arXiv:0707.3311v2 [quant-ph] 27 Jul 2007
Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system
Kartik Srinivasan1, ∗and Oskar Painter2, †
1Center for the Physics of Information, California Institute of Technology, Pasadena, CA
2Thomas J. Watson, Sr., Laboratory of Applied Physics,
California Institute of Technology, Pasadena, CA 91125
(Dated: February 1, 2008)
A fiber taper waveguide is used to perform direct optical spectroscopy of a microdisk-quantum-dot system,
exciting the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong
coupling, the regime of coherent quantum interactions, is demonstrated through observation of vacuum Rabi
splitting in the transmitted and reflected signals from the cavity. The fiber coupling method also allows the
examination of the system’s steady-state nonlinear properties, where saturation of the cavity-QD response is
observed for less than one intracavity photon.
Cavity quantum electrodynamics1, the study of coherent
quantum interactions between the electromagnetic field and
matter inside a resonator, has received attention as both a
testbed for ideas in quantum mechanics and also as a build-
ing block for applications in the field of quantum information
processing2. The canonicalexperimentalsystem studied in the
optical domainis a single alkali atom coupledto a high-finesse
Fabry-Perot cavity. The tremendous progress made in this
system1,2,3,4,5has been complemented by recent research in-
volving trapped ions6, chip-based microtoroid cavities7, inte-
coupled to microsphere cavities9, and semiconductor quan-
tum dots embedded in micropillars, photonic crystals, and
microdisks10,11,12. The latter system has been of particular in-
terest due to its potential simplicity and scalability. In con-
trast to preceding work with semiconductor systems, which
has focused on photoluminescence measurements10,11,12,13,14,
here we use a fiber taper waveguide to perform direct opti-
cal spectroscopy of a microdisk-quantum-dotsystem, exciting
the system throughthe photonic (light) channel rather than the
excitonic (matter) channel. Strong coupling, the regime of co-
herent quantuminteractions, is demonstratedthroughobserva-
tion of vacuum Rabi splitting in the transmitted and reflected
signals from the cavity. The fiber coupling method also allows
us to examine the system’s steady-state nonlinear properties,
where we see a saturation of the cavity-QD response for less
than one intracavity photon. The excitation of the cavity-QD
system through a fiber optic waveguide is key for applications
such as high-efficiencysingle photonsources15,16, and to more
fundamental studies of the quantum character of the system17.
In the most simplified picture, cavity quantum electrody-
namics (cQED) consists of a single two-level atom (or equiv-
alent) coupled to an electromagnetic mode of a cavity. A
more realistic picture includes dissipative processes, such as
cavity loss and atomic decoherence, and excitation of the sys-
tem, either through the atomic or photonic channel. The ob-
served system response is dependent on both which channel
is excited, and what signal is measured. Previous demonstra-
tions of strong coupling between semiconductormicrocavities
∗Electronic address: firstname.lastname@example.org
†Electronic address: email@example.com
and quantum dots (QDs)10,11,12,13,14used non-resonantoptical
pumping to excite the QD stochastically and photolumines-
cence (PL) to probe the system behavior. In this work we ex-
cite the system coherently through the photonic channel, and
detect signatures of cavity-QD coupling in the resonant opti-
cal response. Such optical spectroscopy is commonplace in
atom-Fabry-Perot systems1, but is more problematic in semi-
conductor microcavities due to the comparative difficulty in
effectively coupling light into and out of sub-micron struc-
tures. Toeffectivelyinterfacewiththecavity,we useanoptical
fiber taper waveguide18. Fiber tapers are standard glass optical
fibers that have been heated and stretched to a diameter at or
below the wavelength of light, at which point the evanescent
field of the guided mode extends into the surrounding air and
allows the taper to function as a near-field optic7,19,20,21.
The experimental setup used is shown schematically in Fig.
1(a)-(b). At its core is a customized liquid He cryostat22in
which piezo-actuated stages have been integrated to incorpo-
rate optical fiber taper testing while maintaininga sample tem-
perature as low as 12 K. External cavity tunable lasers op-
tically pump the QD and probe the cavity-QD system near-
and transmitted signals to photodetectors and a spectrometer.
The overall transmission of the fiber taper link is 50% in this
work, and in many cases can be ? 90%, providinga very low-
loss optical channel to probe the system. This allows for the
accurate estimation of quantities such as average intra-cavity
sion of the taper waveguide when coupled to the cavity.
