2aXl0e=xc2ith¯oωnXa0n−d∆∆B wthheerbeieh¯xωciXt0onisbtihnedienngeregny-
1-X -020 -10 0 10 20 0 emission ergy. TheseenergiesaredeterBminedexperimentallyfrom
Detuning (µeV) the emission spectrum. Considering only one linear po-
larization, H or V, and assuming that the laser pulses
FIG. 1. Resonance fluorescence (RF) on a single aremuchfasterthanthefinestructure-inducedquantum
quantum dot excited with a narrowband continuous beat, a three-level system with only one exciton state,
wavelaserandwithbroadbandlaserpulses. (a)Struc- X0 , is sufficient.
ture of the n-i-p diode with epitaxial gate. (b)-(c) RF with | i
narrowband excitation. (b) X1− RF signal versus excitation The exciton and biexciton state are coupled to lon-
power. (c) RF versus laser detuning at an excitation power gitudinal acoustic (LA) phonons in the pure dephasing
of 35pW (points). A Lorentzian fit (red solid line) deter- regime via the deformation potential [29]. We use stan-
mined the FWHM linewidth, 1.96µeV. (d) RF with broad-
dard GaAs parameters and take the excitation param-
bandpulsedexcitationasafunctionofgatevoltage. Thelaser
eters from the experiment leaving the QD size as the
polarization was linear, thechirp positive and thecenter fre-
quency resonant with the neutral exciton X0. (e) Scheme of only fitting parameter. This modelhas been successfully
afolded4f pulse-shapercontrollingthechirpintroducedinto used to describe the phonon influence on Rabi rotations
an ultra-short, transform-limited laser pulse. (f) Generation [34] and on the population inversion via RAP [12, 27].
of a biexciton with broadband, chirped excitation. Scheme For the occupations of the exciton and biexciton states
of the two-photon cascade (left) after chirped excitation of a as well as for the coherences between all involved states
QD (right).
a set of equations of motion is derived within a well-
established fourth-order correlation expansion method
[35]. The equations are then solved numerically.
bindingenergyis positiveandinthe orderofafew meV, The goal of our work is high fidelity biexciton genera-
a typical feature for InGaAs QDs. On driving the opti- tionusingRAP.Ideally,avanishingintermediateoccupa-
cal resonance with a narrowband continuous wave laser tion of the exciton is required. Less critical is a residual
and detecting the resonance fluorescence (RF), we find occupation of the ground state: this reduces only the
that QDs in both samples have linewidths below 2µeV, rate of entangled photon emission but not the entangle-
Fig. 1(c), close to the transform limit [30]. Above sat- ment. A figure of merit is the ratio of biexciton photons
uration on a QD in the n-i-p sample, Fig. 1(a), we de- toexcitonphotons. Theidealcaseisaratioofonewhere
tect a RF single photon count-rate of 5MHz, Fig. 1(b). every exciton photon is part of the two photon cascade
In the RAP experiments, we excite single QDs with the on biexciton decay, Fig. 1(f). In determining a biexciton
full bandwidth of 130fs pulses with a center wavelength creation fidelity we assume that biexciton and exciton
of around 940nm and linear polarization. The spec- photons arecreatedand detectedwith equalprobability.
