Cesium‐vapor‐based delay of single photons emitted by deterministically fabricated quantum dot microlenses [original]

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C esium-V apor-Based Delay of Single Photons Emitted
by Deterministically F abricated Quantum Dot Microlenses
Lucas Bremer, Sarah Fischbach, Suk-In Park, Sven Rodt, Jin-Dong Song, T obias Heindel,
and Stephan Reitzenstein*
Quantum light sources are key building blocks of photonic quantum
technologies. F or many applications, it is of interest to control the arrival time
of single photons emitted by such quantum devices, or even to store single
photons in quantum memories. In situ electron beam lithography is applied
to realize InGaAs quantum dot (QD)-based single-photon sources, which are
interfaced with cesium (Cs) vapor to control the time delay of emitted
photons. Via numerical simulations of the light–matter interaction in realistic
QD-Cs-vapor conﬁgurations, the inﬂuence of the vapor temperature and
spectral QD-atom detuning is explored to maximize the achievable delay in
experimental studies. As a result, this hybrid quantum system allows to
trigger the emission of single photons with a linewidth as low as 1.54 GHz
even under non-resonant optical excitation and to delay the emission pulses
by up to (15.71 ± 0.01) ns for an eﬀective cell length of 150 mm. This work
can pave the way for scalable quantum systems relying on a well-controlled
delay of single photons on a time scale of up to a few tens of nanoseconds.
1. Introduction
Light–matter interaction in atomic vapors is a very attractive
resource for applications in future quantum communication
technologies. [1,2] It is particularly interesting for the realization
of quantum memories with long storage times. [3,4] In addition,
it can be used to frequency-lock single-photon sources with sub-
GHz accuracy in large-scale quantum networks relying on en-
tanglement swapping between diﬀerent sources with identical
emission wavelengths. [5] C ontrolling the propagation of single
L. Bremer , Dr . S. Fischbach, Dr . S. Rodt, Dr . T . Heindel,
Prof. S. Reitzenstein
Institute of Solid State Physics
T echnische Universität Berlin
10623 Berlin, Germany
E-mail: [email protected]
S.-I. Park, Dr . J.-D. Song
C enter for Opto-Electronic Materials and Devices
Korea Institute of Science and T echnology
Seoul 02792, Republic of Korea
The ORCID identiﬁcation number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/qute.201900071
© 2019 The Authors. Published by WILEY-VCH V erlag GmbH & Co.
KGaA, W einheim. This is an open access article under the terms of the
C reative C ommons Attribution License, which permits use, distribution
and reproduction in any medium, provided the original work is properly
cited.
DOI: 10.1002/qute.201900071
photons and the storage of quantum in-
formation are highly relevant to facili-
tate, for instance, the development of pow-
erful quantum computers in the near
future. [6] M oreover , to build large-scale
quantum networks based on quantum re-
peater protocols, [1,7,8] network nodes are
necessary to locally store the information
encoded on single photons acting as ﬂy-
ing qubits. [8,9] In this context, the genera-
tion of slow light by means of light–matter
interaction in an atomic ensemble of al-
kali atoms has been known for several
decades. [10] Only recently , advances in the
development of quantum light sources have
made it possible to combine the underlying
physical principles and device functionali-
ties in the form of hybrid quantum systems.
