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26 DBR. (a) λ Quantum well DBR. ~ 3 µm (b) 50 nm Quantum well ~ 1 µm (c) Quantum well

27 ~ λ/2 ω k (a) (b)

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31 Fiber stem Fiber stem Quantum well - Nanocrystal (a) (b)

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36 ν ν Absorption of a photon (a) Emission of a photon (b)

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40 Cavity mode Atomic transition Intensity Enhanced decay 0 Detuning Time (a) (b)

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43 Frequency domain Time domain Intensity Intensity ω a Ω Rabi (a) ω a + Ω Rabi ω (b) t

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46 Fiber ZnSe lens CO 2 laser Weight (a) (b)

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54 1 (a) p = 1, l = 40 0 Normalized electric field (b) (c) p = 1, l = 400 p = 2, l = Normalized radius

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59 Spectrometer Pulse laser

60 FSR Intensity (Arb. units) Wavelength (nm)

61 Detector Tunable diode laser Tapered single mode fiber Detector

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63 Detector WGM emission Reflection θ Tunable diode laser PTS WGM emission Tunable diode laser Reflection Detector (a) (b)

64 Intensity (Arb. units) Intensity (Arb. units) (a) 1 nm (b) Wavelength (nm)

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70 E... Continuum n = 2 n = 1 Photon K

71 13 nm GaAs Quantum Well 15 nm AlGaAs Barrier AlGaAs GaAs GaAs Capping Layer GaAs Substrate 1.9 ev 1.5 ev 340 mev 60 mev (a) (b)

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74 Uncoupled photoluminescence Coupled photoluminescence P sample CW laser Prism PTS Quantum well Cryostat

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76 (a) Intensity (Arb. units) (b) Wavelength (nm)

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80 Prism GaAs capping layer + AlGaAs barrier Dipole transition GaAs quantum well

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82 Reflection beam Whispering gallery mode emission P Prism sample Quantum well PTS Tunable diode laser Cryostat

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121 Conduction band J e =1/2 Energy Valence band J h =3/2 J h =1/2 Heavy hole Light hole Split-off Γ

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125 Diameter (nm) Energy (mev) U ±1 U 0 L ±1 L ± /d 3 (10 nm -3 )

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129 BS Sample Spectrometer PMT PreAmp Stop Discriminator Fast photodetector TAC MCA (a) PreAmp Discriminator Start 2000 (b) Counts 1000 FWHM = 1.5 ns Time (ns)

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136 (a) D = 4.0 nm Red side 10 K Intensity (Arb. units) (b) D = 5.4 nm Red side 20 K 35 K 10 K 20 K 35 K (c) D = 9.0 nm Red side 10 K 20 K K Time (ns)

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148 on resonance τ 2 = 10.7 ns Intensity (Arb. units) off resonance τ 2 = 12.4 ns Time (ns)

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150 T = 30 K Intensity (Arb. units) (a) D = 5.4 nm, Red side (b) D = 9.0 nm, Red side T = 30 K T = 35 K T = 40 K Time (ns)

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153 F m 0 U ±1 U 0 L ±1 L ±2 τ 10 ns F m = ±1 U τ< 1 ns F m = ±1 L τ spin F m = ±2 (dark state) τ 1 µs (a) (b)

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157 Normalized electric field 1 0 Spatial distribution Nanocrystal doping (a) 1.0 Normalized radius 1 0 Spectral distribution Cavity resonance (b) Detuning

