Researc h Article V ol. 10, No . 1 / 1 January 2020 / Optical Materials Express 76
Deterministicall y fabricated spectrall y-tunab le
quantum dot based single-photon sour ce
M A R C O S CHMIDT , M AR TIN V . H EL VERSEN , S A R A H F I S C H B A C H ,
A R S E N T Y K A GANSKIY , R ONNY S CHMIDT , A NDREI S C H L I W A , T OBIAS
H EINDEL , S V E N R ODT , A N D S T E P H A N R EITZENSTEIN *
Institut für F estkörper phy sik , T ec hnisc he U niv ersität Ber lin, Har denbergstr aße 36, 10623 Berlin, Germany
* st ephan.r eitzenstein@phy sik .tu-berlin.de
Abstract:
Spectrall y-tunable q uantum light sources are ke y elements f or the realization of
long-distance q uantum communication. A deter minis ticall y fabricated single-photon source with
a photon e xtraction efficiency of
η =
(20
±
2) %, a maximum tuning rang e of
∆
E
=
2.5 me V and
a minimum g
( 2 )
(
τ =
0)
=
0.03
±
0.02 is presented. The de vice consists of a single pre-selected
quantum dot (QD) monolithicall y integrated into a microlens that is bonded onto a piezoelectr ic
actuator via gold ther mocompression bonding. Here, a thin gold la y er simultaneously pro vides
strain transf er and acts as a backside mirror f or the QD-microlens to maximize the photon
e xtraction efficiency . The QD-microlens structure is patter ned via 3D in-situ electron-beam
lithograph y (EBL), which allo ws us to pre-select and integrate suitable QDs based on their
emission intensity and energy with a spectral accuracy of 1 me V f or the final device. T ogether
with strain fine-tuning, this enables the scalable realization of single-photon sources with identical
emission energy . Moreo v er , w e sho w that the emission ener gy of the source can be stabilized to
µ
e V accuracy b y closed-loop optical f eedback. Thus, the combination of deterministic f abr ication,
spectral-tunability and high broadband photon-e xtraction efficiency makes the QD-microlens
single-photon source an interesting building bloc k f or the realization of quantum communication
netw orks.
© 2019 Optical Society of America under the ter ms of the OSA Open Access Publishing Agreement
1. Intr oduction
Quantum communication protocols promise secure data transmission based on single-photon
technology [ 1 – 3 ]. In this conte xt, implementations of long-distance quantum k e y distribution
require Bell-s tate measurements in quantum repeaters [ 4 ] to transf er quantum states betw een
different nodes of a communication netw ork. T w o recent e xper iments, which demons trate
entanglement sw apping of entangled photon pairs consecutiv el y emitted by the same emitter ,
impressiv el y underline the high potential of semiconductor QDs in this reg ard [ 5 , 6 ]. Be y ond such
proof-of-pr inciple e xper iments and to enable larg e-scale quantum repeater netw orks, sources
emitting at the same energy , on the order of the homogeneous line width of the emitters, are
required in eac h node of the netw ork.
Semiconductor QDs are promising candidates f or such applications, as the y emit photons with
simultaneousl y close-to-ideal indistinguishability , entanglement fidelity and e xtraction efficiency
when integrated into suitable photonic structures like circular Bragg gratings in a h ybr id device
design [ 7 , 8 ]. Ho w e v er , one has to note that the self-assembled S transki-Krastano v gro wth mode,
which is typicall y used to realize high-quality InGaAs QDs, leads to randomly dis tr ibuted emitters
with v ar ying shape and size, resulting in an emission band with inhomogeneous broadening
of typicall y 10-50 me V . N ote w or th y , v alues of only a f e w me V ha v e been realized f or QDs
gro wn on in v er ted p yramids [ 9 ], which, ho w ev er , is still three orders of magnitude lar ger than
the homog enous linewidth of the QDs. Theref ore, post-gro wth processing is required to meet
the demands of adv anced photonic quantum technology . W ith respect to the requirement of
#379476 https://doi.org/10.1364/OME.10.000076
Jour nal © 2020 Receiv ed 8 Oct 2019; re vised 14 Nov 2019; accepted 14 No v 2019; published 10 Dec 2019

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 77
realizing spectrall y precisely matc hed single-photon sources, deter ministic in-situ optical and
electron beam lithograph y techniq ues [ 10 , 11 ] allo w one to pre-select and integrate br ight emitters
within the QD ensemble with a spectral accuracy of better than 1 me V . In combination with
spectral fine-tuning, that is k e y to achie v e spectral resonance of multiple single-photon sources
within the QD’s homog eneous linewidth of about 1-2
µ
e V , which has high potential to enable
entanglement sw apping between remote sources in lar ge-scale q uantum repeater netw orks in
the future. Moreo v er , the precise tunability of single-photon sources is also beneficial f or the
coupling of single-photon emitters to other k e y components of advanced q uantum netw orks,
namel y quantum memor ies, realized e.g. b y atomic v apors [ 12 ], trapped atoms [ 13 ] or solid state
quantum memories [ 14 ].
