Coherent excitation of a strongly coupled quantum dot - cavity system
Dirk Englund, Arka Majumdar, Andrei Faraon, Mitsuru Toishi, Nick Stoltz, Pierre Petroff, Jelena Vuckovic
CCoherent excitation of a strongly coupled quantum dot -cavity system
Dirk Englund , , Arka Majumdar , Andrei Faraon , , Mitsuru Toishi , Nick Stoltz , Pierre Petroff & Jelena Vuˇckovi´c
1. Department of Electrical Engineering, Stanford University, Stanford CA 943052. Department of Physics, Lyman Laboratory, Harvard University, Harvard MA 021383. Department or Applied Physics, Stanford University, Stanford CA 943054. Sony Corporation, Shinagawa-ku, Tokyo, Japan, 141-00015. Department of Electrical and Computer Engineering, University of California, Santa Barbara,CA 93106
Photonic nanocavities coupled to semiconductor quantum dots are becoming well developedsystems for studying cavity quantum electrodynamics and constructing the basic architec-ture for quantum information science. One of the key challenges is to coherently control thestate of the quantum dot/cavity system for quantum memory and gates that exploit the non-linearity of such a system . Recently, coherent control of quantum dots has been studiedin bulk semiconductor . Here we investigate the coherent excitation of a strongly coupledInAs quantum dot - photonic crystal cavity system. When the quantum dot and cavity areon resonance, we observe time-domain Rabi oscillation in the transmission of a laser pulse.This coherent excitation promises to enable an all-optical method to observe and manipulatethe state a single quantum dot in a cavity. When the detuned dot is resonantly excited, weshow that the resonantly driven quantum dot efficiently emits through the cavity mode, aneffect that is explained in part by an incoherent dephasing mechanism similar to recent the-oretical models . When the detuned quantum dot is resonantly excited, the cavity signalrepresents a spectrally separated read-out channel for high resolution single quantum dotspectroscopy. In this case, we observe antibunching of the cavity mode. Such a single photonsource could allow photon indistinguishability that approaches unity as could lift the lim- a r X i v : . [ qu a n t - ph ] F e b tation due to dephasing and timing jitter
11, 12 . The single photon emission is controlled bythe cavity resonance, which relaxes the demands for spectrally matching quantum dots fortwo-photon interference and may therefore be of use in linear optics quantum computation and quantum communication
14, 15 . The optical system consists of a photonic crystal (PC) cavity fabricated in a 160-nm thickGaAs membrane by a combination of electron beam lithography and dry/wet etching steps, asdiscussed in Ref.17. The membrane contains a central layer of self-assembled InGaAs quantumdots (QDs) with an estimated density of /µ m . The completed photonic crystal is shown in thescanning electron micrograph in Fig.1(c).We employ a grating-integrated cavity (GIC) design for improved input and output coupling .The cavity design is based on a linear three-hole defect cavity . The perturbed cavity design in-creases the directionality of the unperturbed cavity emission and improves the in- and out-couplingefficiency . The integrated grating has a second-order periodicity as indicated in Fig.1(b).We first characterize the QD/cavity system by its photoluminescence. The sample is main-tained between 10 K and 50 K in a liquid-He continuous flow cryostat. A continuous-wave (cw)laser beam at 860 nm excites electron-hole pairs which can relax through a phonon-mediated pro-cess into radiative levels of the QD. This above-band driving case corresponds to the pump fre-quency ω p tuned above the single-exciton frequency that is labeled as X in Fig.1(d). Fig.1(e) plotsthe photoluminescence spectrum. As we sweep the temperature, we observe the anticrossing be-tween the QD emission and the cavity emission that is characteristic of the strong cavity-emittercoupling. From the QD/cavity spectrum, we estimate the system parameters summarized in thetable in Fig.1(d).Next, we resonantly excite the QD by coupling a tunable cw-laser beam into the cavity. Thelaser