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183 PHYSICAL REVIEW A VOLUME 56, NUMBER 4 OCTOBER 1997 Laser emission from semiconductor microcavities: The role of cavity polaritons Xudong Fan and Hailin Wang Department of Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon H. Q. Hou and B. E. Hammons Sandia National Laboratories, Albuquerque, New Mexico Received 3 March 1997 We present an experimental study on the role of cavity polaritons in laser emissions from a GaAs quantumwell microcavity. We show that cavity polaritons play no role in the laser emission process when the cavity is nearly resonant with the excitons. The laser emissions emerge from the bare cavity mode instead of from a cavity-polariton branch and the threshold density is much higher than the saturation density at which cavity polaritons vanish. We also show that the presence of emission doublets near the lasing threshold, which was previously taken as an evidence for laser emission from cavity polaritons, is primarily the result of spatial and/or temporal variations of exciton densities within the excitation volume. S PACS number s : f Nonequilibrium condensation of exciton polaritons coupled exciton-photon modes was first discussed for bulk crystals with dipole-allowed interband optical transitions 1. In such systems, the presence of a relaxation bottleneck near the turning point of the lower polariton dispersion leads to accumulation of polaritons. Stimulated transitions of polaritons into the bottleneck region become important when the occupation number of polaritons in this region exceeds 1. This stimulated transition process is very similar to stimulated emission of photons in a laser and could similarly lead to non-equilibrium condensation of polaritons in the bottleneck region. Coupled exciton-photon modes are qualitatively modified near k 0 in a semiconductor microcavity due to the quantization of photon wave vectors and are referred to as cavitypolaritons 2 3. Nonequilibrium condensation of cavity polaritons can in principle occur at k 0 instead of at the bottleneck region. In the limit excitons couple strongly to the cavity mode, the mass of cavity polaritons near k 0 can become much smaller than the mass of bare excitons. For GaAs quantum-well QW microcavity structures, the polariton mass corresponds to a thermal de Broglie wavelength of 7 m at 4 K, far greater than the exciton Bohr radius of order 0.01 m. It was argued that because of this extremely large thermal de Broglie wavelength, nonequilibrium condensation of cavity polaritons could occur at a density far below the exciton Mott density and therefore could be realized experimentally 4,5. Optical emissions from such a condensate are shown theoretically to be approximately in a coherent state, providing a mechanism for generating coherent laserlike emissions 5. Evidence of nonequilibrium condensation of cavitypolaritons has been reported recently in a GaAs QW microcavity 4. A doublet was observed in emission spectra with one of the emission resonance exhibiting laserlike threshold behaviors. It was argued that this doublet is due to emissions from two branches of cavity polaritons and the laserlike resonance is due to emissions from a nonequilibrium condensate of cavity polaritons. The physical origin of the emission doublet, especially, the role of cavity polaritons in the lasing process has been a subject of considerable debate. In this paper we present an experimental study on the role of cavity polaritons in laser emission from a GaAs QW microcavity. We show that laser emissions emerge from the bare cavity mode instead of from a cavity-polariton branch and that cavity polaritons vanish at densities far below the lasing threshold. Physically, the lasing process is due to stimulated emission of photons rather than condensation of cavity polaritons. Measurements using a pinhole aperture to probe a small region within the excitation volume also reveal that emission doublets observed near the lasing threshold are the result of spatial and/or temporal variations of exciton densities within the excitation volume and cannot be taken as an evidence of persistence of cavity polaritons at the lasing threshold. In addition, exciton localization due to interface fluctuations is suggested as a major obstacle for achieving the elusive nonequilibrium condensation of cavity polaritons. The GaAs QW microcavity used in our study has four 13 nm GaAs QW s placed at the center of a wavelength-long cavity and uses pairs of Al 0.11 Ga 0.89 As/AlAs Bragg reflectors as the top bottom mirror. The cavity length is tapered such that the cavity resonance varies slightly across the sample while the energy of excitons remains nearly constant. All measurements were performed at 10 K unless otherwise noted. Figure 1 a shows reflection spectra of the sample when the cavity is tuned slightly above the heavy-hole exciton absorption line center. At low excitation limit, the reflection spectrum is characterized by two well-resolved cavitypolariton resonances the minimum normal mode splitting of the sample is 2.6 nm. At high excitation limit, the normal mode splitting collapses and cavity-polaritons disappear 6 8. In this limit, reflectivity spectra are characterized by the bare cavity resonance as shown by the dashed curve in Fig. 1 a. The collapse of the normal splitting was shown to be due to ionization of excitons in an earlier study 8. With a further increase in excitation levels the bare cavity resonance moves toward lower wavelength due to mode pulling of the cavity resonance not shown /97/56 4 / /$ The American Physical Society