V ar ious methods ha v e been applied to achie v e spectral control of the QD emission characteris-
tics, often accompanied with dra wbacks: T emperature tuning [ 15 ], f or instance, suffers from
increased phonon-contr ibutions finall y limiting the photon indistinguishability already abo v e
10-15 K [ 16 ]. Electr ic fields can be applied to influence the QD emission via the quantum-
confined S tark effect [ 17 , 18 ]. This scheme, ho we v er , requires comple x doping and electr ical
contacts which complicates the de vice processing. S train-tuning pro v ed to be an e x cellent
alter nativ e, which can be implemented b y integration of the emitter onto a piezoelectr ic mater ial
such as Pb(Mg
1 / 3
Nb
2 / 3
)O
3
-PbT iO
3
(PMN-PT) [ 19 , 20 ]. In addition to the spectral-tunability ,
strain-tuning can be used to control the e x citon binding energies and the fine s tr ucture splitting of
QD states, whic h enables the generation of polarization-entangled photon pairs [ 21 ]. In vie w of
applications of single-photon sources in secure quantum communication scenarios, high photon
e xtraction and collection efficiencies are desirable to achie v e high data transmission rates. So
f ar , only f e w attempts ha v e been made to increase the efficiency of strain-tunable single-photon
sources. In one e xample an e xtraction efficiency of 57% into a numer ical aper ture of 0.8 has
been achie v ed using strain-tunable nano wire antennas [ 22 ].
In this w ork, w e present a br ight spectrall y -tunable single-photon source based on a deter minis-
ticall y fabricated QD microlens combined with a piezoelectr ic actuator b y a flip-chip goldbonding
techniq ue. The applied in-situ EBL techniq ue has the impor tant advantag e that suitable QDs can
be pre-selected b y their emission intensity and emission energy with a spectral accuracy better
than 1 me V bef ore integrating them into photonic nanostructures. Moreo v er , with a positioning
accuracy of about 30-40 nm [ 23 ], broadband enhancement of the photon-e xtraction efficiency is
achie v ed. The mentioned uncer tainty in emission energy of appro ximatel y 1 me V is attributed to
different char ge configurations after integration of the QD into a photonic micros tr ucture with
etched surf aces [ 24 ]. W e sho w that piezo strain-tuning can compensate this spectral uncer tainty
and, thus, promises a scalable route to wards lar ge scale q uantum netw orks based on entanglement
distribution betw een quantum light sources with identical emission energy .
2. Device design and fabrication
The f abr ication of our device in v olv es three main processing steps: Firs t a semiconductor
heterostructure is gro wn b y metal-org anic chemical v apor deposition. Subsequentl y , a flip-chip
gold ther mocompression bonding process is applied, whic h results in a thin GaAs membrane
including the QDs attached to the piezoelectric actuator . In a final step, single QDs are
deter minis ticall y integ rated into microlenses b y means of in-situ EBL.
The gro wth process star ts with an Al
0 . 97
Ga
0 . 03
As la y er with a thickness of 1
µ
m which is
deposited on a GaAs (100) substrate, acting as an etc h stop la y er later on. A bo v e this la y er ,
570 nm of GaAs are gro wn including the InGaAs QDs in a distance of 200 nm to the sample
sur f ace. The QD la y er with a waf er -position dependent density of 10
8 −
10
9
cm
− 2
and an
emission band with an inhomog eneous broadening of 30 me V is centered at 1.33 e V (930
nm). For the flip-c hip bonding process, 200 nm of gold are deposited onto the sample using
electron-beam e vaporation. A dditionall y , a 300 nm gold la y er is ev aporated on a PIN-PMN-PT

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 78
(Pb(In
1 / 2
Nb
1 / 2
)O
3
-Pb(Mg
1 / 3
Nb
2 / 3
)O
3
-PbT iO
3
) cr y stal. This mater ial is c hosen as it has an
increased depoling temperature of
T C =
140
◦ C
and a higher coerciv e field of
E c =
6
k V cm − 1
as compared to the more commonl y used PMN-PT with
T C =
90
◦ C
and
E c =
2.5
k V cm − 1
[ 25 ].
