NANO LETTERS
Cavity QED with Semiconductor Nanocrystals
2006 Vol. 6, No. 3 557-561
N. Le Thomas, U. Woggon,* and O. Scho1 ps Fachbereich Physik, UniVersita¨t Dortmund, Otto-Hahn-Str. 4, 44227 Dortmund, Germany
M. V. Artemyev Institute for Physico-Chemical Problems of Belarussion State UniVersity, Minsk 220080, Belarus
M. Kazes and U. Banin Institute of Chemistry, The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel Received January 2, 2006; Revised Manuscript Received January 21, 2006
ABSTRACT We report on a strongly coupled cavity quantum electrodynamic (CQED) system consisting of a CdSe nanocrystal coupled to a single photon mode of a polymer microsphere. The strong exciton−photon coupling is manifested by the observation of a cavity mode splitting pΩexp between 30 und 45 µeV and photon lifetime measurements of the coupled exciton−photon state. The single photon mode is isolated by lifting the mode degeneracy in a slightly deformed microsphere cavity and addressing it by high-resolution imaging spectroscopy. This cavity mode is coupled to a localized exciton of an anisotropically shaped CdSe nanocrystal that emits highly polarized light in resonance to the cavity mode and that was placed in the maximum electromagnetic field close to the microsphere surface. The exciton confined in the CdSe nanorod exhibits an optical transition dipole moment much larger than that of atoms, the standard system for CQED experiments, and a low-temperature homogeneous line width much narrower than the high-Q cavity mode width. The observation of strong coupling in a colloidal semiconductor nanocrystal−cavity system opens the way to study fundamental quantum-optics phenomena and to implement quantum information processing concepts that work in the visible spectral range and are based on solid-state nanomaterials.
Cavity quantum electrodynamics (QED) systems allow us fundamental studies of coherent interactions of confined electromagnetic fields (cavity photons) and microscopic dipoles (single nanoemitters).1-4 The first cavity QED experiments such as the measurements of the vacuum Rabi splitting (see, e.g., refs 5 and 6) stimulated an intensive search for atom-photon entanglement in cavity QED systems of atomic physics. Coherent interactions of atom-photon quantum systems are proposed to realize a variety of quantum protocols7-10 in quantum information science. The predictions of these quantum protocols relying on cavity QED, as well as the suggestions for sources producing new states of light,11 have stimulated a tremendous technological development toward solid-state-based, compact, and scalable cavity QED systems. As a first step, the vacuum Rabi splitting, which was originally observed with atom beams only,5,6 has been measured recently with epitaxially grown InGaAs quantum dots in micropillars12 and photonic crystals,13 with localized * Corresponding author. Experimentelle Physik IIb, Universita¨t Dortmund, Otto-Hahn-Str. 4, D-44227 Dortmund. Tel: +49-231 755 3767. Fax: +49-231 755 3674. E-mail:
[email protected]. 10.1021/nl060003v CCC: $33.50 Published on Web 02/16/2006
© 2006 American Chemical Society
GaAs excitons in microdisks,14 and with Cooper pair boxes.15 Chemically synthesized colloidal nanocrystals (NC), or quantum dots, are another promising class of photons emitting two-level systems that possess a large optical transition dipole moment compared with atoms and can be incorporated in polymer, glass, or semiconductor microcavities. They can be synthesized with great flexibility in size and shape and can easily be positioned at the electromagnetic field maximum of the cavity, that is, where the coupling strength, g, is maximum. Modifications in the spontaneous emission rate, that is, the Purcell effect,16 as an indication of weak exciton-photon interactions, have already been experimentally demonstrated for CdSe and CdTe nanocrystals.17-20 The synthesis as colloidal nanorods (NRs)21,22 resulted in highly polarized emitters that are optimum for high coupling efficiency with a single cavity mode. Coherent interaction in a coupled emitter-photon system with coupling constant g is observed when g satisfies the condition g > |γe - γc|/4 with γe and γc the irreversible decay rates of the emitter and the confined photon, respectively.23-25 One signature of this, the so-called strong
coupling regime, is a doublet in the spontaneous emission spectrum of the coupled emitter-photon system. When the emitter and photon energy are exactly in resonance, the doublet is split by the energy pΩ ) 2pxg2-(γe-γc)2/16, where pΩ is the Rabi splitting energy. The recent demonstrations of strong coupling with semiconductors12-15 rely on the optimization of g by reducing the cavity size and hence the mode volume, V, and by increasing the dipole oscillator strength, f, because g scales such as g ∝ xf/V (see, e.g., refs 4 and 23-25). In this letter we report on the realization of the strong coupling regime of cavity QED for single CdSe NRs interacting with the photon modes of a dielectric microsphere. Microsphere cavities were chosen because of their very high quality factors, Q,26,27 which can be obtained without advanced microlithography techniques. Despite