184 3234 XUDONG FAN, HAILIN WANG, H. Q. HOU, AND B. E. HAMMONS 56 FIG. 1. Reflection and emission spectra with pulsed excitation at two different exciton-cavity detunings. The solid and dashed reflection spectra are obtained at low and high excitation limits, respectively. Emission spectra are obtained at input intensities of 80, 120, 150, 230, 290, 360 W/cm 2 for a and of 40, 80, 120, 160, 200, 240, 280 W/cm 2 for b. The top emission spectrum is obtained at the threshold pumping intensity. Corresponding emission spectra at various excitation levels are shown in Fig. 1 a. For the emission measurement, the sample is excited off resonantly at a reflection minimum near 755 nm with output from a mode-locked Ti:Sapphire laser. A doublet is observed in emission spectra. At lowest input intensities, the doublet corresponds to the two cavitypolariton resonances in the reflection spectrum and is due to emissions from the two branches of cavity polaritons. Emissions from upper higher energy cavity polaritons are much weaker because of the very low temperature. With increasing excitation levels, the total emission intensity spectrally integrated increases rapidly while the intensity of the lower energy resonance in the doublet saturates. Figure 2 a shows the threshold behavior of the total emission intensity as a function of the input intensity. Figure 2 b shows saturation of the intensity of the lower energy resonance as a function of the input intensity. An emission spectrum above the lasing threshold is also shown as an inset in Fig. 2 a and is completely dominated by the higher energy resonance. Behaviors qualitatively similar to those shown in Fig. 2 are also observed at other exciton-cavity detunings as long as the cavity is resonant or nearly resonant with the excitons. Emission spectra shown in Fig. 1 a along with the threshold behavior shown in Fig. 2 a might lead to an assignment that the doublet in Fig. 1 a is due to emissions from two cavity-polariton branches at all input intensities with the upper polariton going above the threshold with increasing input intensities. This assignment would imply that emissions from the lower lower energy polariton branch should saturate at an input intensity near the lasing threshold. Figure 2 b, however, shows that the output from the lower energy resonance saturates at an input intensity near 50 W/cm 2 much lower than the threshold intensity of 360 W/cm 2. Problems associated with the above assignment become more evident when we examine emission spectra obtained FIG. 2. a Total output intensity as a function of the input intensity. b Output intensity from the lower energy emission resonance as a function of the input intensity. The exciton-cavity detuning is the same as in Fig. 1 a. The inset shows an emission spectrum above the lasing threshold. with the cavity tuned slightly below the exciton resonance see Fig. 1 b. At lowest input intensities, the emission spectra feature a doublet that corresponds to the two cavitypolariton resonances in the reflection spectrum. With increasing input intensities, however, the emission resonance from the upper cavity polariton disappears and a new resonance emerges from between the two cavity-polariton resonances. The energy position of the new resonance agrees with that of the bare cavity resonance and moves toward higher energy with increasing input intensities. We emphasize that the same behavior is also observed when we tune the cavity resonance above the exciton resonance. The approximate agreement in energy position between the upper cavity polariton and the higher energy emission resonance near the lasing threshold shown in Fig. 1 a is coincidental since in this case the bare cavity resonance is close to the upper cavity polariton. The main issue in understanding the above experimental result is whether near the lasing threshold cavity polaritons still remain a valid description for optical excitations in the microcavity. The observation of optical emissions from the bare cavity resonance far below the lasing threshold clearly indicates that the threshold density n th is much greater than the saturation exciton density n s at which normal mode splitting collapses and cavity polaritons vanish 9. This is also supported by the saturation of the lower energy emission resonance at densities much smaller than n th see Fig. 2 b since optical emissions from the lower cavity polaritons are expected to saturate at n s. We therefore conclude that cavity polaritons play no roles in the lasing process and that the laser emission is due to stimulated optical transitions rather than condensation of polaritons. The above model satisfactorily explains the behavior of laser emission and the saturation of optical emission from

