Coherently driven non-classical light emission from a quantum dot

Abstract

Narrow line-widths and the possibility of enhanced spontaneous emission via coupling to microcavities make semiconductor quantum dots ideal for harnessing coherent quantum phenomena at the single photon level. So far, however, all approaches have relied on incoherent pumping, which limits the desirable properties of the emission. In contrast, coherent excitation was recognized to be necessary for providing both improved photon indistinguishability and high efficiency, and offers the quantum control capabilities required for basic qubit manipulations. Here we achieve, for the first time, resonant and coherent excitation of a quantum dot with simultaneous collection of the non-classical photon emission. Second-order correlation measurements show the unique signature of a coherently-driven two-level quantum emitter: the photon statistics become oscillatory at high driving fields, reflecting the coherent evolution of the excitonic ground state of the quantum dot.

Full text

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Coherently driven non-classical light emission
from a quantum dot

A. Muller,1 E. B. Flagg,1 P. Bianucci,1 D. G. Deppe,2 W. Ma,3 J. Zhang,3 G. J.
Salamo,3 and C. K. Shih1*
1Department of Physics, The University of Texas at Austin, Austin, TX 78712
2College of Optics and Photonics (CREOL), University of Central Florida, Orlando,
FL 32816
3Department of Physics, University of Arkansas, Fayetteville, AR 72701

Dated: 07/25/07

Narrow line-widths and the possibility of enhanced spontaneous emission via
coupling to microcavities1-6 make semiconductor quantum dots ideal for
harnessing coherent quantum phenomena at the single photon level7. So far,
however, all approaches have relied on incoherent pumping8-11, which limits the
desirable properties of the emission. In contrast, coherent excitation was
recognized
indistinguishability and high efficiency8-10, and offers the quantum control
capabilities required for basic qubit manipulations12-14. Here we achieve, for the
to be necessary for providing both improved photon
first time, resonant and coherent excitation of a quantum dot with simultaneous
collection of the non-classical photon emission. Second-order correlation
measurements show the unique signature of a coherently-driven two-level
quantum emitter15: the photon statistics become oscillatory at high driving
fields, reflecting the coherent evolution of the excitonic ground state of the
quantum dot.

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One of the most elementary features of the light emitted by two-level quantum
emitters is photon anti-bunching15,16, i.e. the tendency of photons to be emitted one by
one, rather than in bunches. Observation of this purely non-classical effect in solid-
state systems such as semiconductor quantum dots11,17 (QDs) has aroused a great deal
of attention in recent years because it demonstrates their suitability for advanced
single photon experiments. QDs additionally benefit from recent advances in
micropillar1-3, microdisk4,5, and photonic-crystal defect6 cavity-coupling for efficient
light extraction. Therefore, a number of quantum optical and quantum electrodynamic
phenomena, familiar from atomic physics, that have wide implications in quantum
information processing applications, could in principle be realized in monolithic,
scalable solid-state systems.
An important distinction between single-atom and solid-state quantum light
sources, however, is that the former are excited resonantly and can therefore be
driven coherently by a laser15,16. This coherent control substantially shapes the non-
classical light emission and is also a key capability in successful approaches to
deterministic single photon generation with atoms18,19 and ions20. The indirect
excitation via continuum or quasi-resonant states in QD-based sources7 can efficiently
pump the emitters, but not coherently. True resonant excitation and collection of the
light has not been demonstrated yet, although it is well-known that quantum
interference21 and Rabi oscillations12-14,22,23 can be achieved in QDs. Extracting the
single photons generated by an individual QD that is resonantly driven by strong laser
fields has been challenging because of sizable laser scattering in the host crystal that
blinds the single photon detection. Thus, so far, QD states have been either probed
coherently using non-linear optical techniques without collecting the single photon
response12,13,24, or they have been pumped incoherently via an excited state8-11.
Based on a new approach to this problem that utilizes a micro-cavity, we show
here that a single QD can in fact be coherently driven in resonance fluorescence. The
micro-cavity decouples the wave-guided excitation field, introduced in-plane, from
the photon emission resonant with a vertical, or Fabry-Perot cavity mode. In the
strong-excitation regime fast oscillations coherently induced in the dot by the
excitation field profoundly influence the photon statistics. In particular, under

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continuous wave (CW) excitation, the second-order correlation function, as measured
with a high-resolution Hanbury-Brown and Twiss (HBT) setup, exhibits coherent
oscillations at the Rabi frequency, markedly different from the basic anti-bunching
”dip” observed in non-resonant experiments15. These results lay the foundation for a
number of very general quantum optical control capabilities which call for
simultaneous extraction of light. For example, similarly coherent pulsed excitation
could form the basis for a deterministic solid-state single photon source.
laser
emission
(PL)
0
1
2
relaxation
Photoluminescence
(PL) / Excitation (PLE)
spectroscopy:
laser
emission
(“resonance
fluorescence”)
0
1
2
True resonant
excitation:
a
b

Figure 1 Energy level diagram for a quantum dot. a, in photoluminescence spectroscopy.
b, in resonance fluorescence. State 0 denotes the excitonic vacuum, 1 is the excitonic
ground state (one electron-hole pair), and 2 is the first excited state of the dot.