N owadays, self-assembled semiconductor
quantum dots (QDs) allow one to realize
close-to-ideal triggered sources of single
and indistinguishable photons. [11–13]
F urthermore, advanced semiconductor nanotechnology plat-
forms facilitate the deterministic integration of pre-selected
QDs into photonic components with precisely engineered op-
tical properties for instance in terms of the photon extraction
eﬃciency . [12–14] E ven the integration of alkali gases in photonic
microstructures on a chip has been demonstrated in the past. [15]
H owever , interfacing QDs with atomic vapors to form hybrid
quantum systems with enhanced functionality , such as single-
photon delay and photon storage, is highly challenging due to the
intrinsic bandwidth mismatch between the two components and
because of the precise spectral matching required to enable pro-
nounced and reproducible light–matter interaction. While initial
steps in this direction have already been taken, [4,16] storing indi-
vidual quantum states in dilute vapors of alkali metals has not
been mastered yet. Therefore, in order to establish the necessary
technology and experimental techniques and to explore the un-
derlying physics, it is useful to investigate single-photon time de-
lay in a more accessible setting, namely by interaction with tran-
sitions in cesium (Cs) atoms with large dispersion. [17–19]
In our work, we aim at well-controlled light delay in a hy-
brid solid-state atom system based on a deterministically fab-
ricated QD single-photon source (SPS). Deterministic process
ﬂows are undoubtedly of utmost importance when considering
the future transfer of quantum technological concepts into large-
scale practical applications, which require many precisely engi-
neered and fabricated quantum devices. F or this purpose, we
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Figure 1. Schematic view presenting the deterministic fabrication of QD-microlenses by means of 3D in situ EBL: (F rom left to right) First, the sample,
coated with an electron-sensitive resist (CSAR), is mapped at 10 K at a low electron dose of 2.5 mC cm − 2 and the spatially and spectrally resolved
cathodoluminescence signal is detected by a high-resolution grating spectrometer . In the following 3D in situ EBL process step, a lenticular dose pr oﬁle
is introduced into the resist at a higher dose of up to 17 mC cm − 2 over selected QDs with suitable emission wavelength and emission intensity . Here,
the electron dose is chosen to invert the resist locally , that is, to make it insoluble at the QD position. Afterward, the soluble resist is removed in th e
cleanroom using the developer methylisobutylketone (MIBK), so that the remaining resist (forming a microlens) above selected QDs acts as etch mask.
In this way , the lens-proﬁle can be transferred into the semiconductor material by the ﬁnal inductively coupled plasma reactive-ion etching (ICP-RI E)
step.
apply 3D in situ electron beam lithography (EBL) to pre-select
and integrate bright InG aAs QDs with Cs-D 1 compatible wave-
lengths into microlenses with enhanced photon extraction eﬃ-
ciency . N umerical simulations are applied to determine optimum
experimental and operation parameters for interfacing a QD SPS
with dilute Cs vapor in a cell with variable temperature. S electing
the most suitable QD-atom detuning in the spectral range of min-
imum absorption in between the hyperﬁne-split components of
the Cs-D 1 line we achieve complete normalized delays of up to
(1.05 ± 0.01) ns cm − 1 , which translates to an absolute delay of
(15.71 ± 0.01) ns for a cell with an optical path length in Cs vapor
of 150 mm and a temperature of 132.5 °C.
2. Sample T echnology
The goal to interface QDs and atomic vapors with dissimilar opti-
cal properties, for instance in terms of transition linewidths, sets
stringent demands on the quality and emission features of the
solid-state-based single-photon emitters. F irst, the spectral de-
tuning between the emission from the quantum emitter and the
transitions of the atomic ensemble needs to be controlled pre-
cisely with sub-GHz accuracy . S econdly , spectrally narrow emis-
sion lines on a scale of GHz are required to ensure a complete
pulse delay , [18,19] as we discuss below in more detail. Therefore,
we designed and epitaxially grew a semiconductor heterostruc-
ture that includes a single layer of self-assembled InGaAs QDs
as active medium. The wavelength of the QD ensemble emission
band is centered at approximately 914 nm with a full-width at
half-maximum (FWHM) of 30 nm. The heterostructure includes
an AlG aAs/G aAs distributed Bragg reﬂector (DBR) consisting
of 23 mirror pairs followed by a 63 nm G aAs buﬀer layer , the
InG aAs QD layer with an areal density of ≈ 20 µm − 2 ,a n daG a A s
capping layer with a thickness of 400 nm.
The 400 nm thick G aAs capping layer allows us to realize
monolithic G aAs microlenses on top of pre-selected QDs by
means of in situ EBL, as we describe in the following. The mi-
crolenses, together with the lower DBR mirror , enhance the pho-
ton extraction eﬃciency of the embedded QDs from less than 1%
for a simple planar structure to about 30% for an NA of 0.4. [12,20]
The associated (broadband) enhancement of emission increases
the single-photon ﬂux and is thus very helpful for the envisaged
QD-atom coupling experiments. H ere, emission enhancement is
of particular importance at elevated temperatures of the Cs vapor
where high single-photon delays can be achieved at the cost of
increased optical absorption.