185 56 LASER EMISSION FROM SEMICONDUCTOR FIG. 3. Emission spectra collected from the center of the excitation volume. Input intensities used are 80, 160, 240, 280 W/cm 2. Other experimental conditions are similar to that of Fig. 1 a. lower cavity polaritons but does not account for the persistence of emission doublets at or near the lasing threshold. As shown in Fig. 1, the energy position of the lower energy emission resonance follows that of the lower cavity polariton and remains nearly independent of the input intensities. The lower energy emission resonance is therefore associated with the lower cavity polaritons at all input intensities. In contrast, the higher energy emission resonance is due to emissions from the upper cavity polaritons only at very low input intensities and switches to the bare cavity resonance approaching the lasing threshold, as shown earlier. This raises the question that if n th n s, why strong optical emissions from the lower cavity-polariton can still be observed at the threshold pumping intensity. In fact, the presence of a doublet near the lasing threshold was taken to be a crucial evidence for the role of cavity polaritons in the lasing process. Properties of optical excitations in a microcavity depend critically on the density of excitons when the exciton density is near n s. The persistence of lower cavity-polariton emissions near the lasing threshold reflects important effects of spatial and/or temporal variations of exciton densities within the excitation volume. In a typical optical measurement and at a given pumping intensity, the exciton or carrier density varies greatly from the center to the edge. There are always outer regions where the density of excitons falls below n s even when the density of excitons exceeds n s at the center. Optical emissions from these outer regions are characterized by emissions from two branches of cavity polaritons. As a result, emission spectra can feature simultaneously contributions from the bare cavity resonance as well as the cavity polaritons. Note that emissions from the upper-cavity polaritons are more than one order of magnitude smaller than that of the lower cavity polaritons and can be overwhelmed by emissions emerging from the bare cavity resonance near the threshold pumping intensity. Figure 3 shows emission spectra obtained by collecting emissions from only the center region of the excitation volume to eliminate effects of spatial variation of exciton densities. The measurement was done under experimental conditions similar to that of Fig. 1 a but with a 5 m aperture placed at the center of the image of the excitation spot the laser spot size is estimated to be 130 m. As shown in Fig. 3, just below the threshold pumping intensity lower cavitypolariton emissions are one order of magnitude smaller than emissions from the bare cavity resonance. In comparison, at similar pumping intensities emission spectra for the whole FIG. 4. Emission spectra with cw exciton and collected from the center of the excitation volume a and near the edge of the excitation volume b. Input intensities used are 0.05I 0, 0.1I 0, 0.15I 0, 0.2I 0, 0.3I 0, 0.45I 0, 0.65I 0 for a and 0.15I 0, 0.5I 0, 0.85I 0, I 0, 1.5I 0 for b where I 0 is the threshold pumping intensity. Other experimental conditions are similar to that of Fig. 1 a. excitation volume feature nearly equal contributions from the lower cavity-polaritons and the bare cavity resonance see Fig. 1 a. The residual emission from the lower cavitypolaritons near the threshold pumping intensity shown in Fig. 3 is due to temporal variation of exciton densities as we discuss below. Measurements discussed so far have used output from a mode-locked Ti:Sapphire laser and the time interval between successive pulses 13 ns is large compared with the exciton or carrier recombination time of order 1 ns. Under these conditions, both the density and the distribution of electronic excitations in the sample are a function of the time. In particular, there are temporal regions where the density of excitons falls below n s even when the peak exciton density is above n s. This is especially true for sufficiently long delays after an excitation pulse. Therefore, emission spectra obtained with pulsed excitations can still feature contributions from both bare cavity resonance and cavity polaritons even when exciton densities are spatially uniform. Figure 4 a shows emission spectra obtained with offresonant cw excitation and with a 5 m aperture at the center of the image of the excitation spot to eliminate both spatial and temporal variations of excitation densities. Emerging of the bare cavity resonance and correspondingly the saturation of the lower cavity-polariton emission at densities far below n th is clearly observed. Near and below the threshold pumping intensity, emissions from the lower cavity polaritons are now reduced to more than two orders of magnitude smaller than emissions from the bare cavity resonance. Note that, experimentally, it is difficult to compare excitation levels of cw and pulsed pumping and we have used the threshold input intensity as a reference. To further illustrate effects of spatial variations of exciton densities, Fig. 4 b also shows emission spectra obtained by placing a 25 m aperture at the edge of the image of the excitation spot. In this case, the persistence and a continued linear increase of the lower cavity-polariton emission even at intensities above the threshold pumping intensity is observed. These results clearly demonstrate that cavity polaritons vanish at a density far below n th and that the persistence of lower cavitypolariton emissions at the threshold pumping intensity shown

186 3236 XUDONG FAN, HAILIN WANG, H. Q. HOU, AND B. E. HAMMONS 56 in Fig. 1 is due to emissions from spatial or temporal regions where the exciton density is below n s. Finally, we discuss briefly mechanisms that prevent the realization of nonequilibrium condensation of cavity polaritons. Theoretically, quantum statistical effects of polaritons were predicted to be effective when the interparticle distance is small compared with the polariton thermal de Broglie wavelength, which implies that at very low temperature bosonic effects can become important at exciton densities as low as 10 7 /cm 2 in GaAs QW microcavities. Significant buildup of cavity-polaritons near k 0, however, can be prevented by the extremely short polariton life time of order 1 ps along with the long polariton-acoustic phonon scattering time of order 100 ps or longer 10. Another mechanism that can prevent the condensation from occurring is exciton localization. For typical QW structures, interface fluctuations can localize excitons in local minima of the confinement potential These localized excitons behave as fermions rather than bosons. Experimental realization of nonequilibrium condensation of cavity polaritons therefore requires the use of nearly perfect quantum heterostructures where effects of exciton localization are negligible even at extremely low exciton densities. In conclusion, we have shown that cavity polaritons play no role in laser emission from GaAs QW microcavities at low temperature when the cavity is nearly resonant with the excitons. The threshold density is much higher than the saturation density at which normal mode splitting collapses and cavity polaritons vanish. The presence of emission doublets near the lasing threshold, which was previously taken as an evidence for laser emission from cavity polaritons, is the result of spatial and/or temporal variations of exciton densities within the excitation volume. We wish to acknowledge helpful and stimulating discussions with Y. Yamamoto, S. W. Koch, G. Khitrova, and H. Gibbs. The work performed at the University of Oregon is supported by AFOSR. 1 For a recent review, see, L. V. Keldysh, in Bose-Einstein Condensations, edited by A. Griffin, D. W. Snoke, and S. Stringari Cambridge University Press, New York, C. Weisbuch et al., Phys. Rev. Lett. 69, ; T. Norris et al., Phys. Rev. B 50, ; J. Jacobson et al., Phys. Rev. A 51, ; H. Wang et al., Phys. Rev. B 51, R. Houdre et al., Phys. Rev. Lett. 73, ; R. Stanley et al., Phys. Rev. B 53, S. Pau et al., Phys. Rev. A 54, R A. Imamoglu and R. J. Ram, Phys. Lett. A 214, ; A. Imamoglu et al., Phys. Rev. A 53, R. Houdre et al., Phys. Rev. B 52, J.-K. Rhee et al., Solid State Commun. 97, F. Jahnke et al., Phys. Rev. Lett. 77, Although it is difficult to determine the density of excitons with desired accuracy, we estimate that the threshold intensity (380 W/cm 2 ) corresponds to an exciton or electron-hole pair density above /cm S. Pau et al., Phys. Rev. B 51, J. Hegarty and M. D. Sturge, J. Opt. Soc. Am. B 2, H. Wang, M. Jiang, and D. G. Steel, Phys. Rev. Lett. 65, Emission measurements by tuning the cavity resonance far away from the exciton line center give a Stokes shift of 1.5 nm.