tral full-width-at-half-maximum (FWHM) of the pulses This is likely to be a very good assumption. The biexci-
is ∆λ = 10nm. This allows us to address the exciton ton could in principle decay by an Auger process but in
andbiexcitonopticaltransitions(butnotthe transitions practicetheprobabilityofanAugerprocessisverysmall
involving higher shells in the QD) with just one laser (probability of 0.23% [36]); and a re-excitation process
pulse. The transform-limited pulses (repetition rate of duringthe cascadedecayisalsoveryunlikelyonaccount
76MHz)fromapassivelymode-lockedlaserweremanip- ofthehierarchyoftimes(thepulseduration(upto15ps)
ulatedinafolded4f pulse-shaper[31],Fig.1(e),inorder ismuchshorterthantheradiativelifetime(1ns)whichis
3
(a) (b) trate on positive chirp. Introducing a chirp of +0.34ps2
H V y(meV) 1005 EEE123 sthtreetecxhpeesritmheenpt,utlsheet2oX0aneminitsesinosnityrisFesWmHoMre solfow8lpys.witIhn
g
H V ner -5 pulse power than in the Rabi rotation experiment (red
E
-10-4 -2 0 2 4 curve in Fig. 2) but then reaches a very broad maxi-
(c) (d) Time(ps) mum. Both 2X0 and X0 signals reach a common max-
Excitation Power µW Excitation Power µW
imum where the signals correspond closely to the max-
0 2 4 6 8 0 2 4 6 8
z) imum achieved in the Rabi rotation experiment. These
H
al (k40 are the main signatures of RAP. In terms of 2X0 prepa-
gn20 ration, the ratio of 2X0 to X0 emission reaches the ideal
Si
F case of 100% with an error of 5%, proving that we can
R 0
(e) 1 (f) achieve a high fidelity biexciton preparation with RAP,
n
o robust against power and detuning fluctuations.
ati
up0.5 Wenowfocusontheresponseofthesystemtoanega-
Occ -0~.205ppss22 tivechirpof 0.25ps2(pulsedurationof6ps,bluecurves
0 +0.34ps2 in Fig. 2). I−n this case the 2X0 signal rises at smaller
0 2 4 6 0 2 4 6
(g) PulseAreaΘ(π) PulseAreaΘ(π) pulse areas than for positive chirp and in fact at even
delity 1 smmuamlleorfptuhlese2Xar0easisgnthaalnistchoenRsidaberiarboltyatleiosnsst.haTnhethmeasxigi--
Fi0.5
0X nal following a π Rabi pulse. The maximum X0 signal
2 0 is likewise reduced. The highest 2X0 to X0 ratio is 94%
0 2 4 6 8
Excitation Power µW decreasing rapidly at high pulse areas. A negative chirp
works less well at 2X0 creation than a positive chirp.
FIG. 2. Biexciton generation on QD1. (a) Energy level
However, at higher excitation powers the difference be-
scheme. (b) Instantaneous eigenenergies, the dressed states.
(c) 2X0 emission and (d) X0 emission as a function of the tween positive and negative chirp becomes less and less
pronounced.
time-averagedsquare-rootexcitationpowerfordifferentchirp
parameters. (e) and (f) Simulation of the biexciton occupa- An analysis of the calculatedinstantaneous eigenener-
tion and the sum of exciton and biexciton occupations as a gies,thedressedstatesFig.2(b),allowsaqualitativeun-
functionofthepulsearea. (g)Ratiooftheexperimentaldata: derstanding of the physics. Starting in the ground state
2X0/X0. 0 , the system evolves along the lower (red) branch for
| i
positive chirp. Providedthat the pulse area is above the
RAP threshold, the system remains in the lower branch
much shorter than the time separating successive pulses at the 0 and 2X0 avoided crossing such that the sys-
(13ns)). Therefore, we define here the fidelity as the ra- temend|siupin|thebiiexcitonstate 2X0 . Althoughthere
tioofdetectedphotonsfromthetransition(cid:12)2X0(cid:11) (cid:12)X0(cid:11) isnodirectcouplingbetweenthe 0| andi 2X0 states,the
(2X0 photon) and from the transition (cid:12)X(cid:12)0(cid:11) →0 (cid:12)(X0 avoided crossing arises as 0 and| i2X0 |haveia common
(cid:12) → | i | i | i
photons). coupling to the X0 state. Phonons can interrupt the
| i
Fig.2showsdatafromasingleQDinthen-i-Schottky adiabatic transferby causing a jump fromone branchto
device. The laser pulses are centered at the two-photon the other one [12]. For positive chirp, the system starts
biexciton resonance at 944.3nm. The 2X0 and X0 emis- in the lowest energy dressed state and only phonon ab-
sion intensities and their ratio are shown as a function sorption is possible. At 4.2K however, phonons at the
of the square-root of the excitation power in Fig. 2(c), relevant energy scale are frozen out and the probability
(d) and (g), respectively. For close-to-zero chirp (black for absorption is small. Hence the process with positive
curves in Fig. 2), Rabi rotations are observed. At the chirp is barely affected by phonons at low temperature.