The system under investigation consists of InAs QDs em-
bedded in a GaAs microdisk cavity. The InAs QDs are grown
in a self-assembled manner with a density of 300−500 µm−2
on top of an InGaAs quantum well (a so-called dot-in-a-well,
or DWELL23). The DWELL structure resides in the mid-
dle of a 256 nm thick GaAs layer that forms the thin pla-
nar layer of the microdisk (see Fig. 1(c)). Previous studies
of this material24indicate that isolated emission from single
QDs at cryogenic temperature can be seen in the wavelength
range λ = 1290-1310 nm, approximately 50 nm red-shifted
from the peak of the QD ensemble emission.
of diameter D = 2.5 µm are created through electron beam
lithography, plasma dry etching, and wet undercut etching21.
Finite-element-method (FEM) simulations (Fig.
FIG. 1: Schematics of the experimental apparatus and system.
a, Diagram of the experimental setup showing a scanning electron
microscope (SEM) image of a taper-coupled microdisk.
are photodetectors for the reflected/transmitted signals. b, Illustra-
tion of the coupled microdisk-QD system. aCW/CCWare the ampli-
tudes for the clockwise/counterclockwise modes, Pi/R/Tare the in-
cident/reflected/transmitted signals, and κeand κicorrespond to the
fiber-to-cavity coupling and intrinsic cavity field decay rates, respec-
tively. c, SEM image of one of the small microdisk cavities under
study. d, FEM simulations of the radial (Eρ) and e, azimuthal (Eφ)
electric field components of the TEp=1,m=13mode in cross-section.
p denotes the radial order and m the azimuthal mode number. The
shaded triangle indicates the estimated QD position in this work.
the microdisks show that the TE1,13whispering gallery mode
(WGM) is resonant at λ ∼ 1300 nm. This optical mode has
a radiation-limited quality factor Qrad> 108, and an effective
standing wave mode volume Vsw= 3.2(λ/n)3. The peak co-
herent coupling rate for a QD excitonic state of the type stud-
ied here (i.e., spontaneous emission lifetime τsp= 1 ns) with
optimal placement and dipole orientation is g0/2π = 15 GHz.
Since our QDs are not deterministically positioned in the cav-
ity as in recent studies25, the actual exhibited coupling rate g
may be significantly smaller (see Methods). The magnitude of
g relative to the system decayrates, κT(cavity field decay)and
γ⊥(QD dephasing), determines whether the system lies in the
(strong coupling: g > (κT,γ⊥)) regime of cQED1.
The process by which we identify a suitable device for
studying cavity-QD coupling is described in the Methods sec-
tion. Figure 2(a) shows the fiber-taper-collected PL spectrum
from one such device that has been cooled down to 15 K. Op-
tical pumping of the QD is provided by exciting (also through
the taper) a blue-detuned higher-order WGM of the disk at
λP∼ 982.2 nm. The cavity mode, which is fed by background
emission processes13, is the tall peak at the blue end of the
spectrum. The three emission peaks red of the cavity mode are
the fine-structure-split26neutral single exciton lines, Xaand
Xb, and the negatively charged single exciton line, X−.
Further insight into the coupled cavity-QD system from PL
are masked by the limited resolution of our spectrometer (35
pm). In this case the interesting behavior of the cavity-QD
coupling can be studied by resonant spectroscopy of the cav-
ity mode using a fiber-coupled, narrowband (linewidth < 5
MHz) tunable laser. The inset to Fig. 2(a) shows the taper’s
transmission spectrum when it is placed in contact with the
side of the microdisk cavity and the cavity modes are detuned
from the exciton lines. As has been described in previous
work21, imperfections on the surface of the microdisk cause
backscattering that couples the initially degenerate traveling-
wave WGMs. If the backscattering rate γβexceeds the total
cavity loss rate κT, this mode-coupling results in the forma-
tion of standing wave modes which are split in frequency. The
transmission scan of Fig. 2(a) illustrates this effect in our sys-
tem, with TE1,±13modes appearing as a resonance doublet
with splitting 2∆λβ= 31 pm. Each mode has a linewidth of
δλ=13 pm, correspondingto Q =105and κT/2π=1.2 GHz.
To tune the cavity into resonance with the Xaand Xbexci-
ton lines of the QD we introduce nitrogen (N2) gas into the
cryostat22,27. As described in Ref.  and in the Methods
section, this allows for continuous and repeated tuning over a
4 nm wavelength range of the cavity modes. For the first set
of measurements, we operate with an input power of 470 pW
so that the system remains in a weak driving limit with the
estimated bare-cavity intracavity photon number ncav= 0.03.
The normalizedtransmission and reflection spectra over a cav-
ity tuning range of 240 pm are displayed as a two-dimensional
intensity image in Fig. 2(b)-(c). Initially, we see a simple shift
in the center wavelength of the cavity doublet mode, but once
higher-energy exciton line (Xa) of the QD, the spectra change
dramatically. We see that coupling between the Xa-line and
the cavity modes results in a significant spectral splitting (vac-
uum Rabi splitting) that is evidenced in the characteristic anti-
anti-crossing is indicative of the cavity taking on the character
of the QD exciton, and vice versa, when the system becomes
strongly coupled. As the cavity is detuned red of the Xa-line,
the spectra regain their initial bare-cavity doublet shape. Fur-
ther tuning brings the cavity modes into resonance with the Xb
exciton state. Only a small frequencyshift of the cavity modes
(no anti-crossing) is evident in this case, indicating that the Xb
state only weakly couples to either cavity mode.