their relative large mode volume, V, compared to other existing microcavities,4 the microsphere cavities are well suited to observe the strong coupling regime of cavity QED if one achieves the lifting of degeneracy in the angular momentum of the confined photon states. In the following, we first describe the isolation of a single photon state by making use of high-resolution imaging spectroscopy with slightly deformed microspheres. Next we present the spectra of a single CdSe NR and finally discuss the properties of the coupled NR-microsphere system. The microcavities used here are commercial polystyrene spheres with a diameter of d ) 6 ( 0.3 µm, a size optimal for obtaining both a high Q factor and a small mode volume.27 The cavity modes are characterized by angular l, azimuthal m, and radial n photon mode numbers for the n n transverse electric (TEl,m ) and transverse magnetic (TMl,m ) field modes. For a given radial mode number n, for example n ) 1, the free spectral range is around 500 meV, much larger than the homogeneous line broadening of the single CdSe NR spectrum. As a result, a single NR couples only to photon modes with a given n and l mode number. In an ideal microsphere cavity, however, a degeneracy exists that allows (2l + 1) values of the mode number m. This degeneracy has to be lifted by a weak deformation of the microsphere in order to couple to a nondegenerate single photon mode. Figure 1 shows a spectral and spatial characterization of the (2l + 1) modes of a TE141 photon state for a deformed microsphere demonstrating the l degeneracy lifting. The spectrum of this “empty” sphere, that is, without emitters, was excited by a 150-fs pulse of an optical parametric oscillator (OPO) centered at 620 nm and evanescently coupled into the sphere by focusing on the contact point between the sphere and the substrate. The scattered light from the sphere was collected with a high numerical aperture objective (NA ) 0.95) and recorded with a high-resolution imaging spectrometer and a CCD camera. The inset shows the theoretical spectrum for a slightly deformed (oblate) sphere with a relative difference of ∼0.5% between the polar and equatorial radii calculated by first-order perturbation theory.28 The effect of natural shape deformation (symmetry invariance breaking) and the translation invariance breaking due to the sphere/substrate contact point allows the observation of scattered light from 558
Figure 1. (a) Spectrally and spatially resolved scattering spectrum of a TE141 mode of a d ) 6 µm microsphere (linear grayscale) taken from a ∼300 nm wide section of the sphere as shown schematically in the inset. (b) Fine structure of the mode showing the degeneracy lifting for the l ) 41 mode. Inset: theoretical spectrum for a slightly oblate sphere.
different m modes. By selecting a proper spatial region, we measure a minimum mode line width of 20 µeV, which corresponds to a quality factor Q ) Emode/fwhmmode ∼ 105. The calculated spectrum predicts a Lorentzian line shape with 5 µeV width (fwhm) for the different m, while the experimental homogeneous line widths of the individual photon modes vary between 20 and 714 µeV. For an ideal sphere and evanescent excitation, one would expect that only the m ) (l modes can be excited. Here the effect of natural shape deformation (symmetry invariance breaking) and the translation invariance breaking due to the sphere/substrate contact point allows the observation of scattered light from different m modes. For the m modes at energies, Emode, smaller than 1.970 eV, we explain the larger line broadening by an efficient photon escape into the substrate. The nanoemitter that shall be placed in the photon cavity field should have a large dipole oscillator strength, f, in comparison with atoms. To enhance f, we chose CdSe nanorods (NRs), which have an elongated shape along the crystal c axis (hexagonal crystalline lattice), a radius of R ≈ 2.5 ( 0.3 nm, and a length of L ≈ 25 nm. A thin shell of ZnS was grown to increase the emission quantum yield.29 For such emitters it was found recently that the oscillator strength of the energetically lowest exciton transitions is larger than that of spherical CdSe NCs as a result of enhanced excitonic exchange interaction,30,31 resulting in a nanorod radiative decay time τrad e 1 ns. In an ideal CdSe 1D nanorod, the hole states of the ground-state exciton exhibit dominant light hole-character, which is advantageous for low Fro¨hlich coupling constants of the exciton-LO phonon interaction, that is, small widths of the zero-phonon line.32 For spherical CdSe nanocrystals, experiments already show the existence of a very sharp zero-phonon line of a few microelectronvolts (fwhm) along with a broad acoustic phonon background of a few millielectronvolts.33-35 Figure 2 shows the spectrum of a single NR and its photostability Nano Lett., Vol. 6, No. 3, 2006
Figure 2. Spectrally resolved intensity versus time (linear grayscale) of a single CdSe NR (radius R ≈ 2.5 nm, length L ≈ 25 nm) measured by diffraction-limited imaging spectroscopy at T ) 15 K and acquisition time of 1 s each. The inset shows NR spectra at different times illustrating a spectral jump by 700 µeV.