first maximum, the X0 and 2X0 emission intensities are Conversely, for negative chirp the system starts out in
equaltowithinanerrorof5%,thenbothcurvesgodown theupper-mostbranch(bluecurveinFig.2(b)withtime
nearly to zero. At the second maximum, the 2X0 emis- runningfrom“right”to“left”);thesystemcannowjump
sion reduces to 75% of the 2X0 emission. For higher ex- tolowerbranchesbyphononemission,aprocesswhichis
citationpower,weobservemainlyX0 emissionwithlittle possibleevenatlowtemperature. This leadsto asignifi-
emission from the 2X0. At the first maximum it is clear cant probability of exciton and ground state population,
that ultrafast pulses with close-to-zerochirp enable high reducing the fidelity of the RAP process. All these ob-
fidelity preparation of the biexciton by a Rabi rotation. servations correspond well to the experimental data.
However,this π-pulse excitationis verysensitive to vari- The theory provides a quantitative account of three-
ations in the detuning or excitation power. We turn to level RAP in the presence of phonon coupling. We cal-
RAP which potentially offers a more robust scheme. culate the 2X0 and X0 occupations as a function of the
To create the biexciton using RAP, we first concen- pulse area: the 2X0 signalis proportionalto the 2X0 oc-
4
cupation; the X0 signalis proportionalto the sumof the (a) (b)
Excitation Power µW Excitation Power µW
2X0 andX0 occupations. The simulationresultsare also 0 2 4 6 8 10 0 2 4 6 8 10
shown in Fig. 2 and reproduce the main features of the z)150
H
eoxfptehreimReanbtialodscaitlalaetxiotnresmfoerlycwloeslel,-tnoo-tzaebrolycthhierpex(aactbfrooramd nal (k100
g
mmainxiimmuummaattpu1ls.5eπairneath∼eX3π0siingntahle);2tXhe0“sdigenlaayl,eda”b(r“oaacd- RF Si 50
celerated”) ri∼se of the 2X0 signal for positive (negative) 0
(c) (d)
1.0
chirp; the relative signal strengths; and the better RAP
performance for positive chirp. In the theory, the Rabi +0.7 ps²
rotations are not influenced significantly by phonons be- ation0.5 +0.00.0323 ppss²²
cause the Rabi dynamics are too fast for the phonons up -0.31 ps²
to follow. The theoretical results show clearly that 2X0 Occ -0.66 ps²
generation with RAP is strongly (weakly) influenced by
0.0
0 2 4 6 8 10 0 2 4 6 8 10
phonons for negative (positive) chirp for small to mod-
PulseAreaΘ(π) PulseAreaΘ(π)
(e)
est pulse areas. At the highest pulse areas,however, the 1.0
theory predicts essentially perfect RAP independent of
y
thesignofthechirp. Theinterpretationisthatthesplit- elit
tings between the branches at the avoided crossings are Fid0.5
energetically so large that they lie well above the energy 0X
2
rangeofthe phonons whichareefficiently coupledto the
0.0
exciton system [34]. In other words, the wavelength of 0 2 4 6 8 10
the phonons required for scattering between the dressed Excitation Power µW
states becomes much smaller than the size of the QD at
FIG. 3. Biexciton generation on QD2. (a) 2X0 emis-
high pulse area. There is evidence that this reduction
sion and (b) X0 emission as a function of the time-averaged
of the phonon efficiency is also seen in the experiment:
square-root excitation power for different chirp parameters.
theRAPsignalsforpositiveandnegativechirpapproach
(c) and (d) Simulation of the biexciton occupation and the
each other at the largest pulse areas. However, in ad- sumofexcitonandbiexcitonoccupationsasafunctionofthe
dition the experimental signals exhibit a decay at high pulsearea. (e) Ratio of the experimental data: 2X0/X0.
pulse areas which cannot be explained by the phonon
coupling model. Instead, we tentatively attribute this
decay to an occupation of higher energy levels by multi- feature of the experimental data in Fig. 3(a).