has a linewidth below kHz. Using the cross-polarized setup illustrated in Fig.1(a), we ob-serve the transmission of the incident vertically polarized laser via the cavity into the horizontally2igure 1: (a) Cross-polarized confocal microscope setup. (b) E y field in the L3-cavity structure. The structure isperturbed at the sites indicated by dashed circles, as described in Ref. . (c) Scanning electron micrograph of fabri-cated structure. (d) Energy levels of the coupled QD/cavity system showing the two polarization states of the singleexciton (X,Y) and the bi-exciton state (XX). The table lists the system parameters derived from the measurements,where g, κ, γ, γ ∗ are the vacuum Rabi frequency, cavity field decay rate, dipole decay rate, and dipole dephasingrate, respectively. (e) The photoluminescence (PL) shows the QD/cavity anticrossing as the QD is temperature-tunedthrough the cavity. (f) Vacuum Rabi splitting observed in the reflectivity from the strongly coupled QD/cavity system.For comparison, we show the reflectivity of an empty cavity. (g) PL lifetime ∼ ps when the QD is tuned intothe cavity and excitation wavelength λ p = 878 nm. The emission that is expected theoretically, based on the systemparameters in (d) and a 10-ps relaxation time into the single exciton state, is shown in the solid line. The bottom panelplots the corresponding expected excited state population | c e ( t ) | . , which demonstrates thatwe are coherently probing the QD/cavity system. The reflectivity signal nearly vanishes when thelaser field is resonant with the QD single exciton (X) frequency, showing that the QD has a veryhigh probability of being in the optically bright state. We obtain good agreement with theory (solidline fit in Fig.1(f)). In this fit, we used the same parameters as derived from the photoluminescence(PL) data in Fig.1(e). When the quantum dot is on resonance with the cavity and is pumped at878 nm, the PL decays with a characteristic time of 17 ps. The decay time matches a theoreticalmodel based on the system parameters, shown in the solid line in Fig.1(g). The model considersa quantum dot which is pumped into the single-exciton excited state (including timing jitter) andthen decays into free space and the cavity mode (see Methods). The state of the QD is describedby a superposition of ground and excited states, | ψ ( t ) (cid:105) = c g ( t ) | g (cid:105) + c e ( t ) | e (cid:105) . The expected ex-cited state population | c e ( t ) | that is predicted by the fitting model is plotted in the bottom panelof Fig.1(g). Previous measurements of the decay time gave values exceeding 60 ps in the strongcoupling regime , which is longer than expected for the strong coupling regime where the decaytime should be on the order of the cavity ring-down time of ∼ ps for a Q ∼ . We attribute theshort decay time in this case to the observation that nearly all emission collected from the cavityoriginates from the QD. For a very similar system, we previously showed that the cavity mode isstrongly antibunched to ( g (2) (0) ∼ . ) . The perturbed cavity lifts the QD signal far above thebackground and thus eliminates the collection of the long lived emission lines that would degradeantibunching.In the PL and reflectivity measurements described above, we characterized the QD/cavity inthe frequency regime. We will now describe a method to observe the system dynamics by directtime domain measurements of the vacuum Rabi frequency. Instead of the cw probe laser, wenow use a spectrally filtered Ti:Sapphire laser with 40 ps pulses at 80 MHz repetition rate. Sincethe reflected beam intensity is weak when detuned from the cavity (as evident from Fig.1(f)),we performed this measurement when the QD was resonant with the cavity, although a range ofdetunings and vacuum Rabi frequencies are in general possible. In Fig.2, we plot the time-resolvedreflected pump intensity, which is acquired with a streak camera (see Methods). The period of Time-resolved reflectivity measurement shows Rabi oscillation frequency g/ π = 29 GHz. We show threeexcitation powers in (a,b,c). The observations are fit with a full master equation