with time at low temperature after excitation with the 488nm line of an Ar ion laser and detection with an achromatic objective (NA ) 0.85, x60) inside a bath cryostat then imaged onto the N2-cooled CCD of a 0.5-m spectrometer (spectral resolution 100 µeV). The NR emission is linearly polarized parallel to the c axis. It consists of a sharp spectralresolution-limited zero-phonon line (ZPL) and an acoustic phonon sideband, a typical signature of a localized exciton interacting with the acoustic phonon spectrum of the semiconductor nanostructure.30 As stressed by the inset, the spectral position of the ZPL is unchanged over a time interval of 4 s or longer. Such a long spectral stability is sufficient to observe a spectral matching of the cavity mode and the emitter emission. However, this matching is lost if a spectral jump (see Figure 2) occurs. The spectral jitter of the NR spectrum results from the charge fluctuations in the surroundings.36 In this work, we will make use of this spectral jitter as a natural tool to tune the single NR resonance energy of the ZPL. Temperatureinduced resonance tuning, as carried out in refs 12 and 13, cannot be used here to highlight the strong coupling regime because of the effect of spectral wandering and the narrow free spectral range of the cavity mode set. Instead, we measure the NR-cavity spectra over a long time interval and analyze the line shape for on/off resonant NR emission for a consecutive sequence of spectra. After characterization of the spectral properties of the cavity modes and the NR emitter separately, we now gather these two systems together and study their coherent interaction. By positioning the NR tangentially aligned on the sphere surface, it will excite predominantly TE modes with m ) (1 with the photon quantization axis defined perpendicular to the emitter polarization.37 With the spectral jitter of the NRs in mind, which is larger than the m mode line width, a Rabi splitting can only be detected during a certain transit time at lowest temperatures, T e 15 K. The samples, held together with the microscope optics inside a bath cryostat, are excited with the 488-nm line of an Ar ion laser. The emission from single modes is spatially selected by imaging spectroscopy using a high-resolution 2m-imaging spectrometer with a spectral resolution of 7 µeV and reading-out of only a few selected CCD channels (signal-to-noise ratio N Nano Lett., Vol. 6, No. 3, 2006
Figure 3. Left: exemplary spectra of four typical stages of nanorod detuning that are observable during the acquisition time. Bottom: reference sphere without nanorods. Γ denotes the fwhm obtained from a Gaussian line fit (thin solid line), tint is the integration time for each spectrum. Right: Spectra aligned with respect to their nanorod detuning energy demonstrating the avoided level crossing behavior.
≈ 10). We record for about 200 cavity modes a sequence of spectra during ∼400 s with an acquisition time of 4 s each, which, on one hand, is sufficiently long to have a detection intensity above the noise level, and, on the other hand, short enough to be within a time range without spectral jumps. For about 5% of modes we found a mode line shape that splits into a doublet symmetrically around a center energy with values for the splitting energy, pΩexp, between 30 and 45 µeV. Arguments for the observation of single NR coupling to nondegenerate photon modes are the following: the unlikely event of simultaneous spectral jumps of two identical NRs and the agreement of the observed Rabi splitting, which is of similar size for all NR-cavity mode spectra, with the calculated value (see below). In Figure 3 we show two exemplary set of spectra from different microspheres with CdSe NRs electrostatically attached to the surface. The samples, together with the microscope objective, are placed inside a bath cryostat and held at T ) 5 K. Figure 3 (left) shows for one sphere the four typical stages of nanorod detuning that are observable during the recording time with a clear line splitting for the NR in resonance. In contrast, the reference sphere without nanorods shows a much smaller mode line width and unchanged resonance energy with time. The assignment to the stage “detuned NR” is not primarily done by the observation of a separate side peak but in addition by the observation of a line narrowing of the (Purcell-effect enhanced) NR spectrum and the cavity mode width when the detuning energy increases (see Figure 4). In Figure 3 (right), we plot the spectra not according to their acquisition number but arranged them with respect to their nanorod detuning energy, allowing us to reconstruct the avoided level crossing behavior expected for the strong coupling regime. Along with the development of a doublet, the strong coupling regime should also be manifested in a modification of the 559
Figure 4. Line width (fwhm) vs detuning energy, ∆ENR, for the single nanorod (full symbols) and the cavity mode width (open symbols).