The deterministic QD-microlens fabrication is based on the
powerful 3D in situ EBL technique, [21] as described in Fi g u re 1 .
It uses a scanning electron microscope equipped with a helium
(H e) ﬂow cryostat, an elliptical mirror , and a high-resolution spec-
trometer to perform cathodoluminescence (CL) spectroscopy at
10 K. A dditionally , it includes a pattern generator with an ex-
tended home-built software kit allowing for joint operation and
synchronization between CL spectroscopy and EBL. Based on
this customized system, the deterministic fabrication process
starts with CL mapping of about 50 µm × 50 µm write ﬁelds of
the above-described QD-sample to identify suitable QDs based
on their emission intensity and wavelength, which are required
to match the target transitions of the Cs vapor near the D 1 line at
894.59296 nm in vacuum. [22] Prior to the in situ EBL process, the
sample is spin-coated with an 85 nm thick layer of CSAR resist,
which is exposed homogenously during the CL mapping by an
electron beam dose of 2.5 mC cm − 2 . Directly after CL mapping,
the EBL software automatically selects suitable QDs within the
target wavelength of (894.6 ± 0.5) nm. The electron beam is di-
rected to the respective QD positions, where microlenses with a
numerically optimized base width of 2.8 µm are written in the
resist by varying the dose from 17.0 mC cm − 2 at the center of the
microlens to 4.5 mC cm − 2 at its edge. In this way , the resist gets
locally inverted so that it becomes insoluble in the subsequent de-
velopment process which is performed at room temperature in
the cleanroom after sample transfer . The resulting microlenses of
resist material are aligned to the preselected QDs (about 3–5 QDs
per write ﬁeld) with 30–40 nm accuracy [23] and act as etch masks
in the ﬁnal plasma enhanced reactive ion etching step. In this
highly anisotropic etching process, the uncovered semiconductor
material is removed (including the QD layer in the write ﬁelds).
The EBL written lens proﬁle is transferred into the semiconduc-
tor material so that we obtain G aAs microlenses, each with single
monolithically integrated pre-selected QDs with a process yield
exceeding 90%. The resulting QD-based single-photon sources
are well suited to explore the QD-atom interaction and temporal
delay in Cs vapor as we experimentally show in S ection 3.2.
3. Interfacing Single Photons with Atomic V apor
T o understand the inﬂuence of dense Cs vapor on the optical
properties of a propagating light pulse, it is necessary to describe
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Figure 2. a) The real part of the refractive index n and absorption coeﬃcient 𝛼 of Cs in the vicinity of the resonant frequency of the D 1 transition at a
vapor temperature of 100 °C. While n (upper panel) shows the typical dispersion line shape, 𝛼 (lower panel) is an inhomogeneously broadened Lorentz
line for each of the four transitions between the four hyperﬁne energy levels. The curves are calculated with ElecSus. [24] b) Schematic presentation of
the associated Cs-D 1 energy-level diagram with the hyperﬁne structure. c) Group velocity and the resulting temporal delay as a function of the spectral
detuning from the Cs-D 1 line for various temperatures between 25 and 140 °C. The transmission of a 150 mm long Cs cell is color-coded as indicated
by the scale bar .
the macroscopic response of matter to an incident electromag-
netic wave. In the case of an optically thin non-polar gas, this de-
scription can be done by considering its electrical susceptibility .
The susceptibility of the gas is strongly frequency dependent in
the region of the intra-atomic transitions, which is discussed in
S ection 3.1. In S ection 3.2, we perform numerical simulations to
study wavelength dependent light–matter interaction eﬀects in
a diluted gas of Cs atoms. S ubsequently , the theoretical results
are compared to an experimentally observed controllable delay of
light pulses from a QD-microlens.
3.1. Electric Susceptibility
The high interest in alkali atoms, and vapors thereof, in quan-
tum nanophotonics is explained by their well-deﬁned and com-
paratively simple energy-level scheme. This simpliﬁes the the-
oretical description of the associated light–matter interaction
and is beneﬁcial for well-controlled experiments to explore and
utilize this interaction. In fact, of all multi-electron atoms, al-
kaline elements are most similar to hydrogen, resulting in a
simple energy-band diagram with distinct spectrally separated
absorption lines.