model using the parameters givenabove; in all three plots, the photon flux into the cavity is scaled equally from the measured incident power (0.1nW,0.23 nW, 1 nW before the lens). ps closely matches the expected Rabi period T = 2 π/g = 40 ps. At higher pump power, the Rabioscillation becomes less visible (Fig.2(c)). In all observed cases, we found good agreement withtheory (plotted in solid lines), which is obtained using a quantum Monte Carlo simulation (seeMethods). The fits assume the values of g, γ, and κ obtained from spectral measurements, i.e., PLand reflectivity. The time-resolved reflectivity presented here offers a direct tool for coherentlymanipulating the state of the QD/cavity system.We will now consider the resonant driving of the quantum dot when it is detuned from thecavity and will demonstrate the use of the cavity mode as a convenient read-out and pumpingchannel for resonant single quantum dot spectroscopy and single photon generation. We first lowerthe temperature to 10K, which blue-detunes the dot by δ = λ d − λ c = − . nm from the cavityresonance. The laser excitation is polarized at 45 ◦ to the cavity mode, where its alignment can beoptimized for the reflectivity signal shown in Fig.1(f). Then we scan the laser across the QD andcavity resonances, as shown in Fig.3. The excitation laser power is ∼ nW before the objectivelens. Precisely when the laser becomes resonant with the QD, we observe a strong emission intothe cavity mode. Thus the cavity represents a strong read-out channel for resonant quantum dotspectroscopy: the resonantly driven QD emits into the cavity mode, which is far detuned and easyto separate spectrally. Alternatively, if the cavity mode is pumped, the QD single-excition line5adiates. Figs.3(b,c) plot spectra when the (QD,cavity) are pumped.Fig.3(d) plots the integrated cavity emission as a function of the laser pump wavelength λ p . The QD absorption linewidth is measured to be lower than . nm (2 GHz) – about fivetimes narrower than the ∼ . nm resolution of our . m spectrometer. The excitation lasershowed slight mode-hopping; if improved, the resolution should be considerably below 2 GHz.This cavity-enhanced spectroscopy technique adds an important tool to the repertoire for resonantsingle quantum dot spectroscopy . Resonance fluorescence from a QD in a cavity was pre-viously reported in a planar optical cavity ; however, the excitation geometry used in Ref.28 isdifficult to realize in cavity designs for high Purcell regime or strong coupling, such as photoniccrystals or microdisks. The cavity-enhanced spectroscopy shown here should be applicable forsolid state cavity QED systems with many cavity designs, so long as the QD has a large enoughpure dephasing rate to drive the cavity. Fig. 3(e) plots the integrated QD intensity as the laser isscanned over the cavity resonance. The QD dot then emits with a linewidth that appears limited bythe our spectrometer resolution of (0.03 nm).The mechanism that allows the quantum dot to drive the far off-resonant cavity is not yetcompletely clear. It has previously been reported that quantum dots that were pumped throughhigher excited states or the QD wetting layer can drive the cavity even when it is far detuned
22, 29, 30 .Several recent theoretical models attribute the off-resonant driving of the cavity mode to a puredephasing mechanism of the quantum dot . We describe our experimental data with a quantummaster equation model that considers the dephasing as an additional Liouvillian L d which dependson a dephasing rate γ ∗ (see Methods). The dephasing term allows driving of the cavity (QD)through the QD (cavity), as is shown in the fit in Figs.3(c,d), where we used γ ∗ = 0 . g . This valueof γ ∗ was measured independently (see Fig.4(f)) and agrees with values cited in the literature forresonant excitation studies .To explore the effect of pumping the off-resonant dot, we measured the cavity emission atvarious detunings of the QD exciton. At each cryostat temperature given in Fig.3(h), we tune the6w excitation laser to the QD, keeping the power constant at ± . nW before the lens. Theintegrated cavity intensity