Strongly correlated photons on a chip
Andreas Reinhard,1, ∗Thomas Volz,1, ∗Martin Winger,1Antonio
Badolato,2Kevin J. Hennessy,1Evelyn L. Hu,3and Ata¸ c Imamo˘ glu1
1Institute of Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
2Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
3School of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138, USA
(Dated: August 16, 2011)
Optical non-linearities at the single-photon
level are key ingredients for future photonic quan-
tum technologies .Prime candidates for the
realization of strong photon-photon interactions
necessary for implementing quantum informa-
tion processing tasks  as well as for studying
strongly correlated photons [3, 4] in an integrated
photonic device setting are quantum dots em-
bedded in photonic crystal nanocavities.
we report strong quantum correlations between
photons on picosecond timescales.
(a) photon antibunching upon resonant excita-
tion of the lowest-energy polariton state, prov-
ing that the first cavity photon blocks the sub-
sequent injection events, and (b) photon bunch-
ing when the laser field is in two-photon reso-
nance with the polariton eigenstates of the second
Jaynes-Cummings manifold, demonstrating that
two photons at this color are more likely to be in-
jected into the cavity jointly, than they would oth-
erwise. Together, these results demonstrate un-
precedented strong single-photon non-linearities,
paving the way for realizing a single-photon tran-
sistor  or a quantum optical Josephson inter-
Cavity quantum electrodynamics (cQED) studies the
quantum limit of light-matter interaction where a sin-
gle two-level quantum emitter is coupled to a single cav-
ity mode . In the strong coupling regime of cavity-
QED where the coherent interaction strength between
the emitter and the cavity mode exceeds the dissipative
rates, the elementary excitations (polaritons) have an an-
harmonic spectrum (Fig. 1a).
system embodies the ultimate non-linear optical device
enabling the observation of photon-photon interactions
at the single-photon level . Various implementations
of cavity-QED systems have been reported with atoms
in high finesse cavities , with quantum dots (QDs) in
different types of monolithic cavities [9–12] and in the
microwave domain [13–15]. Recent experiments in the
optical domain using a single atom coupled to Fabry-
Perot  or toroidal cavities  have demonstrated the
As a consequence, this
∗These authors contributed equally to this work.
strongly coupled to a PC cavity. a) Non-linear Jaynes-
Cummings level scheme up to the second manifold. b) Sketch
of the experimental setup with crossed-polarized laser sup-
pression. c) On-resonance cw scattering spectrum for a probe
power of 1 nW. The black trace was recorded without the
additional re-pump laser. With the re-pump switched on, the
resonant signal from the polaritons is restored (red trace).
Resonant scattering spectroscopy of a QD
photon blockade effect by observing photon antibunch-
ing in correlation measurements. Photon bunching upon
two-photon excitation of the second Jaynes-Cummings
manifold has been observed for a single atom cavity-QED
system . In the solid-state, early results in quantum
dot (QD) cavity-QED systems indicating optical non-
linearities have been reported [19, 20].
Here, we show that a single QD deterministically cou-
pled to a photonic crystal (PC) defect cavity exhibits
pronounced photon antibunching as witnessed by a re-
duction in two-photon scattering events from the strongly
coupled polariton mode by more than 40 % upon reso-
nant excitation – a clear indication of photon blockade.
By tuning either the laser or the cavity mode frequency
to ensure resonant two-photon excitation of the higher
arXiv:1108.3053v1 [cond-mat.mes-hall] 15 Aug 2011
polariton states , we observe that the photon emis-
sion is strongly bunched with an increase in simultane-
ous two-photon scattering events by 50 %. Hence, we
demonstrate for the first time direct access to the second
manifold of the Jaynes-Cummings ladder in an integrated
solid-state photonic device.