Ne xt, the QD sample is placed upside-do wn onto the piezoelectr ic actuator with the tw o gold
la y ers facing eac h other (cf. Fig. 1 (a)). A pressure of 6 MP a at a temperature of appro ximately
600 K is applied f or 4 hours to achie v e a strong cohesion of the gold la y ers.
Fig. 1.
Schematic illus tration of the fabrication process of a tunable QD microlens: (a)
Gold ther mocompression bonding of the la y er structure including InGaAs QDs, f ollo w ed by
a w et etching s tep to remo v e the GaAs substrate and the etch s top la y er . (b) Mapping process
f or the in-situ EBL. Suitable QDs are chosen and integrated into microlens structures. (c)
The PIN-PMN-PT is contacted to transf er strain to the QD microlens f or spectral-tuning of
the single-photon emission.
In the ne xt step, the upper GaAs subs trate is remo v ed by a s tir red solution of h ydrogen pero xide
and ammonium h ydro xide until the etching s tops at the Al
0 . 97
Ga
0 . 03
As la y er . The latter is remo v ed
b y h ydrochlor ic acid suc h that a semiconductor membrane with a thic kness of 570 nm remains
on top of the gold la y er .
T o enhance the photon-e xtraction efficiency and to pre-select br ight QDs with a specific
emission energy , 3D in-situ EBL at 10 K is applied. This method allo ws us to con v enientl y
choose QDs with a tar g et emission energy and high emission intensity within a scanned area of
the sample b y their cathodoluminescence (CL) characteristics. Figure 1 (b) illus trates the CL
mapping process. Sample areas of 20
µ
m x 20
µ
m are scanned and suitable QDs are chosen.
A microlens is wr itten into the resis t on top of it, which is afterwards de v eloped such that the
structure can be transf er red into the GaAs top la y er b y reactiv e-ion-enhanced plasma etching.
The whole selection and EBL process tak es less than 10 minutes per wr ite field, eac h including
up to about 5 QD-microlenses, so that tens of such de vices with emission at the targ et w a v elength
can be realized in a f e w hours. For more details on the 3D in-situ EBL process w e ref er to [ 11 ].
The final de vice is sho wn in Fig. 1 (c). The device and lens g eometr y w ere optimized bef orehand
using the commerciall y av ailable software-pac kag e JCMsuite b y the company JCMw av e, which
is based on a finite-element method. The optimum lens g eometr y leads to a photon e xtraction
efficiency of 42% f or a numer ical aper ture of 0.4 and is identified as a spher ical segment with a
height of 370 nm and a radius of 1264 nm.
3. Micr o-photoluminescence characterization
The optical proper ties of the final de vice are in v estig ated b y means of micro-photoluminescence
spectroscop y under non-resonant e x citation (laser wa v elength: 665 nm) at a temperature of
10 K with a spectral resolution of 27
µ
e V . Figure 2 (a) sho w s a spectr um of a QD microlens
de vice (QDM1) at saturation of the e x citonic lines. Ex citation-po w er - and polar ization dependent
measurements are used f or the assignment of the emission lines to respectiv e quantum dot states.
The most intense line at
E X − =
1.3520 e V is identified as a char g ed e x citonic transition (X
−
), the

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 79
transition at
E X =
1.3536 e V as the neutral e x citonic transition (X) due to its polar ization splitting
of
∆ E FSS =
7
µ
e V , while a char ged bie x citonic line is obser v ed at
E X X + /− =
1.3490 e V . T o e valuate
the photon-e xtraction efficiency
η
of the microlens de vice, w e use a Titan-Sapphire laser ( f
=
80
MHz) to e x cite the QD state X
−
at saturation and detect the emitted photons using a calibrated
e xper imental setup (cf. Exper imental Section). At zero bias v oltage applied to the piezo element
w e obser v e
η ( X − ) = ( 17 ± 2 )
% f or the char g ed e x citonic transition with a line width of 46
µ
e V
(FWHM). This v alue is smaller than 42% e xpected f or an optimized spher ical microlens, where
the de viation is mainly attributed to the nonideal shape of the realized str ucture with noticeable
sur f ace roughness and a rather flat top. Indeed, a micromesa with similar geometry w ould yield a
photon e xtraction efficiency of 18% [ 26 ]. Thus, fur ther w ork needs to f ocus on a more precise
lithograph y and processing of spher ical microlenses or circular Bragg reflectors on top of a gold
bonded structure to enhance the e xtraction efficiency .