C oncerning the present experiment, only transitions within
the non-degenerated energy level 6s 1 of Cs are of relevance. The
optical response of a dilute thermal vapor of Cs atoms to a prop-
agating electromagnetic wave is given by its complex refractive
index n c , which can be derived in a textbook like manner from
the weak-probe electric susceptibility 𝜒 given by
n c = √ 1 + 𝜒 (1)
The electric susceptibility of an ensemble of Cs atoms is
then calculated numerically using ElecS us, [24] which considers
temperature dependent Doppler- and self-broadening. The sus-
ceptibility is directly proportional to the number density of Cs
atoms, which increases almost exponentially with temperature.
Fi g ur e 2 a shows an example of the real part of the refractive index
n and the absorption coeﬃcient 𝛼 of Cs vapor for a temperature
of 100 °C. The refractive index is approximately one for strong
detuning from the D 1 resonance frequency and shows the typi-
cal dispersion line-shape associated with anomalous dispersion
for all four transitions of the hyperﬁne structure (see F igure 2b).
Based on the refractive index, it is possible to calculate the group
velocity v g via
v g = c
n ( 1 − 𝜔
n
dn
d 𝜔 ) ≈ c
n + 𝜔 dn ∕ d 𝜔 (2)
where c is the speed of light and 𝜔 the angular frequency . [25] Co n -
sidering Equation (2), it is obvious that in areas where the refrac-
tive index has a large positive gradient, a low group velocity—and
thus a large delay—is to be expected as desired for many target
applications in photonic quantum technology . F igure 2c shows
the corresponding group velocity for various temperatures. The
smallest group velocities are expected in the immediate vicinity
of the resonance frequencies of the hyperﬁne structure. H owever ,
even at moderate temperatures the absorption in these regions is
very high, and in practice, it is usually important to ﬁnd a good
balance between the lowest possible group velocity and the low-
est possible optical absorption. F or this purpose, it is important to
know about the interdependence of delay , absorption, and vapor
temperature, and Fi g ur e 3 can serve as a decision-making aid. In
F igure 3, the local maxima in the transmission of Cs vapor , result-
ing from the hyperﬁne splitting of the ground state ( + 840 MHz
related to the Cs-D 1 line) and from the splitting of the excited
state ( + 5067 MHz), are compared in relation to absorption and
delay for diﬀerent color-coded temperatures. The mirrored posi-
tion at − 4085 MHz is not shown for the sake of clarity , as the
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Figure 3. C alculated delay as a function of the absorption coeﬃcient for
the spectral positions + 840 and + 5067 MHz relative to the Cs-D 1 line. The
y -axis on the right side shows the resulting delay for a 150 mm long path
through the Cs vapor corresponding to our experimental conditions. The
corresponding Cs vapor temperature ( T Cs ) is color-coded.
curve is almost identical to the one for + 5067 MHz. The posi-
tion of − 4085 MHz is therefore not discussed further in the fol-
lowing. The ﬁgure shows that for a given absorption coeﬃcient,
the delay time in case of + 840 MHz detuning is always higher .
F or technical reasons (related to the maximum cell temperature
of 120 °C), it is interesting to consider the spectral position at
+ 5067 MHz for the QD–atom interaction, because it features
larger delays than for + 840 MHz detuning at low and interme-
diate temperatures. H owever , the higher dispersion of the group
velocity must be considered for + 5067 MHz detuning, which dis-
torts light pulses of ﬁnite spectral width.