Conventional photoluminescence (PL) or photoluminescence excitation (PLE)
spectroscopy (Fig. 1a) naturally relies on fast intra-band carrier relaxation: even when
the laser is brought in resonance with an excited state of the dot or with the
continuum, emission still primarily occurs from the lowest excitonic state. This is in
contrast to true resonant excitation (Fig. 1b), when the laser is exciting the same state
from which emission occurs. In order to detect this “resonance fluorescence”, self-
assembled InGaAs QDs were grown epitaxially between two distributed Bragg
reflectors (Fig. 2) making up a two-dimensional micro-cavity that supports both
waveguide modes and Fabry-Perot modes. While the sample is maintained at low
temperature in a liquid helium cryostat, a single mode optical fibre, mounted on a
three-axis inertial walker, is brought within a few microns of the cleaved sample
edge. Through this fibre, a tunable CW Ti:Sapphire laser is launched into a

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Lower mirror
Upper mirror
Cleaved
sample
edge
Quantum dot
Fibre
laser
Coupled fluorescence
GaAs substrate ~8 K
Waveguide
mode
Fabry-Perot
mode

Figure 2 Experimental setup for orthogonal excitation and detection. The sample,
attached to the cold finger of a liquid He cryostat, is excited from the side with a tunable CW
laser that is introduced via a single mode optical fibre. The QD emission coupled to a Fabry-
Perot mode of the cavity is efficiently extracted in the orthogonal direction.

waveguide mode of the cavity to excite the dots. The QD emission is spectrally
coupled to a Fabry-Perot mode of the cavity and collected by a micro-PL setup
equipped with a two-dimensional charge coupled device (CCD) detector mounted on
an imaging spectrograph. We focus here on QDs coupled to a cavity mode centered at
~915 nm. When the laser frequency is scanned over the excitonic ground-state of a
single QD, the resonance fluorescence is observed as a bright peak in the CCD
images, localized both spectrally and spatially. The intensity ratio between the QD
emission and residual laser scattering can be as high as 1000:1 due to the
orthogonality of the waveguide and Fabry-Perot modes. The laser bandwidth is less
than 40 MHz, narrow enough that the total integrated fluorescence intensity as a
function of detuning measures the homogeneous line-width of the ground state
transition (Fig. 3). For this particular dot we obtain a full width at half maximum
(FWHM) of 5.1 µeV (
ps 250
2=
T
) at 7 K.
The measurements described above demonstrate that the resonant emission
from a QD ground state can be extracted essentially background-free while the dot is
being coherently driven. Under strong, resonant CW excitation, the Rabi frequency
Ω= µE0 resulting from the field-dipole interaction can easily exceed the narrow
homogeneous line-width of the dot, given by
2
/ 1 T . Here µ denotes the transition

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-10
Laser energy
0 10
( eV
µ
20
)
Intensity (a.u.)
eV
µ
1 . 5
eV
µ
1
<Ω
h

Figure 3 Spectral lineshape. The time-integrated emission from a single QD is collected
while the exciting laser frequency is scanned over the ground state QD resonance. For this
dot we obtain a FWHM of 5.1 µeV.

dipole moment and
0
E is the amplitude of the exciting field. This harmonic driving
field (frequency ω ) may in general be detuned from the QD transition (resonance
frequency ω0) by an amount ∆ω =ω −ω0. Throughout, we model the QD as a two-
level system composed of a lower state with no exciton, denoted by 0 , and an upper
state, denoted by 1 , in which the dot contains one exciton in its ground state.
The evolution of this system follows the optical Bloch equations which treat
the excitation field classically and assume a dipole interaction with the QD25. The
rotating wave approximation simplifies the equations so that the populations of the
upper and lower states, ( ) tnm
and ( ) t
, and the coherence, ( ) t
α
, are described by:
1
)(
))(*)((
2
)(
T
tn
ttitn
dt
d
−−
Ω
−=
αα
(1)
d
dtα(t) = −iΩ
( ) 1
=
t
and the phenomenological constants T1 and T2 are respectively
2(n(t)− m(t))+ iα(t)∆ω −α(t)
T2
(2)
where ( )
+
mtn
the population decay time and dephasing time. These equations have oscillatory
solutions, which are the well-known Rabi oscillations, and decay with a time
constantT2. Under CW excitation a quasi-steady-state situation is quickly established,
and the corresponding expectation values for the population and coherence are
obtained from Eq. (1) and (2) as:

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n∞(∆ω) =1
2
Ω2T1/T2
−2+ Ω2T1/T2
1/T2+ i∆ω
∆ω2+ T2
∆ω2+ T2
(3)
α∞(∆ω) =iΩ
2
−2+ Ω2T1/T2
(4)
Since the time-averaged fluorescence intensity is proportional to the population,
n∞(∆ω), well-known saturation and power-broadening phenomena can be derived
from equation (3). On resonance (∆ω = 0), the low intensity limit of the line-width
equals
2
/2 T , and saturation occurs when the square Rabi frequency,
2
Ω , is much
greater than the value of (T1T2)−1. The experimental data in Fig. 4 show the evolution
with Rabi energy and serve as a measure of the excitation intensity (the data provide
the proportionality constant between
2
Ω and the laser intensity). The dephasing time,
2 T , determined from the line-width is 250 ps.
4
8
Square Rabi energy
Linewidth (μ eV)
0510
15
eV)(
2
µ
0
b
Intensity (a.u.)
a

Figure 4 Steady-state properties. a, Saturation of the time-integrated emission occurs as the
system enters the strong excitation regime. b, Power broadening of the spectral lineshape. The
excitation linewidth, extracted from lineshapes such as the one shown in Fig. 2, is plotted as a
function of square Rabi Energy.

Despite the steady-state excitation and emission intensity, the single QD
continues to dynamically evolve due to the excitation field. The information of this
evolution, however, is contained in the time-dependent characteristics of the emission
and requires the measurement of correlations. The first-order correlation function, for

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instance, whose Fourier transform is the power spectrum, has been described by
Mollow25 and leads to a well-known spectral triplet. This “Mollow triplet” reflects the
coherent population oscillations at the Rabi frequency Ω that the two-level system
undergoes under sufficiently strong driving fields, leading to sidebands at
frequencies
Ω±
ω
.
The second-order correlation function, which we measure here, is particularly
important in the context of single photon emission. Motivated by the realization of a
high-efficiency, high-speed single photon source based on a QD, second-order
correlation measurements have been reported in a number of contexts in the past few
years. These are typically performed with a HBT setup11,17 in which two fast photo-
detectors and time-counting electronics measure the arrival time difference between
photons emerging from a 50/50 beam splitter. If the emission originates from a single
quantum emitter, the single photon can only take one of the two beam splitter ports
and thus there will be no coincidence counts at zero time delay. This photon “anti-
bunching” stands as an important benchmark for single photon sources.
Despite interest in coherent quantum optical devices, all QD anti-bunching
measurements reported to date have relied on non-resonant, incoherent excitation of
the dots. Observation of an anti-bunching dip does not, in fact, require coherence: it
can be recorded at room temperature26 and under completely incoherent excitation,
such as electrical injection27. CW second-order correlations from a coherently-driven
single emitter, however, reveal a distinct oscillatory signature at high intensities, in
addition to photon anti-bunching. The second order correlation function can be
obtained from
〉++〈=
++
)()()()(),(
) 2(
τττττ
btbtbbtg
, where b and b+ are the field
operators. These are proportional to the QD dipole operators 0 1 and 1 0 ,
respectively25, and we obtain (
0
=∆ω
)28:
)}sin(
'
2/ )
2
T
/ 1
Ω
/ 1 (
){cos(1)(
1
)
11
T
(
2
1
2
21
t
T
t aetg
T
Ω′
+
+ Ω′−=
+−
(5)
where
2
21
2
)
11
T
(
4
1
T
−−Ω= Ω′
and a accounts for a constant background
correction. When
2
/ 1 T
<<Ω
, Eq. (5) reduces to the familiar anti-bunching dip, whose

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-1-1 -1000111222
Time (ns)Time (ns)Time (ns)
0.20.2 0.2
0.6 0.60.6
1.01.0 1.0
g(2)(t)
0.60.60.6
1.01.01.0
0.60.60.6
1.01.01.0
0.60.60.6
1.01.01.0
0.60.60.6
1.01.01.0
0.60.60.6
1.01.01.0
eVeVeV
µµµ
2 . 1
<
2 . 1
<
2 . 1
<ΩΩΩ
hhh
hΩ= 4.0µeV
hΩ= 4.9µeV
hΩ= 6.5µeV
hΩ=9.2µeV
hΩ=11.2µeV
T=7 KT=7 KT=7 K
g(2)(t)
hΩ= 4.0µeV
hΩ= 4.9µeV
hΩ= 6.5µeV
hΩ=9.2µeV
hΩ=11.2µeV
g(2)(t)
hΩ= 4.0µeV
hΩ= 4.9µeV
hΩ= 6.5µeV
hΩ=9.2µeV
hΩ=11.2µeV