is plotted with detuning δ = ω cav − ω qd . In our model, we assume atemperature-dependent dephasing rate γ = γ + α T , with α = 0 . µ eV K − and γ = κ/ .The theory does not fully explain the observation, suggesting that pure dephasing is only a part ofthe off-resonant driving mechanism between the QD and cavity. Phonon-mediated and two-photonabsorption processes probably also play a role, but are not captured in our model.We now explore the pump power dependence of coherent excitation. Fig.3(f) shows thespectrometer intensity at P in = 200 nW. One striking difference is that the features are far moreblurred; we believe this results in part because of increased spectral diffusion at high intensity
33, 34 .A careful scan across the QD, where the tail of the excitation laser is subtracted, gives the cavityemission spectrum shown in Fig.3(g). The scan reveals a second peak when the pump is tuned to λ p = 919 . nm. In Fig.3(h), we plot the cavity emission as a function of excitation power when λ p is tuned to the lines one by one. The single-exciton line shows a linear pump dependence, asexpected. The second line shows a quadratic pump dependence, which suggests a bi-exciton statethat is resonantly pumped by two-photon absorption. The power of this line was too low to confirmthis identification by a cross-correlation measurement with the single exciton emission.We next turn to measurements of the second-order correlation function g (2) ( τ ) to study thequantum nature of the QD/cavity system. We estimate g (2) ( τ ) by a measurement of the autocor-relation using a Hanbury-Brown-Twiss (HBT) setup. With the half wave plate in Fig.1(a) alignedto maximize the cavity emission, we obtain a high isolation of the pump, as shown in Fig.4(a).Under this polarization setting, we observed only the single-excition absorption line through thecavity emission. We spectrally filter the cavity emission using a . nm grating filter before theemission is sent to the HBT setup. The autocorrelation histogram of the cavity emission when theQD is resonantly excited is shown in Fig.4(b). The antibunching depth is limited to g (2) (0) ∼ . because the ∼ ps detector resolution is longer than the excited state lifetime τ ≈ ps, whichis independently measured (see below) and is slower than the 17 ps shown in Fig.1(g) because theQD is detuned from the cavity. 7igure 3: Coherent QD spectroscopy through cavity mode. (a) Intensity on spectrometer when the pump wavelength λ p is scanned across the detuned QD/cavity system (the main laser excitation is accompanied by a red-detuned sidemode that is 200 times lower in intensity; temperature is 10K). When λ p is resonant with the dot (cavity), the cavity(QD) intensity rises. (b) Spectrum when QD is pumped (the middle peak corresponds to the laser side mode) (c)spectrum when cavity is pumped. In (b) and (c), we model the driving mechanism by a pure dephasing process with γ ∗ = 0 . g . The model agrees well with the emission through the cavity (QD) when the QD (cavity) is pumped. (d)The integrated cavity emission as a function of the pump wavelength λ p shows the single exciton absorption resolvedto GHz. (e) The integrated QD emission shows a non-lorentzian dependence on the pump frequency into the cavity.(f) At high pump power, a second line becomes visible at λ p = 919 . nm. (The lines are slightly shifted since thetemperature was, for technical reasons, raised to 18 K). (e) Integrated cavity emission as λ p is scanned. Inset:
Thepower dependence of the two lines suggests exciton (X) and bi-exciton (XX) states. (g) Dependence of integratedcavity emission on QD detuning when the QD is resonantly pumped. . nm. Fig.4(c) shows the autocorrelationhistogram of the cavity emission, which indicates g (2) (0) = 0 . . We believe the main con-tribution to counts near τ = 0 is due to the tail of the pulsed excitation laser. Because both theexcitation and the emission into the cavity are faster than the detector resolution, it is not possibleto distinguish them temporally. We believe the τ = 0 peak should be significantly lower withbetter spectral filtering or higher QD-cavity detuning.The autocorrelation