3.2. Delaying Single Photons
T o experimentally explore the predicted temporal delay induced
by light–matter interaction in Cs vapor , we used the spectroscopy
setup depicted schematically in Fi g ur e 4 . The excitation source is
a pulsed titanium–sapphire laser operating in ps mode with a
tunable emission wavelength between 700 and 1050 nm and a
repetition frequency of 80 MHz. The sample is placed in a H e
ﬂow cryostat at 11.8 K. In order to localize the structures to be in-
vestigated on the sample surface, the broadband light of a white
light source is coupled into the beam path. The microscope ob-
jective used has a numerical aperture of 0.4 at 20 × magniﬁca-
tion. A commercial Cs vapor cell with a length of 75 mm is used
to delay single photons by controlled atom interaction in the Cs
vapor . The cell was passed through twice to double the achiev-
able delay by a total eﬀective length of 150 mm. The temper -
ature is controlled either by a negative temperature coeﬃcient
resistor located inside the housing of the vapor cell or more pre-
cisely by measuring the transmission of the Cs vapor using a tun-
able narrow-band CW laser . F rom the transmission, the temper -
ature can be determined by a ﬁt using ElecS us. [24] This method is
much more accurate than the resistance measurement because
it delivers the temperature of the Cs vapor itself. Using a grating
Figure 4. Schematic view of the spectroscopy setup used for micro-
photoluminescence studies at cryogenic temperatures. The QD sample
to be examined is placed in a He ﬂow cryostat at a ﬁxed temperature be-
tween 5 and 30 K. It is excited by a pulsed titanium–sapphire laser with a
pulse length of 1.2 ps at a repetition rate of 80 MHz. After passing through
optical elements of the detection path, light emitted by the QD is focused
on the entrance slit of a monochromator , which decomposes the sample
signal into its spectral components. The spectral information can be ana-
lyzed either with a CCD or are forwarded after spectral ﬁltering to a ﬁber-
coupled SPCM for time-resolved experiments or a high-resolution FPI. The
additional CCD camera provides a white-light image to facilitate the adjust-
ment and orientation on the sample surface.
spectrometer equipped with a liquid-nitrogen-cooled S i charge-
coupled device (CCD) camera with an overall spectral resolution
of 25 µeV , emission of the QD line under study is spectrally ana-
lyzed and selected to match the wavelength of the target Cs tran-
sitions. A dditionally , the setup includes a high-resolution confo-
cal F abry–Pérot interferometer (FPI) with a free spectral range of
7.5 GHz and a resolution of 0.43 µeV . F or time-resolved µPL ex-
periments the QD emission is directed via the lateral output slit
of the monochromator to a S i avalanche photodiode based single
photon counting module (SPCM) with a temporal resolution of
350 ps. The counting electronics of the correlation module allows
us to measure the time diﬀerence between the trigger signal of
the laser and the detection time of the SPCM for each detection
event. The actual pulse delay due to the hot Cs vapor is obtained
by relating the measured time interval to a reference measure-
ment without a cell.
In our delay experiment, we used a QD integrated determin-
istically into a microlens as described in S ection 2. Fi g u re 5
presents basic spectroscopic information about the investigated
QD-microlens. P anel 5a shows a µPL spectrum of the QD line,
which can be tuned into resonance with the Cs-D 1 line via tem-
perature variation. The excitonic line of the investigated QD-
microlens has an inhomogeneous linewidth of (1.54 ± 0.05) GHz
(FWHM), as measured by the FPI (see F igure 5b) under pulsed
oﬀ-resonant excitation at 800 nm. N oteworthy , the measured
linewidth is by a factor of 7 larger than the homogenous linewidth
of (0.22 ± 0.01) GHz estimated from time resolved measure-
ments shown in F igure 5c. H ere, the enhanced linewidth is at-
tributed mainly to spectral diﬀusion due to excess carriers in
the non-resonantly pumped QD system. Interestingly , the ob-
served linewidth < 3.0 GHz is even smaller compared to values
observed under strict resonant excitation in ref. [19]. This high-
lights the high optical quality of our QD-microlenses. F igure 5d
shows the second-order autocorrelation function g (2) ( 𝜏 ) recorded
with a ﬁber-coupled H anbury Brown and T wiss (HB T)-type setup.
The suppression of the multiphoton emission with g (2) (0) ≪ 0.5
clearly proofs single-photon emission.