individual line shapes of nanorod and cavity mode. To examine these features we plot in Figure 4 the line widths of both nanorod and cavity emission as a function of detuning energy with respect to the nanorod line position. The maximum detuning range is about half of the ∼150 µeV mode spacing, that is, ∼75 µeV. The nanorod emission indeed shows the correct trend of a decrease in line width when the detuning energy increases. It approaches the experimental limit given by the spectral resolution of the 2m-spectrometer. The behavior of the cavity mode is more complex and needs further investigation: after an initial small decrease, the mode width jumps to a larger value in line width that can be caused by either coupling to the acoustic phonon background of the nanorod under study or the jump of a second, differently shaped nanorod into resonance with the cavity mode but without sufficient oscillator strength to enter the strong coupling regime. From the average of the experimental splittings, pΩexp ) 37 µeV, we deduce in the following the coupling constant, gexp, and compare it with theoretical predictions. In the present system, the lifetime broadening of the emitter spectra, pγe, is expected to be small with respect to pγc and can be neglected compared to the experimental photon line width, pγc ≈ 20 µeV, as deduced from radiative lifetime measurements30 and Figure 4. As result, we obtain the estimate pgexp ≈ x(pΩexp)2+(pγc)2/16 and pgexp ) 19 µeV, that is, the strong coupling condition g > |γe - γc|/4 is well satisfied. For comparison, we calculate the coupling constant, gth, using
gth ) λ/2πxπc(2nˆ 2+nˆ NR)/(2nˆ 3τradV) according to ref 25, with the emission wavelength, λ, the emitter radiative decay time in free space, τrad, the effective mode volume, V, the refractive indices of the semiconductor material, nˆ NR, and of the polymer sphere, nˆ , and the vacuum velocity of light, c. The mode volume was approximated by a torus with a length equal to the sphere perimeter and a section radius of λ/nˆ , which gives V ≈ 8 µm3. To obtain consistency between pgexp and pgth, the NR radiative decay times, τrad, have to span the range between 1.6 ns and 0.7 ns, which is in agreement with photoluminescence decay time measurements.30 Let us note here that at T ) 5 K the acoustic phonon sideband is still a nonnegligible contribution to the spectrum (see Figure 2). In refs 38 and 39 it has been theoretically 560
Figure 5. Photon lifetime measured for an ensemble of high-Q T E142 modes for a sphere with and without NRs. The inset shows, for the example of the empty sphere, the typical spectral window that is excited by the femtosecond pulse covering a set of several m-degenerated cavity modes. In addition, the monoexponential (biexponential) fit functions are plotted and the obtained decay times are given.