Fig. 2.
(a) Microscope imag e of CL map areas taken during in-situ EBL with QD microlenses.
(b) Scanning electron microscope imag e of a microlens. (c) Micro-photoluminescence
spectr um of a QD microlens (QDM1) at T
=
10 K. (d) Photon-autocor relation measurements
stating single-photon emission with g ( 2 ) ( τ = 0) = 0.03 ± 0.02.
Ne xt, w e v er ify the single-photon emission of our spectrall y-tunable microlens de vice under
pulsed w etting-la y er e x citation at
λ =
897 nm. The photon-autocor relation measurement at
saturation of the X
−
line in Fig. 2 (d) sho ws pronounced antibunc hing at
τ =
0. T o quantitativ ely
e valuate the suppression of multi-photon emission e v ents, the e xper imental data w as fitted with a
sequence of eq uidistant tw o-sided e xponential functions
g ( 2 ) ( τ ) =
©           «
p 0 e −    τ
t d    + p t
5
Õ
i = − 5
i , 0
e −     
τ −  i
f 
t d
     ª ® ® ® ® ® ® ® ® ® ® ¬
⊗ G ( τ , σ res )
with deca y time
t d
con v oluted with a Gaussian G
( τ )
with
σ res =
300 ps /2
√ 2ln2
width, accounting
f or the timing resolution of the Hanbur y-Bro wn and T wiss setup.
The ratio of the peak amplitudes at zero-time dela y
p 0
and at finite time dela ys
p t
re v eals
the second-order photon-autocor relation v alue
g ( 2 ) ( τ = 0 ) =
0.03
±
0.02 (
t d = ( 0.69 ± 0.01 )
ns).
These results confir m that our adv anced multi-step de vice processing enables the realization of
br ight single-photon sources with a high suppression of multi-photon emission e v ents.

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 80
4. Strain-tunability of single-photon emission
T o demonstrate the spectral tunability of QD emission, a v oltag e of
−
600 to
+
600 V is applied
to the PIN-PMN-PT mater ial, cor responding to an electr ic field F of
−
20 to
+
20 k Vcm
− 1
. A
positiv e (neg ativ e) v oltag e cor responds to an in-plane compression (e xtension) of the piezoelectr ic
cr y stal transf er red to the semiconductor mater ial and the QD la y er . Using the full tuning rang e
results in a shift of the X − emission b y ∆ E = 2.5 me V as sho wn in Fig. 3 (a).
Fig. 3.
(a) Energy tuning of the X
−
emission line of QDM1 b y application of an electr ic field
F to the piezoelectr ic actuator . (b) Extraction efficiency (blac k, left axis), equal-time second-
order photon autocor relation ( g
( 2 )
(
τ =
0)) results (red squares, r ight axis) and calculated
g
( 2 )
(
τ =
0) taking the F -dependent e xtraction efficiency into account (red circles, r ight axis).
X − emission energy f or the full tuning range (blue, right axis).