photon absorption [37]. Inconclusion,wehavedemonstratedthecoherentgen-
eration of a biexciton in a semiconductor quantum dot
Tostress-testbiexcitongenerationwithRAP,weprobe using a single chirped laser pulse. The state preparation
a second QD with much larger biexciton binding energy. has a very high fidelity over a broad range of excitation
RAPismoredifficultinthiscase: thepulsearearequired powers. The sign of the chirp is important: the scheme
forefficient2X0generationincreases,potentiallyentering is robust with respect to phonon scattering at low tem-
theregimeinwhichtheadditionaldecayprocessisactive. perature for positive chirp. A negative chirp results in
The secondQD,embeddedin the n-i-psample Fig.1(a), damping due to phonon scattering. Theoretical calcula-
with biexciton resonance at wavelength 938.2nm, has a tions including a microscopiccouplingto phonons repro-
biexciton binding energy of 3.4meV (the first QD has a duce allthe experimentalfeaturesapartfromadamping
binding energy of 1.5meV). The 2X0 emission intensity in the experiment at high pulse areas.
of the RAP experiment is shown in Fig. 3. Despite the We acknowledge financial support from EU FP7 ITN
largebiexcitonbindingenergy,theratioofthe2X0 toX0 S3NANO,NCCRQSITandSNFproject200020 156637.
signals reaches 90%, Fig. 3(e). The general behavior is AL and ADW acknowledge gratefully support from
thesameasforthefirstQD:aRabirotation-likebehavior DFH/UFA CDFA05-06, DFG TRR160 and BMBF
for minimal chirp and a distinct difference between pos- Q.com-H 16KIS0109.
itive and negative chirp. Again, apart from the decay at
high pulse areas, the theory accounts extremely well for
theexperimentaldata. Notably,wefindthatforstronger
negative chirp values, the phonons also become more ef-
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Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid
adiabatic passage: Supplementary Information
Timo Kaldewey,1 Sebastian Lu¨ker,2 Andreas V. Kuhlmann,1,3 Sascha R. Valentin,4 Arne
Ludwig,4 Andreas D. Wieck,4 Doris E. Reiter,2 Tilmann Kuhn,2 and Richard J. Warburton1
1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
2Institut fu¨r Festko¨rpertheorie, Universita¨t Mu¨nster,
7 Wilhelm-Klemm-Strasse 10, D-48149 Mu¨nster, Germany
1 3IBM Research-Zurich, S¨aumerstrasse 4, CH-8803 Ru¨schlikon, Switzerland
0 4Lehrstuhl fu¨r Angewandte Festko¨rperphysik, Ruhr-Universit¨at Bochum, D-44780 Bochum, Germany
2 (Dated: March 20, 2017)

r
a
M
EXPERIMENTAL METHODS Back-reflected laser light is suppressed with a dark-field
technique leading to an extinction ratio of 107:1 [6, 7].
6
1 The quantum dot samples Typical X1− spectra at low excitation power from sin-
gle QDs in the two samples are depicted in Fig. S1(c)

] and (d). The linewidths are very similar, around 2µeV,
l We studied in this work self-assembled InGaAs quan-
l approximately 2.5 times larger than the transform limit
a tumdots(QD)intwodifferentheterostructures. Inboth
h [6]. A signal:background ratio of more than 1,000:1 is
cases the QDs are embedded in a GaAs diode grown by
- achieved with linearly polarized excitation. A more dis-
s molecular beam epitaxy. One diode is an n-i-Schottky
e structure [1, 2], the other an n-i-p structure [3], Fig. tinct difference between QDs in the two devices appears
m in the saturation behavior, Fig. S1(e) and (f): we de-
S1(a) and (b), respectively. The n-i-Schottky diode uses
t. an n-doped back-contact and a semi-transparent metal- tected single photons with a count-rate of 5MHz from
a then-i-psample,about10timesmorethanfromthe n-i-
lic top-contact (Ti/Au 3 nm/7 nm). The n-i-p sample
m
Schottky sample. The high photon extraction efficiency
on the other hand has an epitaxial top gate made from
- of the n-i-p device, around 10%, results from two im-
carbon-dopedGaAs. Inaddition,then-i-pdiodefeatures
d
provementsin the sample design as discussedabove: the
n adistributedBraggreflector(DBR).Thelayerstructures
n-i-ptypefeaturesaDBRandalsoatransparentepitax-
o are given in Table S1 and Table S2 for the n-i-Schottky
c and n-i-p diode, respectively. In the n-i-p diode, the fi- ial gate.