By positioning an InAs/GaAs QD at an electric-field
antinode of a PC defect cavity in L3 geometry , we
achieve a coherent coupling constant g of 141 µeV. The
cavity has a quality factor Q of about 25 000, correspond-
ing to a cavity photon decay rate κ of 53 µeV. In order
to tune the cavity frequency, we employ a thin-film de-
position technique using nitrogen gas injection . A
crossed-polarization technique ensures efficient suppres-
sion of the excitation-laser light which is back-reflected
from the sample surface [23, 24]; the setup is sketched in
A large majority of QDs , as well as most other
solid-state based emitters such as NV centers , ex-
hibit the phenomenon of blinking, induced by sponta-
neous or induced change of the internal state of the QD,
and leading to an intermittent optical response. Experi-
mentally, we find that the fractional amount of time our
system spends in the neutral QD ground state strongly
decreases with increasing resonant probe power, and is
vanishingly small above 1 nW (see Supplementary Mate-
rial). Incident laser photons thus simply scatter off the
uncoupled cavity, resulting in a spectrum as shown in
Fig. 1c (black trace). In order to overcome this problem,
we use an off-resonant laser just below the edge of the
wetting layer to re-pump the QD into its neutral ground
state. By alternating re-pump and probe intervals, we
partly recover the polariton spectrum shown in Fig 1c
We carry out correlation measurements using resonant
pulses at a duration of Tpulse ≈ 72 ps (FWHM), yield-
ing a ratio between pulse length and polariton lifetime of
2·Tpulse≈ 2.9. Fig. 2 displays correlation histograms for
different laser/cavity detunings. The respective detun-
ings are indicated in the resonant scattering spectrum
shown in Fig 2a. We define the correlation function for
pulsed excitation at zero time delay g(2)
of the central peak divided by the average area of peaks
at other times (see Supplementary Material). First, we
choose the frequency of the pulsed laser to match the
upper polariton transition and obtain significant anti-
bunching with g(2)
pulsed(0) = 0.75 ± 0.06 (Fig. 2c). For
comparison, we turn off the re-pump laser and verify that
photons scattered from the uncoupled cavity mode have
Poissonian statistics (Fig. 2b). As a cross-check, we also
confirmed that the scattered photons from a resonantly
driven cavity mode that is far detuned from all QD tran-
sitions exhibit Poissonian statistics. These experiments
jointly demonstrate that the applied re-pump laser can
be used to switch on the single-photon non-linearity and
pulsed(0) as the area
laser detuning / g
cavity detuning / g
delay (ns)delay (ns)
00 -20 -20-40 -40 202040 40
bunched photon streams. a) Resonant scattering spec-
tra for different cavity detunings close to the neutral exciton
resonance. The circles indicate the detunings for which the
correlation histograms in b – e were taken. The vertical axes
in the histograms specify the photon coincidences per time-
bin of 192 ps. b) Autocorrelation histogram recorded on exact
cavity-exciton resonance without re-pump laser for a detuning
corresponding to the energy of the upper polariton. c) Au-
tocorrelation with the same detunings, but with a re-pump
laser applied. The scattered photons in this case exhibit pho-
ton antibunching. d) Autocorrelation on the lower polariton
for a blue detuning of the cavity of 0.68 g, where the longer
polariton lifetime ensures stronger photon antibunching. e)
Pronounced photon-bunching on the lower two-photon reso-
nance. Note that the small features at ≈ ±10 ns in b – e
originate from cross-talk between the APDs due to secondary
From Poissonian light to antibunched and
to control the statistics of the scattered photons. We
emphasize that the degree of photon antibunching ob-
served in the experiment is limited by the finite excitation
pulse length. Accordingly, a higher degree of antibunch-
pulsed(0) = 0.57 ± 0.02) is observed when the cav-
ity is off-resonant from the exciton, as shown in Fig. 2d
for the lower polariton in the case of blue-detuning of
the cavity mode; here the polariton state lifetime is pro-
longed, making multiple photon absorption events within
a single pulse less likely. Experimentally, we do not ob-
serve a difference between correlations recorded on the
upper and lower polariton if the respective laser and cav-
ity detunings from the exciton change their sign.
When tuning the laser photon energy to half the
energy of the lower polariton eigenstate of the sec-
ond Jaynes-Cummings manifold, we observe photon-
bunching. Fig. 2e displays a corresponding correlation
histogram with g(2)
pulsed(0) = 1.5 ± 0.1.
has its origin in a two-photon transition from the ground
state to the second manifold of the Jaynes-Cummings
ladder. We emphasize that the non-vanishing correla-
tions at zero time delay in the case of photon blockade,
and the moderate bunching-feature on the two-photon
transition have their origin mostly in the particular im-
plementation of the measurement using pulsed laser exci-
tation and slow single-photon detectors; in order to con-
firm that and to explain the principal experimental fea-
tures, we carried out numerical simulations of g(2)
using a Monte Carlo wave function (MCWF) approach
(see Supplementary Material).
counted for the pulsed laser excitation, the non-zero laser
background due to imperfect extinction of the laser re-
flection and the uncoupled cavity resonance due to the
blinking of the dot. Fig. 3a displays the resulting au-
tocorrelation function g(2)
pulsed(0) at zero time delay for
varying cavity and laser detunings.