Besides the tunability of the emission energy , Fig. 3 (a) also re v eals a chang e in the emission
intensity with the applied electr ic field, whic h w e fur ther in v estig ated b y measur ing the photon

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 81
e xtraction efficiency in pulsed e x citation. As can be f ound in Fig. 3 (b), the highest efficiency
is achie v ed at an applied field of
F max =
12
k V cm − 1
with
η ( X − , F max ) = ( 20 ± 2 )
%. The
efficiency decreases do wn to
η ( X − , F min ) = ( 6 ± 1 )
% at the lo w est field v alue
F min = −
20
k V cm
− 1
. A dditionall y , w e in v estig ated the second-order photon autocor relation function f or
different detunings. The suppression of multi-photon emission e v ents
g ( 2 ) ( τ = 0 )
remains
constant and belo w 0.05 o v er a wide tuning range and increases at high neg ativ e electr ic fields
to
g ( 2 ) (
0
) =
0.10
±
0.03 at F
= −
15 k V cm
− 1
. The associated X
−
emission energy plotted in
blue sho w s that we can obtain an effectiv e tuning range of about 1 me V in whic h high e xtraction
efficiency
> ≈
15% and high multi-photon suppression with
g ( 2 ) (
0
) <
0.05 can be achie v ed. This
tuning rang e co v ers well the in-situ EBL spectral accuracy so that a combination of both enables
the scalable realization of SPS with identical emission energy as w e demonstrate in the ne xt
section. An increased g
( 2 )
(0) can be e xplained b y a decrease of the signal ( S ) to uncor related
bac kground ( B ) ratio. T o suppor t this statement w e consider g
( 2 ) ( τ ) =
1
+ ρ 2 ( g ( 2 )
BF ( τ ) − 1 )
., with
ρ =
S
/( S + B )
and the bac kground free v alue g
( 2 )
BF ( τ )
[ 27 ], to descr ibe the field dependence
of g
( 2 )
(0). A direct connection to the photon e xtraction efficiency is obtained b y taking into
account that S is propor tional to the measured e xtraction efficiency (blac k data points in Fig.
3 (b)) and that a constant uncorrelated back ground contr ibution of
η B
is present which leads
to g
( 2 ) ( τ ) =
1
+ ( η De vice /( η Device + η B )) 2 (− 1 )
. under the assumption that the bac kground free
g
( 2 )
BF (
0
)
is zero. V er y good agreement betw een e xper imental data (red squares in F ig. 3 (b),
with
η De vice = η N A = 0.4
) and the calculated v alues (open red circles in F ig. 3 (b)) is obtained f or
η B =
0.0035, which supports our inter pretation of a signal-to-back ground dependent increase of
g
( 2 )
(0) f or neg ativ e F . The strain influence on the e xtraction efficiency could be connected to
electr ic fields caused b y char ge states on the sur f ace of the microlens. The char g e states create a
field distribution around the QD which depends on the e xter nal strain. Pre vious studies sho w ed
that the processing of microstructures b y in-situ EBL giv es a lateral positioning accuracy of
34 nm [ 23 ]. Such a de viation from the center could be sufficient f or the QD to be influenced
b y the mentioned strain-induced electric field distr ibution, leading to a slight separation of the
electron and hole w a v efunction, which in return can reduce the emission rate as w e obser v e
in the e xper iment. Measurements of the deca y time of the QD X - emission yield a value of
appro ximatel y 0.65 ns, which is not significantl y be influenced b y the electr ic field F applied
to the piezo actuator , the r ise time increases from about 200 ps to 350 ps with decreasing F
belo w zero. This chang e of r ise time could indicate a lo w er capture probability in ag reement with
the reduced photon e xtraction efficiency in this field rang e. A more detailed descr iption w ould
require a detailed kno w ledge of the QD position in the microlens whic h is be y ond the scope of
the present w ork.
T o demonstrate the scalability of our de vice concept, we e v aluated the strain-tuning beha vior
of f our additional QD-microlenses QDM2-5 which w ere f abr icated tog ether with QDM1 on the
same sample with the same targ et emission energy . In Fig. 4 the e x citonic emission energies of
these microlenses are plotted relativ e to the X
−
emission of QDM1 as function of the electr ic
field applied to the piezo actuator . The emission energy of all f our lenses can be tuned through
resonance with the emission energy of QDM1 (indicated b y the dashed line). This f eature will be
v er y helpful in future e xper iments aiming at entanglement sw apping betw een remote QD-SPSs.
The f act that spectral resonance between the fiv e sources cannot be achie v ed at the same electr ic
field is not rele vant f or this application, f or which the sample could either be split or different
samples with the same targ et emission energy could be realized b y in-situ EBL.

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 82
Fig. 4.
S train-tuning of f our QD microlenses (QDM2-5) which w ere deter ministicall y
f abr icated together with de vice QD1 on the same piece of sample. The e x citonic emission
energies of these QDM2-5 microlenses are plotted relativ e to the X
−
emission energy of
QDM1. The y can be tuned through resonance with QD microlens QDM1 by appl ying
suitable electr ical fields betw een about − 20 k Vcm − 1 and 10 k Vcm − 1 to the piezo actuator .