[
nallayer,44nmundopedGaAs,placesthep-dopedlayer

2 around a node-position of the standing electromagnetic
v wave in the n-i-p diode. Resonance fluorescence with pulsed excitation
1
In the experiment, the n- and p-doped layers are con-
7
tacted independently. Selective etching of the capping
3 With pulsed excitation, we use the full spectrum of
1 allows the buried p-layer to be contacted. Access to the 130fs transform-limited “ultra-fast” pulses, again excit-
0 n-layer is provided by wet etching of a mesa structure.
ing the QD resonantly. The spectral full-width-at-half-
1. In both devices the n-contact is grounded and a gate maximum (FWHM) of the pulse is ∆λ = 10nm. With
0 voltage Vg is applied to the top gate. The gate voltage thisbandwidthweaddressthegroundstatetransitionfor
7 allows control over the QD charge via Coulomb block-
the particular charge state set by the gate voltage (but
1
ade and excitonic resonances can be shifted by the DC
:
v Starkeffect[1,4,5]. Theperformanceofsinglequantum
i dots(QDs)inbothdiodestructuresisquitesimilar. The
X Function Material Thickness
main advantage of the n-i-p diode over the n-i-Schottky wafer GaAs
r
a device is a strongly enhanced photon extraction. This is buffer GaAs 50nm
achieved on the one hand by the DBR and on the other superlattice, 30 periods AlAs,GaAs 120nm
hand by the low-loss epitaxial gate. spacer GaAs 50nm
electron reservoir (back contact) GaAs:Si 50nm
tunnelbarrier GaAs 25nm
InGaAs QDs InAs ∼1.6 ML
Resonance fluorescence with continuous wave
capping layer GaAs 150nm
excitation
blocking barrier, 68 periods AlAs,GaAs 272nm
capping layer GaAs 10nm
In resonance fluorescence (RF) spectroscopy we inves-
tigated the quantum dot characteristics with a narrow TABLES1. Layersoftheheterostructure,n-i-Schottkydiode.
band (linewidth in sub pm range) excitation laser. The Thequantumdots(QD)areformed bydepositing 1.6 mono-
layer (ML) of InAs.
scattering induced by resonant excitation is detected.
2
Function Material Thickness (a) n-i-Schottkytop- (b) n-i-p p-contact
contact
wafer GaAs V V
g g
buffer GaAs 50nm back-contact SIL n-contact SIL
top contact p-contact
superlattice, 18 periods GaAs, AlAs a 2nm 72nm
superlattice superlattice
DBR,16 periods GaAs, AlAs 2400nm
capping layer capping layer
spacer GaAs 57.3nm
tunnel barrier tunnel barrier
electron reservoir (back contact) GaAs:Si 50nm
n-doped back-contact In n-doped back-contact
tunnelbarrier GaAs 30nm A
InGaAsQDs InAs ∼1.6 ML superlattice s Q
cappinglayer GaAs 153nm D DBR
s
blocking barrier, 46 periods AlAs, GaAs 184nm
p-dopedtop contact GaAs:C 30.5nm wafer superlattice
undopedspacer GaAs 1nm wafer
etch stop AlAs 2nm (c) (d)
25 X
cappinglayer GaAs 44nm z) Γ=1.83µeV Γ=1.96µeV 4R1-
H 20 F
TABLE S2. Layersof theheterostructure, n-i-pdiode. al (k 15 71pW 35pW 3 Sig
n n
g 2 a
not higher energy transitions). The RF response of the RF Si 105 1 l (100
QD is detected with a grating spectrometer. 1-X kH
A scheme of the complete set-up is shown in Fig. S2. 0 0 z
-20 -10 0 10 20-20 -10 0 10 20 )