Here, we directly ac-
In addition to the bunching features originating from
two-photon resonances, we would normally expect strong
bunching when the external laser that drives the cavity
mode is resonant with the bare exciton , as can be
seen in Fig. 3a (dotted vertical line). Unlike in previous
experiments , this bunching-feature is absent in our
experiments as well as in the simulations when the cav-
ity frequency is resonant with the bare QD exciton, since
for this detuning we predominantly detect photons from
instances when the QD remains charged and is thus off-
resonant. Conversely, our experiments demonstrate for
the first time that a coupled QD-cavity device realizes
the anharmonic Jaynes-Cummings model .
simulations, we assumed a pure QD dephasing rate of
¯ hγdeph = 13 µeV in addition to the cavity dissipation
rate κ, consistent with the polariton linewidths observed
in the experiment. This line broadening might stem from
charge fluctuations in the QD environment, partially in-
duced by the re-pump laser, and from phonon-induced
In Fig. 3b and 3c we probe the upper and lower
polariton branches for constant cavity detunings of
(−0.33 ± 0.04)g and (1.04 ± 0.03)g, respectively, by tun-
ing the laser wavelength.
photon correlations from strong antibunching to bunch-
ing maps out the (anharmonic) spectrum of the Jaynes-
Cummings ladder.In addition, we perform correla-
tion measurements for a varying cavity-exciton detuning
at a constant laser-exciton detuning of (0.94 ± 0.05)g,
demonstrating that the nature of strong photon correla-
tions can be tuned by changing either the laser or the
cavity mode frequency. The agreement between exper-
imental values and theoretical expectation is very good
The continuous change in
cavity detuning / g
laser detuning / g
cavity detuning / g
laser detuning / g
-1.0 -0.8 -0.6
laser detuning / g
ings. a) Results of a MCWF simulation close to the neutral
exciton-cavity resonance using experimental parameters de-
termined from linear resonant light scattering measurements.
The blue regions correspond to detunings with sub-Poissonian
statistics, whereas the red regions indicate photon-bunching.
Blue and red dashed lines denote the expected positions of
the polariton frequencies and the two-photon resonances, re-
spectively. The enhanced bunching feature along the dotted
vertical line at zero detuning is a consequence of an interfer-
ence effect, ensuring small occupancy of the cavity mode. The
bold dotted lines indicate the parameter ranges of the three
different data traces displayed in b – d. There, the red dot-
ted traces are the theoretical expectations from the MCWF
Calculated and measured autocorrelation
pulsed(0) for different cavity and laser detun-
in all cases; we emphasize in this regard that the the-
oretical curves provide a prediction based on indepen-
dently determined parameters. The dashed vertical lines
in Fig. 3b-d correspond to the polariton energy (blue)
and the energy of the two-photon transition to the sec-
ond manifold (red), indicating the origin of both the an-
tibunching and the bunching features.
An obvious extension of the results presented here in-
cludes non-linear optics experiments at the single-photon
level, e.g. the realization of a single-photon transistor
. Furthermore, our results elevate this system to an
ultimate optical non-linear building block for more com-
plex structures investigating strong photon correlations
in non-equilibrium settings, such as an optical Josephson
interferometer  or coupled arrays of non-linear cavities
[3, 4, 27]. In connection with recent progress on the fab-
rication of site-controlled QDs within arrays of photonic
crystal cavities  and the ability to tune QD transitions
by up to 25 meV in p-i-n structures , the present work
demonstrates the great potential of QD-cavity systems as
candidates for photonic quantum simulators.
This work is supported by NCCR Quantum Photon-
ics (NCCR QP), research instrument of the Swiss Na-
tional Science Foundation (SNSF) and an ERC Advanced
Investigator Grant (A.I.).
Carusotto for helpful discussions. The authors declare
that they have no competing financial interests. Cor-
respondence and requests for materials should be ad-
dressed to T.V. and A.I. (E-mail: firstname.lastname@example.org,
The authors thank Iacopo
Optical characterization is performed in a liquid he-
lium flow cryostat at a temperature T = 5 − 7 K. A
50× microscope objective (NA = 0.55) is used to illu-
minate the defect region of the PC with a spot size of
about 1 µm. Emitted photons are collected with the
same objective. After cooldown, the cavity luminesces at
a wavelength of around 935 nm, as determined with pho-
toluminescence spectroscopy. In order to tune the cavity
into resonance with the neutral exciton transition, a thin-
film deposition technique using nitrogen gas injection is
used. Even without active deposition of nitrogen, the
cavity mode shows an intrinsic red tuning at a rate up to
0.008 nm/hour. For resonant scattering experiments, we
excite the cavity mode with an actively power-stabilized
narrow bandwidth, mode-hop-free tunable diode laser.