5. Theoretical analysis of strain-transf er and strain-tuning of QD structures
T o fur ther anal yze the effects of the e xter nal s train w e compare our measurements to results
obtained b y theoretical modeling of the microlens device. The additional strain e x er ted b y the
piezoelectr ic actuator is accounted f or by adjus ting the lattice constant
a 0
of the lo w est GaAs
la y er abo v e the gold mir ror to
˜
a = a 0 −
c
· a 0
, and the strain dis tr ibution inside the full GaAs
de vice is calculated in the frame w ork of continuum elasticity . One has to distinguish betw een
the per manent s train caused b y the inherent lattice mismatch betw een the GaAs substrate and
the InGaAs QD, and the effects of the e xter nal strain caused b y the piezo-tuning. Moreo v er ,
the h ydrostatic s train component can be separated from the biaxial strain component. Figure 5
sho w s the calculation results f or the per manent strain without e xter nal influence ((a1) and (b1))
as w ell as the additional strain effects induced b y an applied e xter nal compressiv e as w ell as
tensile strain ((a2) and (b2)). The dis tr ibution across the lens str ucture is almos t unif or m, only a
slight relaxation effect is visible f or the h ydrostatic s train component as compared to the planar
area around the lens. P ossible shear strain w as not tak en into account in the simulations, because
this w ould add a comple xity to the calculation that is outside of the scope of this w ork.
Applied strain ma y affect the energies of the localized electronic s tates via (i) def or mation
potentials, thus, changing the local band positions, (ii) the alteration of the quantization energies,
and (iii) the chang e in electron-hole Coulomb interaction. Careful analy sis using eight-band k
·
p
theor y tog ether with the configuration interaction method [ 28 ], ho we v er , re v ealed that effect (i)
constitutes the go v er ning contr ibution, whereas (ii) and (iii) are onl y minor contr ibutions, which
are neglected in the f ollo wing discussion. The achie v ed tuning of
∆
E
=
2.5 me V cor responds to a
chang e in the lattice constant of c
= ±
1.2
· 10 − 3
f or compressiv e (
+
) and tensile (-) strain. A t the
position of the QD the resulting sum of the relativ e h ydrostatic and biaxial s train components in
all three directions are calculated separatel y to
∆  h y (
c
) = ±
8.1
· 10 − 4
and
∆  biax (
c
) = ±
4.65
· 10 − 3
,
where the h ydrostatic s train is responsible f or band-shifts and the biaxial strain f or the heavy -hole
light-hole splitting [ 29 ]. The sum of both effects is dr iving the c hang e in the luminescence energy .
Combined with the def or mation potentials in In
0 . 7
Ga
0 . 3
As,
a g = −
6725.9 me V f or the h ydrostatic

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 83
Fig. 5.
Calculated h ydrostatic (a1/a2) and biaxial (b1/b2) strain dis tr ibutions in a QD
microlens. (a1/b1) ref er to the situation in absence of e xter nal strain, while (a2) and (b2)
sho w the additional effects b y e xter nal tensile (left) and compressiv e strain (right). The
domain is divided into (i) air , (ii) lens, (iii) QD, (iv) w etting lay er , (v) spacer lay er , and (vi)
the piezoelectr ic actuator . R ed (blue) color indicates the relativ e tensile (compressiv e) strain.
strain and b v = − 1897.2 me V f or the biaxial strain, the ener gy shift can be calculated as
∆ E ( c ) = a g ( ∆  h y ( c )) − 1
2 b v ( ∆  biax ( c )) = ± 1.25 me V.
Using the piezoelectr ic coefficient
d 31 ≈
1500
pC N − 1
as published b y the manuf acturer (CTS
Cor poration), w e can compare the theoreticall y e valuated s train with the e xper imentally applied
v alue. The maximum strain that is induced in one lateral direction dur ing the measurement can
be estimated to
 e xp = d 31 · F max = 1500 pC N − 1 · 20 k V cm − 1 = 3 · 10 − 3 ,
as compared to the theoretical v alue of c
=
1.2
· 10 − 3
. Matc hing the calculation results with
the achie v ed tuning, it can be estimated that a fraction of
c
 e xp =
40 % of the strain effect at the
piezoelectr ic crys tal is transf er red to the position of the s tudied QD.