The ultra-fast pulses from a mode-locked femtosecond
Detuning (µeV) Detuning (µeV)
laserareexpandedandsentintoacompactpulse-shaper. (e) (f)
5
Thepulse-shaperretainsallthespectralcomponentsand Z)0.5 X
controls the amount of chirp as described below. From MH0.4 4R1-
hizearteiotnheopptuiclsseasnpdasasrethtrhoeunghcopuopwleedricnotnotraolsianngdlepmooladre- nal (0.3 3 F Sig
g n
optical fiber. The fiber transports the pulses to a confo- Si0.2 2 a
cal microscope. In the microscope, the excitation pulses RF 0.1 1 l (MH
pass through a linear polarizer, two beam-splitters and 1-X 0 0 z)
are sent to the objective at cryogenic temperature (4.2 0.01 0.1 1 10 100 0.01 0.1 1 10 100
K). The objective, an aspherical lens with a numerical
Excitation Power (nW) ExcitationPower (nW)
aperture of 0.68, focuses the light onto the sample. The
sample is held on a stack of piezo-steppers which allows
aparticularQDtobe placedwithin the focalspotofthe FIG. S1. Resonance fluorescence (RF) spectroscopy
on a quantum dot (QD) with narrowband continu-
microscope. This process is aided by the in situ diag-
ous wave excitation. (a) n-i-Schottky,and (b) n-i-p layer
nostics provided by a camera image of the focus. Light
structure. (c)-(f) Comparison of the RF performance with
scatteredbytheQDiscollectedandcoupledintothede-
narrowbandcontinuouswaveexcitation ofasingleQDinthe
tection fiber. The back-reflectedlaser lightis suppressed n-i-Schottky(left)andn-i-pstructure(right). (c)-(d)Exam-
by a second linear polarizer whose axis is orthogonal to plespectrashowingtheRFsignalasfunctionoflaserdetuning
the axis of the polarizer in the excitation stage. The RF atanexcitationpowerof71pW(c),35pW(d). ALorentzian
signalisdetecteddirectlywithaSPAD(continuouswave fit (red solid line) to the black data points shows a FWHM
of 1.83µeV (c), 1.96µeV (d). The linewidths are similar in
excitation) or with a spectrometer-CCD camera (pulsed
both devices. (e)-(f) RF signal as a function of excitation
excitation).
power for the n-i-Schottky device (e), and n-i-p device (f).
Detecting RF with pulsed excitation also depends on
Thesaturationcountrateisafactoroftenhigherinthen-i-p
suppressingthereflectedlaserlightwiththepolarization- sample.
based dark-fieldtechnique. However,owing to the wave-
length dependence of the polarization optics, the laser
suppression of a broadband pulsed laser is less effective the laser background spectrum. The resulting residual
than with the narrowband continuous wave laser: we laserbackgroundisshowninFig.S3(b)inred. Thespec-
reach an extinction ratio of typically 105:1 with broad- tralshape isexplainedbytheGaussianspectralshapeof
band excitation. We use in addition the spectral mis- the excitation laser along with the quadratic function of
matchbetweenthe broadbandlaserandthe narrowband laser suppression: the laser suppression is most effective
RF to increase the extinction ratio, Fig. S3. The laser at its alignment wavelength and then decays quadrati-
backgroundfalling on the CCD camera does not depend callyinwavelengthsuperimposedbyinterferencefringes.