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188 PHYSICAL REVIEW B VOLUME 56, NUMBER DECEMBER 1997-I Laser emission from semiconductor microcavities: Transition from nonperturbative to perturbative regimes Xudong Fan and Hailin Wang Department of Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon H. Q. Hou and B. E. Hammons Sandia National Laboratories, Albuquerque, New Mexico Received 14 August 1997 We have demonstrated laser emission at densities below the saturation exciton density in a semiconductor microcavity by tuning the cavity resonance to the low-energy side of the inhomogeneously broadened exciton distribution. Laser emission in this regime arises from population inversion of localized excitons at the lowenergy tail of the inhomogeneous distribution. Distinct spectral line shapes of laser emission and especially a large and abrupt change in the lasing threshold are observed when the composite system undergoes a transition from the nonperturbative to the perturbative regimes. The abrupt threshold change is attributed to ionization of excitons occurring in the transition region. S Semiconductor quantum well QW microcavities as a composite exciton-cavity system have provided a unique system for investigating optical and excitonic many-body interactions in a nonperturbative regime. In this regime, coherent dipole coupling rates between the exciton and the cavity mode are large compared with relevant damping rates, leading to the formation of coupled exciton-cavity modes, or cavity polaritons. Effects of cavity polaritons have been observed in various measurements including normal-mode splitting in emission or reflection spectra 1,2 and normal-mode oscillations in transient optical responses. 3,4 Whether laser emission can occur in the nonperturbative regime of semiconductor microcavities has thus far remained an open question. In order to achieve laser emission in the nonperturbative regime, the threshold density n th has to be small compared with the saturation exciton density n sat,at which cavity polaritons start to vanish due to bleaching of the excitonic resonance. 5,6 For typical microcavity configuration, this is not the case and excitonic resonance bleaches at densities far below n th. 7,8 The difficulty in reaching the lasing threshold in the nonperturbative regime stems from the fact that population inversion of excitons cannot be achieved for a homogeneously broadened system without bleaching the excitonic resonance. 9 In order to achieve laser emission from an excitonic system, optical transitions have to involve other processes such as biexcitonic transition, phonon-assisted transition, bosonic condensation of excitons, or exciton localization. 9 Laser emission due to biexcitonic transition and exciton localization has been observed in semiconductors such as II-VI QW s that have a relatively large exciton binding energy. 10 Laser emission from excitons in II-VI QW microcavities has also been observed recently. 11 In this paper we present experimental studies of laser emission in the nonperturbative regime in a composite system of high-q cavity and inhomogeneously broadened excitons. By tuning the cavity resonance to the low-energy side of the inhomogeneous exciton distribution we are able to achieve laser emission at exciton densities considerably below n sat. Laser emissions at these low densities are shown to arise from population inversion of localized excitons. Distinct spectral line shapes of laser emission and especially a large and abrupt change in the lasing threshold are also observed when the composite system undergoes a transition from the nonperturbative to the perturbative regimes. The abrupt threshold change is attributed to ionization of excitons occurring in the transition region. The sample used for our study is a GaAs QW microcavity that has four 13-nm GaAs QW s placed at the center of a wavelength-long cavity and uses pairs of Al 0.11 Ga 0.89 As/AlAs Bragg reflectors as the top bottom mirror. The microcavity is held at 10 K by using a cold-finger cryostat. The cavity thickness is tapered such that the cavity resonance varies across the sample while the energy of excitons remains nearly constant. Figure 1 a shows the energy position of two cavity-polariton branches associated with the heavy-hole hh exciton as we tune the cavity resonance by moving the laser spot across the sample. The minimum normal-mode splitting observed is 2.6 nm. The exciton linewidth is estimated to be 1 nm and the empty cavity linewidth is 0.2 nm, reflecting the high Q factor of the cavity. The threshold pumping intensity I th as a function of the emission wavelength at the lasing threshold is shown in Fig. 1 b the laser spot size is estimated to be cm 2. The threshold is identified from the onset of a rapid increase in the output power and a spectral narrowing in the corresponding emission spectrum the threshold behavior will be discussed in detail later. The sample is excited offresonantly at a reflection minimum near 755 nm with output from a mode-locked Ti:sapphire laser with a 80-MHz repetition rate. The wavelength dependence of I th is obtained by tuning the cavity resonance within the hh exciton absorption profile. As shown in Fig. 1 b, I th decreases significantly below the exciton absorption line center, especially at the lowenergy tail of the exciton absorption before increasing again when the cavity is tuned far below the line center. The mini /97/56 23 / /$ The American Physical Society