6. Closed-loop stabilization of emission energy
A cr itical aspect of our tar g et application in quantum communication netw orks is the long-ter m
spectral stability of our ener gy -tunable SPSs. In this reg ard the w ell-kno wn creep behavior of
piezoelectr ic actuators is a se v ere issue [ 30 ]. T o illus trate this point, the time-dependence of
the emission energy of another s train-tunable QD-microlens de vice is presented in Fig. 6 (a),
where the electr ic field w as chang ed up from zero to 12 k Vcm
− 1
at time t
=
0. In the first 30
minutes of the measurement ser ies, the emission energy increased rather s trongly b y about 350
µ
e V . Subsequentl y , in the ne xt 120 minutes a fur ther linear blue-shift of about 30
µ
e V took
place because of the typical creeping beha vior of the piezo-mater ials, bef ore the emission finall y
approaches a s table v alue. Thus, f or applications requir ing larg e tuning ranges, a s tabilization
time of appro ximatel y 3 hours needs to be considered bef ore stable operation of the SPS in this
open-loop scenar io. Moreo v er , e v en in the ‘stable s tate’ creep related spectral shifts on the order
of se v eral
µ
e V do occur , pre v enting the implementation of entanglement sw apping which req uires
sub- µ e V spectral stability .
T o impro v e the strain-tuning beha vior and the long-ter m spectral stability of our de vices w e
implemented an activ e f eedback loop with a proportional–integ ral–der iv ativ e (PID) controller .
W e use an e xper imental approach similar that reported in Ref. [ 20 ]. Essentiall y , in this rather
straight-f or w ard approach the signal emitted b y the QD-microlens is coupled to a spectrometer
at adjustable time interv als of typicall y a f e w ten seconds to monitor the emission wa v elength

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 84
Fig. 6. (a) Time series of the e x citonic emission energy of a QD-microlens after changing
the piezo field from zero to F
=
12
k V cm − 1
at time t
=
0 in open-loop configuration. (b)
T ime-dependence of emission energy in closed loop configuration using an activ e optical
f eedback control. The jump in intensity at t
=
2 min w as caused by an intentional perturbation
of the sy stem. (c) Zoom-in vie w of the emission energy relativ e to the set point (er ror bars
in shaded gre y). (d) Cor responding his togram of relativ e emission energies with a s tandard
de viation of 0.5 µ e V .
with a spectral accuracy of 0.8-1.0
µ
e V with an integration time between f e w tens milli-seconds
and f e w seconds depending on the signal strengths. W e ins talled a shor t (1 m) single-mode fiber
section in the detection path bef ore f ocusing the optical signal to the input slit of the spectrometer .
This fiber section is cr ucial to enhance the spectral accuracy of the implemented control loop,
as small angle de viations of the detection beam path chang e the position of the emission line
on the spectrometer’s CCD, thus pre v enting a reliable detection of the emission energy with
the required accuracy . W ithin a PID control loop with optical f eedbac k, the center energy of
the targ et emission line is deter mined in each iteration b y Lorentzian fitting of the detected
spectr um and is compared to the setpoint energy . In case of de viations from the targ et energy , the
v oltag e output to the piezo actuator is readjusted to shift the emission line bac k to the setpoint via
adapted strain. T o ensure best per f or mance of the control loop, the optimum PID parameters are
deter mined b y the pulse response of the sy stem.
T o illus trate the functionality of the descr ibed control-loop w e stabilized the emission ener gy
of a QD-microlens to a setpoint of 1.3529485 e V . Figure 6 (b) sho ws the corresponding time
e v olution of the f eedback -controlled center ener gy f or a time per iod of appro ximatel y 90 minutes.
The jump at t
=
2 min marks an intentional (mechanical) perturbation, to test the dynamic
response of the control loop. Within a c haracter istic dynamic response time of about minutes, the
emission energy returns to the setpoint. Subsequentl y , the emission energy is s tabilized efficientl y
b y the control-loop as can be seen in the zoom-in vie w of the emission energy relativ e to the
setpoint. The data yields a s tandard deviation as lo w as 0.5
µ
e V (1.2
µ
e V FWHM) as sho wn

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 85
b y the cor responding histogram (obtained f or the time rang e of 7 to 90 minutes) in Fig. 6 (d).