on the gate voltage,Fig. S3(a), suchthat we canuse the A typical spectrum measured at V = 12mV is shown
g
−
gatevoltagedependenceoftheQDemissiontoconstruct inblack. Sharpemissionpeaksfromtheexcitonandbiex-
3
(a) Wavelength (nm)
excitation 948 946 944 942 940 938 936 934 932 930
fibre
-1.4
output
LP M -1.2
M
PPC
-1.0
CAM detection input M e (V) -0.8
LP M λ/2 FM filter Voltag --00..64
ND e
L at -0.2
G
autocorrelator 0.0
&
FROG 0.2
pulse 0.4
(b)
X shaper 80k
Y z) 40k
H
Z M M s ( 0
M unt 80k
o
Croystat S λ/2 L PH L C 40k
4.2 K M M beamL PH L M 0
948 946 944 942 940 938 936 934 932 930
expander
Wavelength (nm)
SPAD/ pump femtosecond
spectrometer laser laser M
FIG.S3. Laserbackgroundsubtractionresonanceflu-
orescence spectroscopy using broadband, pulsed ex-
FIG. S2. Scheme of the complete set-up. Ultra-short citation. (a) The RF signal as a function of gate voltage
pulses were manipulated in a pulse-shaper, coupled into a withoutbackgroundsubtractionmeasuredwithanexcitation
single mode glass fiber and sent to a confocal microscope power of ∼8µW corresponding to a pulse area of around 3
mounted on a bath cryostat. The pulses were characterized π. (b) One spectrum from (a) at a gate voltage of −0.012V
withacombinationofautocorrelator andfrequency-resolved- is shown as black curve in the upper panel. Distinct peaks
gating(FROG).Thesampleisheldatatemperatureof4.2K from the exciton and trion are visible together with a broad
in the bath cryostat on an xyz-positioner. A mini spectrom- laser background. The reconstructed laser background (from
eter (MS) measures thespectral profile of thepulses. allspectrain(a))isshowninred. Thebluecurveinthelower
panelshowsthedifferenceoftheblackandtheredcurve,the
resulting signal after background subtraction.
citon appear on top of the laser background. The signal
after background subtraction is shown in the lower plot
in blue. Before background subtraction, the maximum
signal to background ratio in a narrow spectral window
around the emission line is 22:1.
chirpiszero,alarger(smaller)distanceleadstonegative
Pulse shaping: introducing chirp
(positive)chirp. Thetemporaldurationofthe pulsesex-
iting the laser is 130fs (intensity FWHM); the temporal
Chirp is introduced into the transform-limited laser
durationcanbe stretchedup to 15ps correspondingto a
pulses by a compact, folded 4f pulse-shaper [8, 9]. The chirp in the range from 0.7ps2 to 0.7ps2.
scheme is depicted in the main paper in Fig. 1. The −
unchirpedpulse is diffractedby a highresolution,blazed
grating(1800groovespermm)andthenfocusedbyalens
ontoamirrorpositionedinthefocalplane. Fromherethe We characterized the chirp with a combination of a
lighttravelsbackunderasmallanglewithrespecttothe FROG and autocorrelator. This allows us to reveal the
diffraction plane allowing a spatial separation of incom- presenceofanyhigh-orderphasetermsandpreventthem
ing and outgoing pulses. The distance between grating byanoptimaladjustmentofthepulse-shaper. Thechirp
and lens controls the chirp [8]. The lens and the mir- ismeasuredbothinthefreespacemodeandalsoafterthe
ror are mounted on a translation platform. Moving the optical single mode fiber in order to determine the sign
platform with respect to the grating changes the chirp: of the chirp and to compensate for the chirp introduced
if the distance matches the focal length of the lens the by the fiber itself.
4
THEORETICAL MODEL Parameter Value
density ρ 5370kg/m3
Hamiltonian sound velocity cLA 5.1nm/ps
electron deformation potential constant De 7 eV
hole deformation potential constant Dh −3.5 eV
The Hamiltonian is composed of four parts
TABLE S3. Parameters used in the calculations.
H =H +H +H +H ,
c c-l ph c-ph
with H denoting the electronic structure, H the
c c-l The corresponding matrix elements for deformation
carrier-light coupling, H the free phonons and H
ph c-ph potential coupling to electrons and holes are
the carrier-phononcoupling.