shown that if there is a perfect matching between the cavity mode and the ZPL then the Rabi frequency is exponentially suppressed by a factor exp(-S/2) as a result of excitonphonon coupling, where S is the Huang-Rhys parameter. This parameter, deduced from the intensity ratio of the first LO replica and the ZPL from the CdSe NRs µPL spectra, ranges between ∼0.04 and ∼0.16. It implies only a small correction of the Rabi splitting energy by the excitonphonon coupling. However, the ZPL is most of the time not in resonance with the ∼20 µeV wide mode and the emission coming from the acoustic phonon sideband, which spreads over ∼5 meV, can flow through the mode in a weak coupling regime. For this reason the mode is always “switched on” and can be detected even without being in the strong coupling regime. To support our results, we compare finally the photon lifetime for microspheres with and without NRs at T ) 5 K (Figure 5). A resonant 120-fs pulse of the OPO was tuned in resonance to a set of cavity m-modes having the same n and l mode number within a narrow spectral window (see inset of Figure 5). For the detection of both the emptymicrosphere and NR-microsphere photon lifetime, we use a spectrometer and a synchroscan streak camera with a time resolution of 5 ps. When no emitters are on the sphere, the cavity photon decay is monoexponential with a decay time of ∼30 ps, implying that all excited modes have roughly the same homogeneous line width of ∼22 µeV, in agreement with the empty-sphere spectral line width measured, for example, in Figure 3. The superimposed modulation is explained by a beating between the different excited m photon modes. The decay curve of the coupled NR-cavity photon system is more complex. For the spheres covered with a submonolayer of NRs, we observe two decay regimes: a fast, almost monoexponential decay of ∼10 ps followed by a slow exponential decay of 60 ps. We assign the fast decay to modes that are not in the strong coupling regime but spectrally broadened because of the nanorod absorption. For these (majority) modes we measured a fwhm between 50 and 70 Nano Lett., Vol. 6, No. 3, 2006
µeV, which is in good agreement with a ∼10 ps photon lifetime component. The slower decay is attributed to the decay of the 5% modes in the strong coupling regime. For these modes the decay time is two times longer than the decay of the same modes without NRs, which is a striking signature of the strong coupling regime. From the average line broadening (fwhm) of the Rabi doublet given by (1/2)(pγe + pγc),23,24 and assuming γc . γe, the change in photon lifetime with and without coupling to nanoemitters is just the factor of 2 measured in our experiment. Summarizing, we have presented a study of the strong coupling regime of cavity QED with semiconductor nanocrystals in microsphere cavities using spectrally and timeresolved imaging spectroscopy. With colloidal CdSe NRs, we add a new material class for which solid-state-based cavity QED was implemented. This might stimulate applications of colloidal NCs in photonic crystal cavities, which are expected to have the smallest possible mode volumes. Acknowledgment. We thank W. Langbein and E. Herz for experimental assistance and sample preparation. Financial support from the EU Project HPRN-CT-2002-00298, the DFG project Wo477/18, the GRK 726 (U.W.), and the DIP and the James Franck program (U.B.) is gratefully acknowledged. References (1) Berman, P.; Ed. CaVity Quantum Electrodynamics; Academic: San Diego, 1994. (2) Rabi, I. I. Phys. ReV. 1937, 51, 652. (3) Allen, L.; Eberly, J. H. Optical Resonances and Two-LeVel Atoms; Wiley: New York, 1975. (4) Gerard, J. M.; Gayral, B. Physica E 2001, 9, 131. (5) Thompson, R. J.; Rempe, G.; Kimble, H. J. Phys. ReV. Lett. 1992, 68, 1132. (6) Brune, M.; Schmidt-Kaler, F.; Maali, A.; Dreyer, J.; Hagley, E.; Raimond, J. M.; Haroche, S. Phys. ReV. Lett. 1996, 76, 1800. (7) Pellizzari, T.; Gardiner, S. A.; Cirac, J. I.; Zoller, P. Phys. ReV. Lett. 1995, 75, 3788. (8) Cirac, J. I.; Zoller, P.; Kimble, H. J.; Mabuchi, H. Phys. ReV. Lett. 1997, 78, 3221. (9) Duan, L. M.; Kimble, H. J. Phys. ReV. Lett. 2004, 92, 127902. (10) Mabuchi, H.; Doherty, A. C. Science 2002, 298, 1372. (11) McKeever, J.; Boca, A.; Boozer, A. D.; Buck, J. R.; Kimble, H. R. Nature 2003, 425, 268. (12) Reithmaier, J. P.; Sek, G.; Lo¨ffler, A.; Hofmann, C.; Kuhn, S.; Reitzenstein, S.; Keldysh, L. V.; Kulakovskii, V. D.; Reinecke, T. L.; Forchel, A. Nature 2004, 432, 197. (13) Yoshie, T.; Scherer, A.; Hendrickson, J.; Khitrova, G.; Gibbs, H. M.; Rupper, G.; Ell, C.; Shchekin, O. B.; Deppe, D. G. Nature 2004, 432, 200.