measurements demonstrate the use of the resonantly driven QD as anon-demand single photon source. Such a single photon source has several advantages over pre-viously reported QD-based single photon sources. The coherent driving mechanism eliminatestiming jitter which results from the random relaxation time of electron-hole pairs under above-resonant excitation. Furthermore, the emission is stabilized by the cavity frequency. The photonindistinguishability can approach unity, albeit at the cost of efficiency . In quantum dots thatare incoherently pumped through a higher excited state, the combination of dephasing and timingjitter appears to limit the mean wavefunction overlap to about ∼ % for the types of QDs em-ployed here . Since the emission occurs through the cavity, it is easier to match the emission fromdistant QDs for applications such as remote QD entanglement via interference of single photonsemitted
14, 15 .We performed time resolved measurements of the emission of the resonantly excited QD intothe cavity mode. Fig.4(d) shows the 40-ps pump pulse and cavity emission, measured simultane-ously on a streak camera. The QD-driven cavity emission lifetime is τ ∼ ps when the dot isdetuned by δ = − . nm. We can use this lifetime measurement to infer the dephasing rate. Wefit the decay time by a Monte Carlo simulation of the master equation, where the QD begins in theground state and is driven by the 40-ps pump pulse (see Methods). All parameters except for γ ∗ are fixed as before. The fit gives γ ∗ = 0 . g . 9igure 4: (a) Resonant QD excitation at 10K. For the autocorrelation measurements, the cavity emission is filteredto a width of 0.2 nm. (b) Autocorrelation histogram of cavity emission when the QD is pumped resonantly at a powerof nW in cw mode. (c) Pulsed autocorrelation measurement. (d) Time-resolved resonant pumping of the quantumdot and emission into the cavity mode. A theoretical fit to the cavity emission yields an estimate of the pure dephasingrate.
10e have studied coherent excitation of a strongly coupled QD/photonic crystal cavity sys-tem, with three main results. First, time-resolved reflectivity measurements on the QD/cavityshow the vacuum Rabi oscillation of the dot in the cavity and enable a direct means for observ-ing and manipulating the QD. Second, we considered the resonant driving of a cavity-detuned dotwhich efficiently populates the cavity mode, adding insight to previous non-resonant studies ofthis phenomenon
22, 29, 30 . This cavity-controlled read-out channel allows high-resolution, resonantsingle quantum dot spectroscopy. Third, we demonstrated an on-demand single photon sourcerelying on a resonantly driven quantum dot. This source promises unity indistinguishability .Since the emission frequency is set by the cavity resonance, which is easier to control than theinhomogenously distributed QD frequency, this source is furthermore appealing for creating en-tanglement by photon interference
14, 15 . In the future, much larger coupling efficiencies will berequired. The all-optical techniques discussed here are compatible with integrated photonic crystalstructures, where cavities coupled to single quantum dots may be connected through networks ofwaveguides and other chip-integrated elements.
Acknowledgements
We thank Hideo Mabuchi for helpful discussions. Financial support was provided bythe Office of Naval Research (PECASE and ONR Young Investigator awards), National Science Foundation,Army Research Office, and DARPA Young Faculty Award. A.M. was supported by the SGF (Texas Instru-ments Fellow). Work was performed in part at the Stanford Nanofabrication Facility of NNIN supported bythe National Science Foundation.
Competing Interests
The authors declare that they have no competing financial interests.
Correspondence
Correspondence and requests for materials should be addressed to Dirk Englund (email:[email protected]).
MethodologyHBT
In autocorrelation measurements, light is filtered to 0.2 nm, directed through a 50:50 beamsplitter, and coupled through multi mode fibers to single photon counter modules. Coincidences11re recorded on a time interval analyzer.