The sample is mounted such that there is a 45◦angle be-
tween the polarization axes of the cavity mode and the
laser. By sending the collected light through a single-
mode fiber with mounted fiber-polarization controllers
and a subsequent analyzer, we have precise control over
the extinction of the reflected laser light. The photons
scattered off the cavity are detected with an avalanche
photo diode (APD) in single-photon counting mode.
Off-resonant re-pump scheme
For the off-resonant re-pumping of the system, we use
an additional cw titanium-sapphire laser at a wavelength
of 857.2 nm. Using an acousto-optical modulator (AOM)
we excite the QD with rectangular laser pulses at a repe-
tition rate of 0.5−1 MHz. In between the re-pump pulses,
we probe the system by triggering the APD readout.
For photon correlation measurements, we replace the
cw probe light by resonant pulses from a mode-locked
titanium-sapphire laser in ps mode, with a repetition rate
of 76.3 MHz. In order to filter the broadband pulses we
send them through a 750 mm grating spectrograph and
couple the diffracted light into a single-mode fiber. The
transmitted pulse is approximately Gaussian with a typ-
ical width of 0.018 nm. Using a streak camera we con-
firm that the resulting pulses have near-Fourier-limited
durations of about 72 ps. The dependence of photon cor-
relations on the laser frequency are obtained by rotating
the grating of the spectrograph and consequently filter-
ing out different parts of the pulse spectrum. Measure-
ments depicting the dependence of photon correlations
on the cavity resonance frequency on the other hand are
carried out by exploiting an intrinsic cavity wavelength
drift of about 0.006 nm/h while keeping the laser fre-
quency fixed. We perform autocorrelation measurements
with a Hanbury-Brown and Twiss set-up, consisting of a
50:50 beam splitter and an APD at each output. Photon
arrival time differences are determined with a time-to-
amplitude converter and plotted in a histogram.
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 Photon antibunching can also be observed when the cou-
pled emitter-cavity system is not in the strong coupling
Laser-induced quantum dot blinking
In resonant spectroscopy, far below saturation psatof
the system, the detection rate of scattered photons is ex-
pected to grow linearly with excitation power pexc. In
stark contrast, we observe highly nonlinear power de-
pendencies at picoWatt (pW) level, which is five or-
ders of magnitude smaller than the cw saturation power
psat ≈ 850 nW (for an estimated 2 % laser-cavity cou-
pling). The polariton signal saturates at pexc≈ 10 pW,
whereas the uncoupled cavity resonance appears at the
same power level with a super-linear power dependence,
as seen in Fig. S 4a. We attribute this behaviour to
laser-induced QD-blinking, which could originate from
relaxation of optically excited QD states either into a
dark exciton or an electron (hole) charged state. The re-
sulting long-lived states (denoted by |h? in Fig. S 4b shift
the exciton resonance off the cavity frequency, such that
the cavity resonance becomes uncoupled from QD reso-
nances. For excitation powers below 5 pW, only the po-
laritons appear in the spectrum. For increasing incident
optical power, however, the laser-induced charge/spin-
pumping causes a reduction of neutral ground state oc-
cupation such that the polariton signal saturates. Above
pexc ≈ 100 pW, the bare cavity resonance completely
dominates the spectrum.
We determine the average lifetime of these long-lived
charged/dark QD states as well as the neutral ground
state lifetime, by measuring the second order auto-
correlation function of the uncoupled cavity and the po-
laritons, respectively. By extracting the lifetimes from
the correlation traces, like the ones shown in Fig. S 5a, we
identify the metastable charged/dark QD state lifetimes
to be of several ms. In contrast, the neutral ground state
lifetime is about ≈ 300 µs for pexc= 10 pW, with a signif-
icant reduction for higher excitation powers, as shown in
Fig. S 5b . This is consistent with our assumption and
motivates the use of a non-resonant re-pump laser that
randomly re-shuffles the internal QD state. We imple-
ment this strategy by exciting the system just below the
wetting-layer resonance and observe a relaxation proba-
bility into the neutral ground state of 0.3 − 0.4. Using a
pump-probe scheme, we are able to partially suppress the
influence of blinking and obtain a time-integrated spec-
trum that exhibits a three-peak feature (see Fig. 1c in
the main text).