Nano Lett., Vol. 6, No. 3, 2006
(14) Peter, E.; Senellart, P.; Martrou, D.; Lemaitre, A.; Hours, J.; Gerard, J. M.; Bloch, J. Phys. ReV. Lett. 2005, 95, 067401. (15) Wallraff, A.; Schuster, D. I.; Blais, A.; Frunzio, L.; Huang, R. S.; Majer, J.; Kumar, S.; Girvin, S. M.; Schoelkopf, R. J. Nature 2004, 431, 162. (16) Purcell, E. M. Phys. ReV. 1946, 69, 681. (17) Gaponenko, S. V., Bogomolov, V. N.; Petrov, E. P.; Kapitonov, A. M.; Yarotsky, D. A.; Kalosha, I. I.; Eychmu¨ller, A. A.; Rogach, A. L.; McGilp, J.; Woggon, U.; Gindele, F. J. LightwaVe Technol. 1999, 17, 2128. (18) Kulakovich, O.; Strekal, N.; Yaroshevich, A.; Maskevich, S.; Gaponenko, S. V.; Nabiev, I.; Woggon, U.; Artemyev, M. V. Nano Lett. 2002, 2, 1449. (19) Fan, X.; Lonergan, M.; Zhang, Y.; Wang, H. Phys. ReV. B 2001, 64, 115310. (20) (a) Artemyev, M. V.; Woggon, U.; Wannemacher, R.; Jaschinski, H.; Langbein, W. Nano Lett. 2001, 1, 309. (b) Woggon, U.; Wannemacher, R.; Artemyev, M. V.; Mo¨ller, B.; LeThomas, N.; Anikeyev, V.; Scho¨ps, V. Appl. Phys. B 2003, 77, 469. (21) Hu, J.; Li, L.; Yang, W.; Manna, L.; Wang, L.; Alivisatos, A. P. Science 2001, 292, 2060. (22) Kazes, M.; Lewis, D. J.; Ebenstein, Y.; Mokari, T.; Banin, U. AdV. Mater. 2002, 14, 317. (23) Andreani, L. C.; Panzarini, G.; Ge´rard, J. M. Phys. ReV. B 1999, 60, 13276. (24) Carmichael, H. J.; Brecha, R. J.; Raizen, M. G.; Kimble, H. J.; Rice, P. R. Phys. ReV. A 1989, 40, 5516. (25) Thra¨nhardt, A.; Ell, C.; Khitrova, G.; Gibbs, H. M. Phys. ReV. B 2002, 65, 035327. (26) (a) Fan, X.; Lacey, S.; Palinginis, P.; Wang, H.; Lonergan, M. Opt. Lett. 2000, 25, 1600. (b) Brun, T. A.; Wang, H. Phys. ReV. A 2000, 61, 323071. (27) Buck, J. R.; Kimble, H. J. Phys. ReV. A 2003, 67, 033806. (28) Lai, H. M.; Leung, P. T.; Young, K.; Barber, P. W.; Hill, S. C. Phys. ReV. A 1990, 41, 5187. (29) Mokari, T.; Banin, U. Chem. Mater. 2003, 15, 3955. (30) Le Thomas, N.; Herz, E.; Scho¨ps, O.; Woggon, U.; Artemyev, M. V. Phys. ReV. Lett. 2005, 94, 016803. (31) Shabaev, A.; Efros, A. L. Nano. Lett. 2004, 4, 1821. (32) (a) Go¨ger, G.; Betz, M.; Leitenstorfer, A.; Bichler, M.; Wegscheider, W.; Abstreiter, G. Phys. ReV. Lett. 2000, 84, 5812. (b) Betz, M.; Go¨ger, G.; Leitenstorfer, A.; Bichler, M.; Abstreiter, G.; Wegscheider, W. Phys. ReV. B 2002, 65, 085314. (33) (a) Palinginis, P.; Wang, H. App. Phys. Lett. 2001, 78, 1541. (b) Palinginis, P.; Tavenner, S.; Lonergan, M.; Wang, H. Phys. ReV. B 2003, 67, 201307(R). (34) Gindele, F.; Hild, K.; Langbein, W.; Woggon, U. Phys. ReV. B 1999, 60, R2157. (35) Woggon, U.; Gindele, F.; Wind, O.; Klingshirn, C. Phys. ReV. B 1996, 54, 1506. (36) Empedocles, S. A.; Norris, D. J.; Bawendi, M. G. Phys. ReV. Lett. 1996, 77, 3873. (37) (a) Mo¨ller, B. M.; Artemyev, M. V.; Woggon, U.; Wannemacher, R. Appl. Phys. Lett. 2002, 80, 253. (b) Mo¨ller, B. M.; Woggon, U.; Artemyev, M. V.; Wannemacher, R. Appl. Phys. Lett. 2003, 83, 2686. (38) Wilson-Rae, I.; Imamoglu, A. Phys. ReV. B 2002, 65, 235311. (39) Zhu, K.-D.; Li, W.-S. Phys. Lett. A 2003, 314, 380.
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