Time-domain dynamics of QD/cavity system
Fig.2: We reflect ps pulses from the cavity.The temperature of the cryostat is adjusted to tune the single exciton transition into the cavity.The spectral and spatial alignment are optimized with the scanning cw laser in the cross-polarizedarrangement shown in Fig.1(a). The reflected beam is now recorded on a Hamatsu C5680 streakcamera.A quantum Monte Carlo simulation based on Ref.40 is used to model the time-dependentreflectivity. The values for g, κ, γ, ∆ λ are taken from the spectral characterization. A Gaussianclassical field E ( t ) = E exp( − t / σ t ) drives the cavity mode with a FWHM of 40 ps. The QDis initialized into the ground state | g (cid:105) . With all other system parameters fixed, the amplitude E is adjusted for the experiment with lowest power of P in = 0 . nW. This calibration fixes E forexperiments with higher power. Each simulation yields the time-dependent cavity photon number (cid:104) a ( t † ( t ) a ( t ) (cid:105) .From the reflectivity in Fig.1(f), we estimate the QD has a probability of being in an opti-cally dark state of p D ≈ . , meaning that a background signal corresponding to an empty cavityreflectivity must be added, giving (cid:104) a † ( t ) a ( t ) (cid:105) (cid:48) = p D (cid:104) a † ( t ) a ( t ) (cid:105) g =0 + (1 − p D ) (cid:104) a † ( t ) a ( t ) (cid:105) , wherewe set g = 0 for the first term and p D = 0 . . The final fit is obtained by convolving (cid:104) a † ( t ) a ( t ) (cid:105) (cid:48) with the streak camera response of ps.Fig.1(g): To model the PL when the QD is tuned to the cavity and excited incoherentlythrough a higher energy level, we use the Monte Carlo simulation described above, but initialize theQD in the excited state | e (cid:105) . The time jitter is modeled by finding a weighted average of relaxationtimes, with a 1/e time of ps.Fig.4(d): In the Monte Carlo simulation, the QD is detuned by δ and driven resonantly. TheQD is initialized into the ground state and the single-excition transition is driven by the classical12eld. The Hamiltonian now has a driving term E ( t )( σ + + σ − ) , where σ + , − are the raising andlowering operators of the quantum dot. Supplemental MaterialDephasing model
The Master equation describing a QD (lowering operator σ = | g (cid:105) (cid:104) e | ) coupledto a cavity mode (with annihilation operator a ) is given by dρdt = − i [ H, ρ ] + κ aρa † − a † aρ − ρa † a ) + γ σρσ † − σ † σρ − ρσ † σ ) + γ d σ z ρσ z − ρ ) (1)where γ , κ and γ d accounts for QD population decay, cavity population decay and QD pure de-phasing; σ z = [ σ † , σ ] . H is the hamiltonian of the system without considering the losses and isgiven by H = ∆2 a † a − ∆2 ( σ z ) + ig ( σa † − aσ † ) (2) ∆ is QD-cavity detuning and the reference energy is the mean of QD and cavity energy. Using eq.1 one can write (cid:28) dadt (cid:29) = ( − i ∆2 − κ (cid:104) a (cid:105) + g (cid:104) σ (cid:105) (3) (cid:28) dσdt (cid:29) = ( i ∆2 − γ − γ d ) (cid:104) σ (cid:105) + g (cid:104) σ z a (cid:105) (4)(5)These two coupled equations are solved. Initial condition a (0) = 1; σ (0) = 0 and a (0) = 0; σ (0) =1 correspond to pumping the cavity and the dot respectively. Let us define A = (cid:0) − i ∆2 − κ (cid:1) and B = (cid:0) i ∆2 − γ − γ d (cid:1) and λ − = A + B − (cid:112) ( A − B ) − g , λ + = A + B + (cid:112) ( A − B ) − g .When the dot is pumped, the solution