Figure 2(d) shows a series of reflection scans for a zoomed-
are in resonance. In general, the character of these spectra are
complicated by the bimodal nature of WGM cavities. To ade-
quately model the system, we use a quantum master equation
(QME) as presented in Ref. . The model is used to solve
for the steady-state reflected and transmitted signals from the
cavity as a function of parameters such as cavity-exciton cou-
FIG. 2: Reflection and transmission spectra from a strongly cou-
pled microdisk-QD system. a, Fiber-collected PL spectrum at a
pump power of 30 nW showing the cavity mode (?), Xa(◦), Xb(?),
and X−(×) lines. The inset shows a transmission scan of the bare-
cavity mode. b, Measured transmission and c, reflection spectra as a
function of laser-QD detuning (∆λla) and cavity-QD detuning (∆λca),
where the cavitywavelength istuned by the N2adsorption. Transmis-
sion and reflection spectra are normalized to unity. d, Experimental
data and e, model plots for a series of reflected spectra in the central
120 pm region of cavity tuning. The dashed lines in e are guides-to-
the-eye for the exciton-like and cavity-like tuning.
pling and excitonic dephasing (the bare-cavity properties are
known from detuned cavity spectra). One other important pa-
rameter is the relative phase, ξ, between the surface-scattering
and exciton mode coupling. The QD-cavity coupling strength
with the standing wave modes, gsw1,2, is modified relative to
that for traveling wave WGMs by a factor of (1±eiξ)/√2.
A seriesofreflectedspectraproducedbythemodelis shown
in Fig. 2(e) for a set of parameters, listed in Table I, which
best estimates the measured reflected signal intensity, exciton
linewidth, relative coupling to the two standing wave modes,
and anti-crossed splitting.These parameters place the Xa
exciton state and the TE1,13WGM in the good-cavity limit
(g > γ⊥> κT) of the strong coupling regime. We note that
the achieved gsw1is about six times smaller than the maxi-
mum possible value based on the cavity mode volume, and
is likely due to the QD position being sub-optimal. We es-
timate that the QD is located 300-400-nm inwards from the
position of peak field strength of the TE1,13mode (see Fig.
1(d)), with the dipole-moment of the Xa-line oriented radially
and that of the Xb-line oriented azimuthally. This picture is
consistent with the orthogonal Xa-Xbpolarization26and their
relative measured coupling strengths.
The rate at which a single exciton can scatter incoming cav-
ity photons is limited, resulting in a saturation in the strongly-
coupled QD-cavity response for large enough input power.
Two parameters used to characterize nonlinear processes in
cQED are the critical atom number N0and saturation photon
number m0, which gauge the number of atoms needed to al-
ter the cavity response and the number of photons needed to
saturate the atomic transition, respectively1. These parame-
ters are given by N0= 2κTγ⊥/g2and m0= γ?γ⊥/4g2. In our
system N0= 0.44 and m0= 0.02 for the standing wave mode
(sw1) that couples most strongly to the QD. This indicates that
a single QD strongly affects the cavity response (which Fig.
2 clearly indicates), while even an average intracavity photon
number that is less than one can saturate the QD response.
shown in Fig. 3, where the cavity is tuned into resonance with
the Xa-line near the center of the anti-crossing region (scan
marked ’i’ in Fig. 2(d)), at which point the resonance peaks
arenearlyequalmixturesofexcitonandcavitymode. Fig. 3(a)
shows a plot of the measuredreflected signal normalizedto in-
put power (∆R) along with the modeled steady-state response
of the cavity under weak driving conditions (ncav= 0.03). As
the input power to the cavity increases, Fig. 3(b) shows that
the spectral splitting due to cavity-QD interaction (2∆λg) be-
gins to diminish as the exciton saturates, and finally reaches
a regime where the splitting is nearly two times smaller and
due to surface-scattering (2∆λβ). Fig. 3(c) plots the result-
ing mode splitting (2∆λg/β) and peak ∆R as a function of the
optical drive power. Both the splitting and reflected signal be-
gin to saturate towards their bare-cavity values for ncav= 0.1.
The QME model (dotted lines) predicts very similar behav-
ior, albeit with a slightly higher drive power saturation point.
Both data and model, however, show an extended saturation
regime as expected due to the quantum fluctuations of a single
dipole29. Such saturation behavior has previously been exper-
imentally observed in atomic systems3.