Impor tantl y , this value compares w ell with the typical homogenous line width (appro ximatel y
1-2
µ
e V) of the InGaAs QDs under study and, thus, can pa v e the w ay f or future entanglement
sw apping e xper iments betw een remote quantum light sources.
7. Experimental section
7.1. In-situ electron beam lithogr aph y
With the in-situ EBL s tep, QDs are chosen b y their cathodoluminescence (CL) signal and
integrated into microlens structures. The samples are prepared b y spin-coating with the electron-
beam resist AR -P 6200 (CS AR 62) and mounted onto the cold finger of a He-flo w cr y ostat of a
customized scanning electron microscope f or lo w -temperature operation at 10 K. The reaction of
the resist during de v elopment depends on the applied electron dose dur ing e xposure. This resist
has a positiv e-tone regime at lo w electron doses, which are used f or mapping of the CL signal.
The luminescence signal is f ocused into a monochromator and detected with a Si c harg e-coupled
de vice camera. Based on that data, QDs are chosen and micros tr uctures are wr itten into the
resist abo v e them with a higher electron dose. A bo v e a cer tain threshold v alue, the resist enters a
neg ativ e tone regime, such that the s tr uctures remain after de v elopment. The transition rang e to
the complete neg ativ e-tone regime is used to create quasi-3D designs (see R ef. [ 11 ] f or details).
Finall y , dr y etching is perf or med b y inductiv ely -coupled-plasma reactiv e-ion etching.
7.2. Optical measurements
The sample is mounted in a helium-flo w cr y ostat and cooled do wn to 10 K. It is optically e x cited
using a T itan-Sapphire laser that can be operated in quasi-continuous w a v e (CW) or pulsed
( f
=
80 MHz) mode. The photoluminescence is collected using a microscope objectiv e with an
N A of 0.4 and spectrally dispersed b y a g rating monochromator , bef ore it is detected using a Si
char g e-coupled de vice camera. The setup is also equipped with a fiber -coupled Hanbur y -Bro wn
and T wiss setup using single-photon counting modules based on Si a valanc he photo diodes. T o
e valuate the e xtraction efficiency into the first lens of our e xper imental setup, the transmission of
the complete setup w as measured to be
η Setup = ( 1.1 ± 0.1 )
% f ollo wing the procedure descr ibed
in R ef. [ 11 ]. Using a laser with repetition rate f a detected count-rate
n QD
cor responds to a
photon-e xtraction efficiency of
η De vice = n QD
η Setup ∗ f
. Fur thermore, the photon e xtraction efficiency
is defined as
η De vice = η geo η X −
, where
η g eo
denotes the purel y geometrical contr ibution to the
photon e xtraction efficiency of the de vice, while
η X −
the probability of emitting a photon b y
the X
−
per e x citation pulse. The latter includes the occupation probability and the quantum
efficiency of this QD transition, which can be influenced b y the applied mechanical s train under
non resonant e x citation.
8. Conc lusion
In conclusion, w e presented a spectrall y -tunable single-photon source with a maximum photon
e xtraction efficiency of
η = ( 20 ± 2 )
% and a total tuning rang e of
∆
E
=
2.5 me V . This tuning
rang e is reduced to about 1 me V when f ocusing on an operation regime of
η >
15% and g
( 2 )
(0)
<
0.05. The emission energy of our de vice is pre-selected with an accuracy of about 1 me V b y
using in-situ EBL applied to a planar sample bonded onto a piezoelectr ic actuator via flip-chip
gold ther mocompression bonding. In addition, a f eedbac k -loop is implemented whic h enables
loc king the emission energy with a s tandard de viation of 0.5
µ
e V (FWHM: 1.2
µ
e V). Thus, the
achie v ed effectiv e tuning can ser v e to adjust the emission to meet the e xact transition energy
required e.g. f or entanglement distribution in multi-node quantum netw orks or f or the inter f acing
of QD based single-photon sources with quantum memories.

Researc h Article V ol. 10, No . 1 / 1 Jan uar y 2020 / Optical Mater ials Express 86
Funding
Bundesministerium für Bildung und Forsc hung (03V0630, 13N14876); Deutsche F orschungsg e-
meinschaft (R e2974/8-1, SFB787); Hor izon 2020 Frame w ork Programme (MIQC2, SIQUST).
Disc losures
The authors declare no conflicts of interest.
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Why institutions use Plag.ai for originality review, entry 47

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