in time domain is given by a ( t ) = ( e λ + t − e λ − t ) g (cid:112) ( A − B ) − g (6)and σ ( t ) = ( A − B )( e λ − t − e λ + t ) + (cid:112) ( A − B ) − g ( e λ − t + e λ + t )2 (cid:112) ( A − B ) − g (7)13o the spectrum emitted by the cavity ( S cav ) and by the QD ( S QD ) are given by (by virtue ofQuantum Regression theorem): S cav ( ω ) = g ( A − B ) − g (cid:12)(cid:12)(cid:12)(cid:12) ω − λ − − ω − λ + (cid:12)(cid:12)(cid:12)(cid:12) (8) S QD ( ω ) = 12(( A − B ) − g ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) A − B + (cid:112) ( A − B ) − g ω − λ − − A − B − (cid:112) ( A − B ) − g ω − λ + (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (9)Similarly, if the cavity is pumped, then depending on the other initial condition one can solve andget: a ( t ) = ( B − A )( e λ − t − e λ + t ) + (cid:112) ( A − B ) − g ( e λ − t + e λ + t )2 (cid:112) ( A − B ) − g (10) σ ( t ) = ( e λ − t − e λ + t ) g (cid:112) ( A − B ) − g (11)So the spectrum becomes: S cav ( ω ) = 12(( A − B ) − g ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) B − A + (cid:112) ( A − B ) − g ω − λ − − B − A − (cid:112) ( A − B ) − g ω − λ + (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (12) S QD ( ω ) = g ( A − B ) − g (cid:12)(cid:12)(cid:12)(cid:12) ω − λ − − ω − λ + (cid:12)(cid:12)(cid:12)(cid:12) (13)In our experimental setup as the collection efficiency from cavity is much higher compared to QD,hence we can assume that in experiment what we are observing is S cav ( ω ) .14. Imamoˇglu, A., Awschalom, D. D., Burkard, G., DiVincenzo, D. P., Loss, D., Sherwin, M., andSmall, A. Phys. Rev. Lett. (20), 4204–4207 November (1999).2. Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J. M., andHaroche, S. Phys. Rev. Lett. , 5166–5169 (1999).3. Li, X., Wu, Y., Steel, D., Gammon, D., Stievater, T. H., Katzer, D. S., Park, D., Piermarocchi,C., and Sham, L. J. Science (5634), 809–811 (2003).4. Yao, W., Liu, R. B., and Sham, L. J.
Phys. Rev. Lett. , 030504 July (2005).5. Xu, X., Sun, B., Berman, P. R., Steel, D. G., Bracker, A. S., Gammon, D., and Sham, L. J. Science (5840), 929–932 (2007).6. Jundt, G., Robledo, L., H ¨ogele, A., F¨alt, S., and Imamo ˘glu, A.
Physical Review Letters (17), 177401 (2008).7. Press, D., Ladd, T. D., Zhang, B., and Yamamoto, Y.
Nature , 218–221 Nov (2008).8. Naesby, A., Suhr, T., Kristensen, P. T., and rk, J. M.
Phys. Rev. A (4), 045802 (2008).9. Yamaguchi, M., Asano, T., and Noda, S. Opt. Express (22), 18067–18081 (2008).10. Auff`eves, A., G´erard, J.-M., and Poizat, J.-P. ArXiv/0808.0820 (2008).11. Santori, C., Fattal, D., Vuˇckovi´c, J., Solomon, G. S., and Yamamoto, Y.
Nature (6907),594–7 October (2002).12. Kiraz, A., Atat¨ure, M., and Imamoˇglu, I.
Phys. Rev. A , p.032305–1–032305–10 March(2004).13. Knill, E., Laflamme, R., and Milburn, G. J. Nature , 4652 (2001).14. Simon, C. and Irvine, W. T.
Physical Review Letters (11), 110405+ (2003).15. Childress, L., Taylor, J. M., Sorensen, A. S., , and Lukin, M. D. Phys. Rev. A , 052330(2005). 156. Englund, D., Toishi, M., and Vuckovic, J. in preparation (2008).17. Englund, D., Fattal, D., Waks, E., Solomon, G., Zhang, B., Nakaoka, T., Arakawa, Y., Ya-mamoto, Y., and Vuˇckovi´c, J. Phys. Rev. Lett. , 013904 July (2005).18. Akahane, Y., Asano, T., Song, B.-S., and Noda, S. Nature , 944–947 October (2003).19. Englund, D., Faraon, A., Fushman, I., Stoltz, N., Petroff, P., and Vuˇckovi´c, J.