In order to phenomenologically describe the inﬂuence of
the Cs vapor on the single-photon pulse shape in the delay
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Figure 5. a) µPL spectrum of the QD-microlens excited at saturation with 80 MHz repetition frequency . The marked emission line can be tuned into
resonance with the Cs-D 1 line by temperature variation of the QD. b) High-resolution spectrum of the corresponding QD measured with an FPI. The red
curve shows a Lorentzian ﬁtted to the measurement data. c) Lifetime measurement for the QD emission line from (b). The lifetime 𝜏 1 = (0.72 ± 0.02)
ns is extracted from a linear ﬁt to the falling edge of the pulse. The coincidences are scaled logarithmically . d) Measured HBT autocorrelation functi on
for the QD reveals high multi-photon-suppression with g (2) (0) ≪ 0 . 5.
experiments, an exponentially modiﬁed G aussian function y ( 𝜏 )
is assumed based on W ildmann ’s model. [18]
y ( 𝜏 ) = A
t 0
e
1
2 ( w t
t 0 ) 2 − 𝜏 − 𝜏 c
t 0 ( 1
2 + 1
2 Erf [ 𝜏 − 𝜏 c
w t
− w t
t 0 ]) (3)
A, w t ,a n d 𝜏 c denote the amplitude, the standard deviation
and the position of the G aussian proﬁle, t 0 the relaxation pa-
rameter of the exponent, and Erf(z) the G aussian error function.
The function can be obtained in its basic form from a convo-
lution of a G aussian function, reﬂecting the time resolution of
the setup, and an exponential decay function, describing the de-
cay of the excited two-level system. Using this model function,
it is possible to describe both non-delayed pulses and delayed
pulses subject to dispersion and to predict the expected tempo-
ral delay for diﬀerent detunings and temperatures of the Cs cell.
F or this purpose, we describe the inhomogeneously broadened
single-QD emission line by a G aussian function. As the trans-
mission through the Cs vapor is a function of the spectral posi-
tion (see F igure 2c), the broadened QD line has to be weighted
with this dependence. This dependence is considered by multi-
plying the two functions (in frequency representation), resulting
in a modiﬁed lineshape whose frequency components are subject
to individual frequency-dependent absorption. Thus, in general,
the photon pulse has a non-G aussian lineshape after passing the
dispersive Cs vapor . S ubsequently , the modiﬁed line shape is in-
serted for the amplitude A in Equation (3) and the delay for the
position 𝜏 c of the unmodiﬁed G aussian to obtain the frequency
dependent amplitude and delay of the photon pulse. The remain-
ing parameters, w t = 0.54 ns and t 0 = 0.74 ns are determined by
ﬁtting Equation (3) to a non-delayed pulse. Integrating the result-
ing expression over all relevant frequencies, a model function is
obtained which phenomenologically describes the intensity of a
photon pulse in the presence of absorption and dispersion as a
function of time.
T aking the measured linewidth of the considered excitonic line
into account, the question arises whether and at which detuning
light–matter interaction with the Cs vapor can result in a com-
plete delay of the photon pulse. In this context, we refer to com-
plete delay , if all photons in a statistical ensemble of photon trans-
mission trials are delayed and the signal at approximately zero
delay is negligible. F or the given QD linewidth of 1.54 GHz, com-
plete delay , which is highly preferable for applications, is achieved
close to the Cs-D 1 line, that is, close to zero detuning, where a
plateau with high transmission extends from about − 2t o3G H z .
The corresponding calculated transient is presented in Fi g u r e 6 a
for detunings in the range of − 0.2 to 1.8 GHz when considering
a 150 mm long Cs vapor cell at a temperature of 130 °C. In this
spectral region, the entire pulse is delayed by about 14 ns, where
the delayed pulse-shape depends only slightly on the detuning. In
fact, a shift away from the ideal position of + 840 MHz only leads
to a stronger temporal broadening of the pulse but not to a split-
ting into a non-delayed and delayed part. The normalizations of
the graphs in F igure 6a,b are chosen so that the total transmission
can be read oﬀ from the respective maximum of a curve. F rom
the inset of F igure 6a it becomes clear , that only for linewidths
larger than 10 GHz a pronounced weakly delayed second pulse is
formed. This comparatively wide spectral range is an advantage
of Cs over R ubidium, where this window is smaller ( ≈ 7G H z ) .