Finally, we emphasize that the blinking observed in
our QD-cavity system is by no means unique and is ob-
served by most groups working with such systems [2, 3].
Depending on the particular device, however, the effect
is more or less pronounced .
FIG. S 4:
onance. a) At a resonant probe power of 3.2 pW only the
polaritons are observed. For increasing excitation powers, the
uncoupled cavity mode dominates the spectrum, while the po-
lariton peaks saturate. b) Level scheme: pumping of charged
or dark neutral states |h? occur when the polaritons are ex-
cited. The recovery rate into the neutral ground state Γh−0
is below 103s−1. c) Power dependent peak height of the un-
coupled cavity resonance, which provides a direct measure of
charged/dark state occupation.
Low power spectra on cavity-exciton res-
FIG. S 5: Lifetimes of the neutral quantum dot ground
state and the charged/dark states. a) Auto-correlation
traces on the lower polariton resonance (black trace) and the
uncoupled cavity resonance (red trace) at a probe power of
15 pW. The lifetime ratio reveals that the system spends an
order of magnitude more time in a state other than the neutral
ground state due to laser-induced charge/spin pumping. b)
Lifetimes of the neutral ground state (black trace) and the
charged/dark states (red trace) as a function of excitation
Determination of second order correlations at zero
The second order auto-correlation function g(2)(τ)
provides a direct measure of the statistics of emitted
light. The degree of antibunching or bunching is simply
given by the value at zero time delay g(2)(0). When the
cavity is resonant with the exciton, we expect g(2)(0) =
0.34 on the lower polariton according to a simulation us-
ing our experimental parameters. The width of the dip
/ peak in g(2)(τ) is given by the polariton state lifetime,
which is in our case on the order of tens of ps. Since
the APDs we use have a much higher timing jitter, they
cannot be used to measure g(2)(0) under cw laser exci-
tation. In order to overcome this limitation, we measure
the auto-correlation function by exciting the system with
short resonant pulses with a pulse-width similar to the
polariton lifetimes. We define g(2)
the central peak divided by the average area of peaks at
other times. In order to have a realistic comparison be-
tween theory and our experimental data, we use a Monte
Carlo wave function (MCWF) approach to obtain an es-
timate of g(2)
pulsed(0) as the area of
A theoretical estimate of g(2)
pulsed(0) we measure is given by
dt2I (t1)I (t2)
where G(2)(t1,t2) = ?g|ˆC†(t1)ˆC†(t2)ˆC (t2)ˆC (t1)|g?,
I (t) = ?g|ˆC†(t)ˆC (t)|g?, and Trepis the time difference
between two laser pulses. Here, |g? denotes the system
ground state, before a laser pulse has excited the sys-
tem. The system collapse operatorˆC (t) =
evolves according to the non-Hermitian effective Hamil-
tonian (in the interaction picture with the rotating frame
of the laser center frequency) Heff(t) = HJC+Hint(t)−
ton annihilation operator and ˆ σ+, ˆ σ−are the exciton cre-
ation and annihilation operators.
Cummings Hamiltonian and Hint =
notes the interaction with the Gaussian laser pulse,
Ω(t) = Ω0exp
−2 ln(2)t2/ T2
ity dissipation rate, γ the exciton spontaneous recombi-
nation rate and γdeph the exciton pure dephasing rate;
the latter may stem from phonon mediated coupling of
the two dressed polariton states. In order to determine
G(2)(t1,t2) and I (t), we use a Monte Carlo wavefunc-
tion approach, as described in Ref. . The calculations
are performed with the experimentally determined val-
ues, λexciton= 937.25 nm, ¯ hg = 141 µeV, ¯ hκ = 53 µeV,
¯ hγ = 0.66 µeV, and ¯ hγdeph= 13 µeV. For a typical pulse
duration of 72 ps (FWHM), a pulse energy of 82 eV and
an estimated laser – cavity coupling efficiency of 2 %, we
obtain ¯ hΩ0≈ 24 µeV.
√κ ˆ a(t)
?κ ˆ a†ˆ a + γ ˆ σ+ˆ σ−+ γdeph
?, where ˆ a is the cavity pho-
HJC is the Jaynes-
?ˆ a + ˆ a†?