Use of an optical-fiber-based waveguide to efficiently probe
the microcavity-QD system opens up many interesting possi-
bilities for future devices and studies. In particular, excita-
tion and collection through the optical channel allows for high
resolution spectral and temporal studies of individual QD dy-
namics and a direct probe of the intra-cavity field. Studies
of the quantum fluctuations of the strongly-coupled system17,
through field and intensity correlations of the optical signal,
are also now possible. An immediate application is the cre-
ation of an efficient fiber-coupled single photon source, while
interface can serve as a means to transferquantuminformation
to and from the QD. In comparison, atomic systems have the
considerable advantages of homogeneity, much lower dephas-
ing, and an energy level structure compatible with more com-
plex manipulations of the quantum system. Nitrogen-vacancy
centers in diamond9,30have been viewed as a system that can
surement apparatus described here is equally applicable to this
and other systems, and we are hopeful that it can be built upon
TABLE I: Quantum master equation model parameters. See Methods for definition of Vtwand η.
(GHz) (GHz) (rad.)
(GHz) (GHz) (GHz)
FIG. 3: Power dependence of the QD-microcavity system. a, Re-
flection spectrum from the QD-microdisk system near resonance (po-
sition (i) in Fig. 2) under weak driving. The solid red line is the
measured reflected power normalized to input power; the dashed blue
line is a QME model of the system. b, Normalized (to unity) reflected
signal of panel a as a function of drive strength (dropped power in the
bare-cavity, Pd) and detuning from the short-wavelength resonance
peak (∆λl). c, Measured and modeled saturation of the mode split-
ting and peak reflected signal level versus drive strength (ncav(bottom
axis), Pd(top axis)). The model is only plotted up to a drive power of
ncav= 1 due to size limitations on the cavity mode Fock space which
can be simulated.
to further progress the developmentof solid-state cQED nodes
Device identification A linear array of microdisk cavities is fabricated,
with the disk diameter of 2.5µm nominally held fixed. Fluctuations in lithog-
raphy cause the TE1,13mode wavelength to vary over a 1290-1310 nm range.
We pump each device through the fiber taper and on resonance with one of its
WGMs in the 980 nm band24. This selectively excites QDs that lie in the disk
periphery and overlap with the TE1,13mode. For those devices in which iso-
lated QD emission is observed, we examine the spectral position of the TE1,13
mode relative to the QD states through PL and cavity transmission. A digital
wet etching process25provides a cavity mode blue shift of 0.8 nm/cycle. This
wet etch is repeated until the cavity mode lies blue (and within 1 nm) of the
desired QD single exciton lines. N2adsorption is then used to red-shift the
mode into resonance with the desired exciton line.
Transmission/Reflection measurements The tunable laser used in trans-
mission measurements provides a narrowband single mode laser line (< 5
MHz) and continuous wavelength tuning through dithering of a piezo ele-
ment. The transmitted and reflected signals are detected by TE-cooled (1 kHz
bandwidth) and LN2-cooled (150 Hz bandwidth) InGaAs photodetectors, re-
spectively. In order to reduce detector noise the transmission and reflection
signals are low-pass filtered (30 Hz cut-off) and the scans are averaged 10-20
times to produce the spectra of Fig. 2. PL is spectrally dispersed through
a 550 mm Czerny-Turner spectrometer and detected on a 512 element LN-
cooled InGaAs array (25 µm x 500 µm pixel size). The effective spectrometer
resolution is 35 pm.
Cavity tuning Nitrogen is released into the chamber in discrete 5 second
increments, with the flow rate adjusted so that a tuning level of ∼10 pm/step
is achieved. Once the shift is complete, the transmission and reflection spectra
are acquired as described above. At temperatures above 28 K, the N2can be
removed from the disk surface and the cavity mode reset back to its original
wavelength allowing for repeated tuning cycles.
Effective mode volume and g The FEM-calculated traveling wave mode
volume of the TE1,13WGM isVtw= 6.4(λ/n)3. The coherent coupling rate of
the exciton to the traveling wave mode is gtw= η
η accounts for the position and orientation of the exciton dipole (η = 1 for an
exciton dipole oriented parallel with, and positioned at, the peak of the cavity
mode electric field).
Quantum master equation simulations Reference  presents an ap-
propriate model for our system. We numerically solve the steady-state QME
for the system’s density matrix, from which the transmitted and reflected spec-
tra from the cavity are generated. A Fock space dimension of 6 for each cav-
ity mode was used in modeling the drive power dependence of the system
shown in Fig. 3. The expectation of the commutation between creation and
annihilation operators for each mode was calculated to ensure accuracy of the
The authors thank Sanjay Krishna and Andreas Stintz of the Center for
High Technology Materials at the University of New Mexico for providing
material growth in support of this work.
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