In contrast, it is not possible to completely delay the pulse for
the given linewidth in the area of strong anomalous dispersion.
This is shown in F igure 6b for a vapor temperature of 70 °C. In
addition to the strongly delayed part, a weakly delayed pulse is al-
ways formed, the intensity of which increases with increasing dis-
tance from the ideal position of + 5067 MHz. If the ideal position
is met exactly , the intensity of the components is approximately
the same. F urther simulations, considering the resulting pulse
shape as a function of the QD linewidth, show that linewidths
below 900 MHz are necessary in the region of strong anoma-
lous dispersion to achieve a complete pulse delay (see inset of
F igure 6b). Based on these theoretical considerations, in experi-
ment, the QD emission line was shifted by temperature tuning to
the optimum position of + 840 MHz. N oteworthy , it is non-trivial
to exactly match this target spectral position due to the techni-
cally demanding calibration in the absolute spectral position of
the FPI and because sub-0.1-K temperature changes already lead
to spectral shifts of 0.2 GHz, taking the measured temperature
coeﬃcient of 2.1 GHz K − 1 in the temperature range around 12 K
into account. F its to the experimental delay data (see F igure 6c)
revealed that the spectral matching of the QD line was
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Figure 6. a,b) Simulations of the photon delay in a 150 mm long Cs vapor cell. A spectral Gaussian emission line with a FWHM of 1.54 GHz is assumed
for diﬀerent spectral detunings relative to the Cs-D 1 -line. The graphs are normalized so that the value of the global maximum of a curve corresponds to
the total transmission of the pulse. The relative position of the emission line is varied and the vapor temperature (130 °C for (a) and 70 °C for (b)) is ke pt
constant. The insets show the respective fraction of strongly delayed photons of the total integrated pulse area as a function of the linewidth (FWHM) of
the QD line. The ideal position of a) + 840 MHz and b) + 5067 MHz was assumed. c) Experimental results (circles) obtained for single photons emitted
from QD-microlenses that are delayed by a Cs vapor cell with an eﬀective length of 150 mm. The experimental data are well described by simulations
(solid lines) based on Equation (3). d) C alculated transmission versus detuning for a 150 mm long Cs vapor cell at 70 °C.
actually not perfect in our experiment ( + 1350 MHz instead of
+ 840 MHz). This slight detuning of the frequency , which is more
than an order of magnitude below the monochromator resolu-
tion, is not attributable to the accuracy of the temperature tuning,
but to the aforementioned diﬃculty of precisely determining ab-
solute frequencies. The temperature control took place with an
accuracy of about 0.02 K, which corresponds to an uncertainty of
the central frequency of the QD line of 42 MHz.
The measured PL transients are presented in F igure 6c, where
the normalization of the curves was chosen based on the corre-
sponding simulations. The absorption could not be measured ac-
curately , since the count rate changed on time scales of a few min-
utes due to sample drifts. In addition, the setup eﬃciency was
aﬀected by the cells’ heating power , as the nearby mirrors in the
beam path were slightly misaligned at high cell temperatures.
As the vapor temperature increases, also the delay of the pulse
increases as expected. All measured delays are accurately repro-
duced by the simulations. W e achieved a complete pulse delay
of (15.7 ± 0.1) ns. F or a comparison with the maximum delays
achieved in previous reports, the delay is considered indepen-
dent of the length of the vapor cell. The measured delay achieved
in our experiment of (1.05 ± 0.01) ns cm − 1 almost reaches the
highest value reported so far (1.08 ns cm − 1 [19] ), while clearly out-
performing other works (0.27 ns cm − 1 , [26] 0.36 ns cm − 1 , [18] and
a partial delay of 0.96 ns cm − 1 [17] ). The resulting transmission
of 29%—subsequently determined by a simulation—is compar -
atively high due to the narrow emission linewidth of the QD-
microlens. S imulations show that the transmission of a 150 mm
long Cs vapor cell at a temperature of 132.5 °C is at least 15%
0 5 10 15 20 25 30
0.1
0.2
0.3
y t i s n e t n i d e z i l a m r o N
Delay / ns
T Cs = 132.5°C
QD linewidth / GHz
1 2 3 4
5 6 7
8 9 10
Figure 7. Simulations of the photon delay in a 150 mm long Cs vapor
cell for diﬀerent QD linewidths. A spectral Gaussian emission line with
aF W H Mo f1 . 5 4G H za t + 840 MHz with respect to the Cs-D 1 -line is as-
sumed. The graphs are normalized so that the value of the global maxi-
mum of a curve corresponds to the total transmission of the pulse.