Nature (6),857–61 (2007).20. Thompson, R. J., Rempe, G., and Kimble, H. J.
Phys. Rev. Lett. (8), 1132–1135 Feb (1992).21. Waks, E. and Vuˇckovi´c, J. Phys. Rev. Lett. (153601) April (2006).22. Hennessy, K., Badolato, A., Winger, M., Gerace, D., Atature, M., Gulde, S., Falt, S., Hu, E. L.,and Imamoglu, A. Nature , 896–899 (2007).23. Toishi, M., Englund, D., et al. submitted (2008).24. Kroner, M., Lux, C., Seidl, S., Holleitner, A. W., Karrai, K., Badolato, A., Petroff, P. M., andWarburton, R. J.
Applied Physics Letters (3), 031108 (2008).25. Al´en, B., Bickel, F., Karrai, K., Warburton, R. J., and Petroff, P. M. Applied Physics Letters (11), 2235–2237 (2003).26. H¨ogele, A., Seidl, S., Kroner, M., Karrai, K., Warburton, R. J., Gerardot, B. D., and Petroff,P. M. Phys. Rev. Lett. (21), 217401 Nov (2004).27. Vamivakas, A. N., Atature, M., Dreiser, J., Yilmaz, S. T., Badolato, A., Swan, A. K., Goldberg,B. B., Imamoglu, A., and Unlu, M. S. Nano Letters , 2892 (2007).28. Muller, A., Flagg, E. B., Bianucci, P., Wang, X. Y., Deppe, D. G., Ma, W., Zhang, J., Salamo,G. J., Xiao, M., and Shih, C. K. Physical Review Letters (18), 187402 (2007).29. Strauf, S., Hennessy, K., Rakher, M. T., Choi, Y.-S., Badolato, A., Andreani, L. C., Hu, E. L.,Petroff, P. M., and Bouwmeester, D. Phys. Rev. Lett. (12), 127404 (2006).160. Kaniber, M., Laucht, A., Neumann, A., Villas-Bˆoas, J. M., Bichler, M., Amann, M.-C., andFinley, J. J. Physical Review B (Condensed Matter and Materials Physics) (16), 161303(2008).31. Langbein, W., Borri, P., Woggon, U., Stavarache, V., Reuter, D., and Wieck, A. D. Phys. Rev.B (3), 033301 Jul (2004).32. Favero, I., Berthelot, A., Cassabois, G., Voisin, C., Delalande, C., Roussignol, P., Ferreira,R., and G´erard, J. M. Physical Review B (Condensed Matter and Materials Physics) (7),073308 (2007).33. Berthelot, A., Favero, I., Cassabois, G., Voisin, C., Delalande, C., Roussignol, P., Ferreira, R.,and Gerard, J. M. Nat Phys (11), 759–764 November (2006).34. Favero, I., Berthelot, A., Cassabois, G., Voisin, C., Delalande, C., Roussignol, P., Ferreira,R., and G´erard, J. M. Physical Review B (Condensed Matter and Materials Physics) (7),073308 (2007).35. Vuckovic, J., Englund, D., Fattal, D., Waks, E., and Yamamoto, Y. Physica E Low-Dimensional Systems and Nanostructures , 466–470 May (2006).36. Englund, D., Faraon, A., Zhang, B., Yamamoto, Y., and Vuckovic, J. Opt. Express , 5550–8April (2007).37. Faraon, A., Fushman, I., Englund, D., Stoltz, N., Petroff, P., and Vuckovic, J. Opt. Express (16), 12154–12162 (2008).38. Takano, H., Song, B.-S., Asano, T., and Noda, S. Opt. Express (8), 3491–3496 (2006).39. Tanabe, T., Notomi, M., Kuramochi, E., Shinya, A., and Taniyama, H. Nature Photonics ,49–52 (2006).40. Tan, S. M. J. Opt. B: Quantum Semiclass. Opt.1