We consider a three-level system consisting of the q
ge/h = D Fe/h,
ground state |0i, the single exciton state |X0i and the q r2Vρ¯hcLA e/h q
biexciton state 2X0 yielding the Hamiltonian for the
| i with V the normalization volume, ρ the mass density of
electronic system
thecrystal,andD the deformationpotentialcoupling
e/h
Hc =¯hωX0 X0 X0 +¯hω2X0 2X0 2X0 . constants for electrons/holes. We take GaAs parameters
| ih | | ih |
as listed in Table S3. The exciton coupling matrix el-
Here, ¯hωX0 is the energy of the neutral exciton and ement is obtained from the electron and hole coupling
¯hcoωu2nXt0in=gf2oh¯rωtXhe0 b−ie∆xcBitoisntbhiendeinnegrgeyneorfgyth∆eBb;ietxhceitgornouancd- maTtrhiexinelfleumeennctesobfythgeqQ=Dggqee−omgqeht.ryisdescribedinterms
state energy has been set to zero. For the binding en- oftheformfactorFe/h. WeassumeasphericalQDmod-
q
ergy we take the experimentally determined values (cor-
eled by a harmonic confinement potential yielding the
rectedforthe polaronshift) ∆ =1.4meV forQD1 and
B form factors
∆ =3.2 meV for QD2.
B
We model the carrier-light interaction in the usual Fe/h =exp q2a2 /4 ,
dipole and rotating wave approximation resulting in the q (cid:16)− e/h (cid:17)
following Hamiltonian for the three-level system: wherea arethe electron/holelocalizationlengths. To
e/h
fit the experimental data we used a = 5 nm and a =
1 e h
H = ¯hΩ(t) X0 0 + 2X0 X0 +h.c., 2 nm. We note that similar values have been used in the
c-l
2 | ih | | ih |
(cid:0) (cid:1) theoreticalmodelingofphonon-assistedstatepreparation
h.c. denoting the Hermitian conjugate. Here the instan- schemes [11].
taneous Rabi frequency Ω(t) with ¯hΩ(t) = 2M E(t) For the theoretical modeling of the light-induced dy-
·
enters,givenby the positive frequency component ofthe namics we use the density matrix formalism. The in-
electric field E(t) and the dipole matrix element M. finite hierarchy of phonon-assisted variables appearing
For the carrier-phononinteraction, we account for the in the equations of motion is truncated using a fourth-
deformation potential coupling to longitudinal acoustic order correlationexpansion. It has been shown that this
(LA) phonons which has been shown to be the main method gives very reliable results in a two-level system
source of decoherence in most typical QDs [10]. The [10, 12, 13]. Here we have extended this approach to
Hamiltonian of the free phonons is given by the three-level model. This extension is straightforward,
howeverthenumericalcomplexityincreasesconsiderably.
Hph =h¯ ωqb†qbq, Based on this formalism, we calculate the occupations
Xq of the biexciton 2X0 2X0 and the neutral exciton
| ih |
X0 X0 states.(cid:10)Note that a(cid:11)lso all coherences between
with the creation (annihilation) operators b†q (bq) of a t(cid:10)h|eseihstat|e(cid:11)saswellasone-andtwo-phononassistedden-
phonon with wave vector q and frequency ω = c q,
q LA| | sity matrices are fully included in the calculation.
c being the longitudinal sound velocity.
LA
The carrier-phonon interaction is described by the
standardpure-dephasingHamiltonian. Assumingforthe
Chirped laser pulses
biexciton wave function a product of exciton wave func-
tions, the Hamiltonian reads
To model the optical excitation, we consider an elec-
H =¯h n ν ν g b +g∗b† , tric field which describes a linearly chirped Gaussian
c-ph ν| ih | q q q q laser pulse. Such a chirped pulse is generated from a
Xq,ν (cid:0) (cid:1)
transform-limited Gaussian laser pulse of the form
where the factor n counts the number of the excitons
ν Θ t2
w0h,icnhνa=re1pfroersenνt =in tXh0e ,staantde |nννi,=i.e2.,fonrνν= =0 fo2rX|0νi.= Ω0(t)= √2πτ0 exp(cid:18)2τ02(cid:19)exp(−iωLt)
| i | i | i | i | i
5
with pulse duration τ0, central laser frequency ωL, and [3] J. H. Prechtel, A. V. Kuhlmann, J. Houel, A. Ludwig,
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Ω(t)= exp exp iω t at2 . Warburton, Phys.Rev.B 77, 245311 (2008).
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