higher compared to values reported in ref. [19] (recalculated to
the same cell length) due to the signiﬁcantly smaller linewidth
in our experiment. Also, the group velocity dispersion (GVD) is
reduced accordingly . The signiﬁcant inﬂuence of the linewidth
on pulse-shape and absorption can also be seen in Fi g u re 7 ,
which shows the photon delay for diﬀerent line widths. On the
one hand, the previously described occurrence of an undelayed
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fraction for large linewidths can be observed. On the other hand,
the inﬂuence of the linewidth in the sub-GHz range manifests
itself in the decreasing transmission with increasing linewidth
and, in addition, the GVD depends strongly on the spectral width.
This results in a strong disturbance of the temporal pulse-shape
for linewidths > 2G H z .
4. C onclusion
In the present work, we explored light–matter coupling in a Cs
vapor cell, which allowed us to delay single photons emitted from
a deterministically fabricated QD-microlens. The latter were real-
ized by a 3D in situ EBL process by selecting bright QDs with suit-
able emission wavelength and integrating them in monolithic
QD-microlenses via a plasma etching step. This way , we enhance
the photon extraction eﬃciency of target QDs emitting at Cs-
D 1 line compatible wavelength. The excellent optical properties
of the fabricated SPSs are reﬂected in a narrow QD linewidth
of 1.54 GHz, being crucial for the interfacing of QD lines with
atomic vapor , as absorption and GVD are determined by this im-
portant property . Using detailed numerical simulations, the in-
ﬂuence of the spectral position and the linewidth of the QD emis-
sion on the resulting temporal shape of a light pulse after passing
through the Cs vapor was investigated for diﬀerent vapor temper -
atures in the range of 25 to 140 °C. It was shown that the local
maximum in the transmission of Cs vapor at + 840 MHz relative
to the Cs-D 1 line is superior to that at − 4085 and + 5067 MHz,
not only due to the broader spectral window , but also due to
the lower absorption for a given temporal delay . Based on the
simulations, it was possible to delay photons emitted by a QD-
microlens at a maximum of (15.71 ± 0.01) ns (corresponding
to (1.05 ± 0.01) ns cm − 1 ) under optimized experimental condi-
tions. M oreover , due to the narrow linewidth of the studied QD-
exciton of 1.54 GHz, the light pulse was completely delayed with
comparatively low absorption and a low distortion of the origi-
nal pulse shape due to the small group velocity dispersion. Our
results highlight the high potential of light–matter interaction
in dilute Cs vapor to control the propagation of single photons
emitted by deterministically fabricated quantum light sources. In
future, such precisely engineered quantum light emitters could
enable the realization of ﬂexible photon delay modules and
quantum memories with a variety of applications in photonic
quantum technology .
Acknowledgements
The authors acknowledge funding from the German F ederal Ministry of Ed-
ucation and Research (BMBF) through the VIP-project QSOURCE (Grant
No. 03V0630), the German Research F oundation via projects SFB787,
Re2974/9-1, and from the project EMPIR JRP 17FUN06 SIQUST (the EM-
PIR initiative is co-funded by the European Union’s Horizon 2020 research
and innovation program and the EMPIR Participating States). T .H. ac-
knowledges funding of the BMBF via the project QuSecure (Grant No.
13N14876) within the funding program Photonic Research Germany . The
authors at KIST acknowledge the support by IITP grant funded by the Ko-
rea government (MSIT) (No. 20190004340011001).
C onﬂict of Interest
The authors declare no conﬂict of interest.
Keywords
atomic vapors, delays, deterministic fabrication, quantum dots, single-
photon sources
Received: June 12, 2019
Revised: July 27, 2019
Published online: September 12, 2019
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