189 56 LASER EMISSION FROM SEMICONDUCTOR FIG. 2. Emission and reflection spectra at low excitation limit and at a sample position where I th is below I sat. FIG. 1. a The wavelength of cavity polaritons at different sample positions. b Threshold pumping intensity as a function of the emission wavelength at the lasing threshold. The exciton line center is determined from reflection and emission spectra when the cavity is far detuned from the exciton resonance. The dashed line in b indicates the level of saturation pumping intensity. mum I th is more than one order of magnitude smaller than I th at the line center. Note that the observed wavelength dependence cannot be accounted for by band-gap renormalization. For GaAs QW s, energy shifts of exciton resonance due to band-gap renormalization are nearly canceled by the decrease in the exciton binding energy and the energy position of the excitonic resonance remains nearly independent of the excitation level. 6,12 The drastic decrease in I th results from effects of exciton localization in QW s, as we will discuss in detail later. 13,14 The dashed line in Fig. 1 b also indicates the level of saturation pumping intensity at which cavity polaritons start to vanish due to bleaching of the excitonic resonance. I sat is measured when the cavity is tuned to near the exciton absorption line center since I sat is independent of the excitoncavity detuning. Experimentally, we determine I sat by measuring the pumping intensity at which optical emissions from the lower energy cavity-polariton branch start to saturate. Note that I sat can also be determined by measuring the pumping intensity at which normal-mode splitting starts to collapse although spatial and temporal variation of exciton densities within the excitation region can significantly complicate the measurement as shown in an earlier study see Ref. 7 for a detailed discussion on measurements of I sat. The minimum I th (24 W/cm 2 ), which is achieved in a spectral region 3 nm below the exciton absorption line center, is considerably below the saturation pumping intensity I sat 50 W/cm 2, suggesting that laser emission at very low pumping intensities occurs in the nonperturbative regime. Although it is difficult to determine precisely exciton densities in our study, we estimate that the minimum I th corresponds to an exciton density of /cm 2, which is well below the exciton Mott density. The very small I th is also in part due to the small loss or high Q factor of the microcavity since in order to achieve lasing actions gain has to be greater than the loss. We now examine emission spectra when the cavity is tuned to below the exciton absorption line center for signatures of cavity polaritons near the lasing threshold. Figure 2 shows as a reference both reflection and emission spectra obtained at low excitation limit and with the cavity tuned to the spectral region where very low I th is obtained. Two pronounced cavity-polariton resonances are observed in the reflection spectrum, indicating that the composite system is still in the nonperturbative regime, 15 although the energy separation between the bare mode and the corresponding coupled mode is now smaller than that when the cavity is at the exciton line center. A direct comparison of the reflection and emission spectra shows that the emission resonance is due to lower cavity polaritons. The spectral linewidth of the polariton emission is 0.25 nm. Emission spectra obtained with increasing pumping intensities are shown in Fig. 3. Below a pumping intensity of 12 W/cm 2, the emission is due to spontaneous emission from lower cavity polaritons. Approaching I th, a laser emission emerges directly from the lower cavity-polariton branch as shown in Fig. 3 a, in an agreement with I th I sat. At the threshold pumping intensity of 26 W/cm 2, a rapid increase of the emission intensity see the inset of Fig. 3 a is clearly observed and the emission linewidth is also reduced from 0.25 to 0.1 nm. With further increase in pumping intensities, the laser emission shifts gradually to lower wavelength as shown in Fig. 3 b. This blueshift is the result of mode pulling of the cavity resonance. Figure 3 a also shows that the laser emission is accompanied by a broad resonance at the lower cavity-polariton resonance even when the pumping intensity is above I th. For the pulsed excitation we have used, the duration between successive pulses 13 ns is long compared with the exciton lifetime, which means that laser emission is a transient process and the density of excitons or carriers varies as a function of the time. Hence, even if the pumping intensity is above I th, spontaneous emissions from lower cavity polaritons will eventually become important when the exciton density falls below n th. 16 The ratio A L /A B, where A L and A B are the spectrally integrated intensity of the laser emission and the broad resonance, respectively, also reflects directly relative pumping intensity (I I th )/I th as we will discuss further later.