. κ denotes the cav-
In the experiments, the suppression of the non-
interacting reflected laser light is not perfect (≈
50 000), and consequently, our measurements are sub-
ject to interference effects between cavity emission and
laser light. Possible reasons for incomplete suppression
are a mixing of polarization states when the light tra-
verses the collection fiber or the analyzer, or depolariza-
tion effects due to the reflection at the photonic crys-
tal membrane. We take the phase difference φ between
the laser light that drives the Jaynes-Cummings system
and the non-interacting (reflected) laser to be φ = −π/2;
this value corresponds to the (experimentally optimized)
largest ratio between detected cavity photons and laser
background. We emphasize that we have a control over
both the amount of laser suppression and the phase dif-
ference φ, by the use of fiber-polarization controllers.
As described in the previous section, the system is in
the desired neutral ground state in only r = 30−40 % of
the cases in average. Experimentally, we cannot distin-
guish between on- and off-resonant cases, and the result-
ing correlation function is a sum of both on-resonant and
the Poissonian off-resonant correlation functions. Thus,
at zero time delay
pulsed(0) + (1 − r)E2
on+ (1 − r)E2
where Eonis the average detected energy per pulse of the
Jaynes-Cummings system, as described above, and Eoff
the respective pulse energy of the uncoupled cavity emis-
sion, together with the non-interacting laser light back-
ground. Close to the cavity-exciton resonance, g(2)
should exhibit a bunching peak on the exciton transi-
tion (see Fig. S 6a). This bunching-feature is absent in
pulsed(0) (Fig. S 6b) due to the predominant detection
of photons scattered from the uncoupled cavity mode.
For the rest of the discussion here and in the main text,
we will omit the tilde and refer to equation (2) as the
definition of correlations at zero time delay.
Simulations on the lower polariton reveal a reduction
of the non-classical part
pulsed(0) − 1
repeated photon absorption/emission events within a sin-
gle laser pulse, excitations of more than one resonance
due to the broad pulse spectrum and the large laser-
cavity coupling with Ω0<
∼κ. For Fourier-limited Gaus-
sian laser pulses, we find a minimum of g(2)
for a laser pulse duration of about 50 ps, as shown in
Fig. S 7a. In the experiments, we measure the spec-
trally filtered pulses to have slightly larger durations of
Tpulse≈ 72 ps. This corresponds to a ratio between pulse
duration and polariton lifetime ofκ
???. The reasons are
pulsed(0) = 0.75
2·Tpulse≈ 2.9. For in-
laser detuning / g
emitted photons / pulse
laser detuning / g
emitted photons / pulse
FIG. S 6: MCWF simulations on cavity-exciton reso-
nance. a) Assuming that there is no QD-blinking, the system
spectrum exhibits only the two polariton peaks (black line).
There is a strong bunching peak for zero laser-exciton detun-
ing in g(2)
with QD-blinking (r = 0.4) yield a spectrum (in time average)
with a three-peak feature (black line); the middle uncoupled
cavity peak causes the bunching feature in ˜ g(2)
pulsed(0) (red line). b) Simulations of the real system
pulsed(0) to vanish
pulse duration (ps)
0 50100150 200250
pulse energy (eV)
FIG. S 7:
parameters. Blue traces indicate probing of the lower po-
lariton and red traces the lower two-photon resonance. a)
ergy of 82 eV. b) g(2)
72 ps pulses.
Simulations of g(2)
pulsed(0) for different pulse
pulsed(0) as a function of pulse duration for a fixed pulse en-
pulsed(0) as a function of pulse energy for
creasing pulse energy, the calculated
creases, as shown in Fig. S 7b. We typically work with
pulse energies between 40 and 100 eV, which corresponds
to 0.6 − 1.5 scattered photons per pulse on laser-cavity
resonance for the estimated coupling efficiency of 2 %.
pulsed(0) − 1
The efficiency of the generation of non-classical light
improves with a slight cavity-exciton detuning. A blue
detuning of the cavity by g with respect to the exciton
resonance yields g(2)
pulsed(0) = 0.63 for the lower polari-
ton. This reduction in g(2)
pulsed(0) originates predomi-
nantly from the prolongation of the polariton lifetime
which reduces the likelihood of multiple photon absorp-
tion events within a single pulse.
 When comparing polariton and cavity lifetimes in Fig.
S 5b, we would expect efficient emission from the uncou-
pled cavity already at 5 pW. However, cavity emission is
strongly suppressed, since an initial polariton excitation is
required to bring the QD into a charged/dark state.
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 Cassabois, G. personal communication, (2011).
 Faraon, A. et al. Coherent generation of non-classical light
on a chip via photon-induced tunneling and blockade. Na-
ture Physics 4, 859-863 (2008).
 Molmer, K. et al. Monte Carlo wave-function method in
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