Figure 5 Second-order correlation function. g(2)(t) is recorded with a Hanbury-
Brown and Twiss setup for various excitation amplitudes.

width, however, is now determined by both
1 T and
2 T . This is unlike the incoherent
situation, where the width of the notch is usually assumed to be given only by
1 T .
When
2
/ 1 T
>>Ω
, on the other hand, there are oscillations that persist within a time
2 T . These oscillations originate in the coherent population oscillations that the dot
undergoes, and are the same that give rise to the Mollow triplet25,28. Since the field
creation and annihilation operators are proportional to the atomic operators, the dot’s
population oscillations result in a photon state that in general is in a superposition of
vacuum and single photon states. Upon detection of a “start” photon at one of the
beam splitter outputs in the HBT setup, the system is guaranteed to be in the ground
state. Therefore, the arrival probability of a “stop” photon at the other output
measures the amplitude in the superposition state of a photon that had evolved

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coherently with the field for a time t, the delay between the two detections.
Mathematically, this can be understood from a factorization of the second-order
correlation function into two parts16,29: the mean steady-state intensity from the QD,
∞
n , and the mean time-dependent intensity, )(tn
, from a QD that started in the
ground state at 0
=
t , due to a quantum “jump” into the ground state immediately
following photon emission.
We observe these exact features in our experimental measurements. A high-
resolution HBT setup (~80 ps time resolution) is used to measure the second order
correlation function of the light emitted by the same dot as in Fig. 3 and Fig. 4. In Fig.
5 it is plotted for various excitation amplitudes, increasing from bottom to top. The
anti-bunching evolves into the oscillatory function described by Eq. (5), with a
frequency increasing with excitation amplitude. At the highest intensity, several
periods of oscillations are clearly visible. In these measurements (~30 min integration
time), no spectral filter was used, but a confocal aperture in the collection path
spatially filtered the emission from nearby dots. The residual laser scattering, which
by itself gives rise to a constant second order correlation function, was subtracted
from the raw data. At the lowest (highest) intensity shown, this contribution was 5%
(30%). The corrected data were then fit using Eq. (5) and the extracted Rabi energies
are displayed in Fig. 5. The decay times used for the fit were
ps 350
1=
T
and
ps 250
2=
T
. Better quantitative assessment will require separate direct measurements
of
1 T , for example using time resolved single photon counting. Nonetheless,
12
2TT <

is frequently reported from QDs, and might be due to elastic contributions from
exciton-phonon scattering or to measurement inhomogeneities, such as spectral
diffusion, that occur on time scales faster than our acquisition times (~1 s). If loss of
coherence was only due to radiative processes we would expect
12
2TT =
.
The possibility of coherently controlling the photon emission from a single
solid-state emitter offers new opportunities for quantum information applications. For
example, almost all proposed schemes for implementing basic qubit-photon interfaces
strictly require resonant coherent control with simultaneous extraction of the photons.
Together with cavity quantum electrodynamics, coherent control is also necessary for

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deterministic single photon sources with high efficiency and indistinguishability8,
based on recent results with trapped atoms and ions18-20. Such realization will
necessitate extending the techniques presented here to pulsed excitation and QDs in
three-dimensional micro-cavities, in which the cavity can substantially modify the
dots’ emission properties. This could be achieved with the all-epitaxial micro-cavities
described in Ref. 30 which are ideally suited to introduce a wave-guided laser, but also
with photonic crystal defect micro-cavities, or microdisks using the correct geometry.
In conclusion, we have demonstrated coherently controlled non-classical light
emission from a single QD in a planar micro-cavity. The cavity is used to extract the
light emitted at the same frequency as the strong excitation laser, nearly background-
free. Consequently, the second-order correlation function of this single QD resonance
fluorescence could be measured both in the weak and strong excitation regime. When
the Rabi frequency exceeds the decoherence rate of the dot, the coherent oscillations
are directly visible in the second-order correlation function as high frequency
oscillations. These results are a first step towards a coherently driven single photon
source with both high efficiency and indistinguishability.

Acknowledgements
The authors acknowledge financial support from the National Science Foundation
(DMR-0210383 and DMR-0606485 and DGE-054917), and the W. Keck foundation.

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*To whom correspondence should be addressed. shih@physics.utexas.edu
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