190 XUDONG FAN, HAILIN WANG, H. Q. HOU, AND B. E. HAMMONS 56 FIG. 3. Emission spectra at various pumping intensities as indicated in the figure. The data are obtained at the sample position used for Fig. 2. The dashed curve in a is the emission spectrum at the lasing threshold and the dotted curve in b is the emission spectrum just below the saturation pumping intensity. The inset shows the threshold behavior in the input-output relation. When the pumping intensity exceeds I sat, an additional and pronounced broad resonance appears at nm as shown in Fig. 3 b while the broad resonance at the lower cavity-polariton resonance can still be observed see the logscale plot in the inset of Fig. 4. When exciton densities exceed n sat, both reflection and emission spectra of the composite system should be characterized by the bare-cavity resonance. The position of the additional broad emission resonance, which is independent of the pumping intensity and is 0.4 nm away from the lower cavity polariton, agrees well with that of the bare-cavity resonance deduced from the dispersion shown in Fig. 1 a. This additional broad emission resonance is due to spontaneous emission coming out of the FIG. 4. The ratio of spectrally integrated intensities of the laser emission and the broad emission resonance shown in Fig. 3. The inset is a log-scale plot of the emission spectra in Fig. 3 when the pumping intensity is above the saturation intensity. The two arrows in the inset indicates positions of spectrally broad emissions at the lower cavity-polariton resonance dashed arrows and the barecavity resonance, respectively. bare-cavity mode and occurs when the exciton density exceeds n sat but is still below the threshold density for laser emission in the perturbative regime where cavity polaritons vanish. Emission spectra obtained near I sat further reveal a striking change in the effective threshold pumping intensity when the composite exciton-cavity system undergoes a transition from the nonperturbative regime to the perturbative regime. As discussed earlier, the ratio A L /A B where A B is now the spectrally integrated intensity of both broad resonances as a function of the pumping intensity can be used as a measure of (I I th )/I th. For pumping intensities just below I sat, a very large ratio is observed as shown in Fig. 4, indicating a relatively large (I I th )/I th. In comparison, when the pumping intensity reaches just above I sat, the ratio drops drastically, reflecting a small (I I th )/I th and correspondingly an abrupt increase in the lasing threshold. These results indicate that I th in the perturbative regime is considerably higher than I th in the nonperturbative regime. Similar behaviors have also been observed at other sample positions where I th can be smaller than I sat. As we tune the cavity resonance, the abrupt threshold change always occurs near I sat and at the wavelength of the bare-cavity resonance. This rules out the possibility that the abrupt change in (I I th )/I th is the result of a slight change in the laser gain and the lasing threshold as the laser emission shifts gradually toward lower wavelength. We also note that when the exciton density falls from above n sat to below n sat but is still above the threshold density for laser emission in the nonperturbative regime, we expect an additional laser emission near the lower cavitypolariton resonance. The emission spectra obtained when the pumping intensity is greater than I sat, however, show no second laser emission resonance, suggesting that n sat is bistable, i.e., n sat occurring with decreasing densities is smaller than that with increasing densities. Such bistable behaviors have been predicated and observed for composite atom-cavity systems. 17 A detail discussion is beyond the scope of this paper. For comparison, Fig. 5 also shows the threshold behavior at a sample position where I th is just above I sat. At low excitation limit, the emission resonance from the lower cavity polariton is at nm. For pumping intensities above 30 W/cm 2, the output power increases superlinearly as shown in the inset. Signatures of spectral narrowing are also evidenced at a pumping intensity of 50 W/cm 2 see the dotted curve in Fig. 5 a, indicating that the composite system is close to the lasing threshold. The emission spectrum, however, broadens again with further increase in the pumping intensity, reflecting a large increase in the effective threshold intensity when the pumping intensity exceeds I sat as we have discussed earlier. The lasing threshold is eventually reached at a pumping intensity of 100 W/cm 2 with laser emission wavelength at nm. Note that when the cavity resonance is tuned further toward the exciton line center, cavity polaritons vanish far below the threshold and play no roles in the lasing process. 7 Experimental results discussed above show that at the low-energy tail of the exciton inhomogeneous distribution, I th can become considerably smaller than I sat and that lasing threshold increases abruptly when the pumping intensity is increased from below to above I sat, reflecting qualitative dif-

191 56 LASER EMISSION FROM SEMICONDUCTOR FIG. 5. Emission spectra at various pumping intensities as indicated in the figure. The data are obtained at a sample position where I th is just above I sat. The dotted curve in a shows spectral narrowing. The dashed curve in b is the emission spectrum at the lasing threshold. The inset in b shows the threshold behavior in the input-output relation. ferences in laser emission in the perturbative and the nonperturbative regimes. Similar results have also been observed with cw excitations. The significant broad resonance in emission spectra obtained with pulsed excitations, however, allows us to obtain a quantitative measure of the threshold change across I sat. To understand the physical origin of laser emission at pumping intensities below I sat we first turn to the drastic decrease in I th below the absorption line center shown in Fig. 1 b. The decrease in I th below the line center can be explained by effects of exciton localization. For a typical QW, there always exist monatomic layer fluctuations at the interface. At low temperature, these interface fluctuations localize excitons at local potential minimum. As a result, exciton energy depends on the local environment and the excitonic system is inhomogeneously broadened. After an off-resonant excitation, excitons at higher energies will relax toward the bottom of the inhomogeneous distribution through emission of phonons and will accumulate at the low-energy tail of the distribution, leading to a Stokes shift of the emission with respect to the absorption line center. 13 Note that the spectral relaxation time of localized excitons is short compared with the exciton recombination time. 14 When a given localization site is occupied by an exciton, population inversion is achieved for this site. In this regard, localized excitons behave just like an inhomogeneously broadened atomic system but with spectral relaxation. For localized excitons at a given energy, the pumping intensity for achieving population inversion depends on the total number of available localization sites at this energy and also on details of spectral relaxation. Pumping intensities for achieving population inversion of excitons at very low energies can be much smaller than those at higher energies since states at very low energies are more likely to be occupied and also because the total number of available localization sites at these energies is relatively small. In principle, population inversion at the low-energy tail of the inhomogeneous distribution can be achieved at extremely low exciton densities and without significant reduction in the overall coupling strength between the excitonic system and the cavity. Although a detailed understanding of laser emission in the nonperturbative regime still awaits further theoretical development, experimental results discussed above can be qualitatively understood by considering the linear dispersion model that has been used to describe coupled excitations in composite systems. In this model, the cavity-polariton resonance, especially the cavitylike polariton resonance, can be viewed as an effective cavity resonance with the frequency of the effective resonance modified by the dielectric response of the active media inside the cavity. 18 For a high-q microcavity containing an inhomogeneously broadened excitonic system, a threshold density below the exciton saturation density or the exciton Mott density can be achieved by tuning the cavity resonance to the low-energy side of the inhomogeneous distribution. In this case, laser emission near the lower cavitylike polariton resonance such as that shown in Fig. 3 a occurs in the nonperturbative regime in the sense that I th is below I sat and that cavity polaritons still persist at or near the lasing threshold. The laser emission, however, arises from population inversion of localized excitons at the low-energy tail of the inhomogeneous distribution. It should be noted that laser emission in the nonperturbative regime discussed above does not imply that coherent energy exchange between excitons and cavity photons plays any direct role in the lasing process. Coherent normal-mode oscillations require the presence of a macroscopic polarization of excitons, or more specifically, a coherent superposition of two cavity-polariton branches. We also note that in principle normal-mode oscillations can contribute to optical emission processes even when incoherent excitations are used. For a composite atom-cavity system, strong optical interactions between the cavity and an initially inverted atomic system can lead to a macroscopic polarization through a super-radiant process and can result in oscillatory superradiant emission. This ringing regime of super-radiance has been demonstrated by using Rydberg atoms in a high-q resonant optical cavity. 19 The ability to achieve population inversion of excitons in a high-q microcavity as shown in this paper suggests the possibility that with appropriate systems we might be able to observe this ringing regime of super-radiance in a semiconductor microcavity. We attribute the large and abrupt change in I th occurring near I sat to ionization of excitons to continuum states. Recent studies have shown that for pumping intensities below I sat, the reduction in the exciton oscillator strength is very small while the exciton linewidth can broaden significantly. 6 Theoretical calculations have further indicated that the bleaching of excitonic resonance and the corresponding vanishing of cavity polaritons occur quite abruptly when the normalized band edge approaches the 1s exciton resonance. 6 The estimated peak exciton density of order /cm 2 at I sat is in general agreement with the theoretical prediction for the exciton Mott density. The abrupt threshold increase shown in Fig. 4 thus reflects directly this ionization of excitons into continuum states. Laser emission from localized excitons

192 XUDONG FAN, HAILIN WANG, H. Q. HOU, AND B. E. HAMMONS 56 features a considerably lower threshold pumping intensity while laser emission due to population inversion of an electron-hole plasma has a much higher threshold and occurs at the bare cavity resonance. In this respect, laser emission from microcavities near I sat can also be used as a unique and extremely sensitive probe for important many-body processes such as the exciton to continuum transition. In conclusion, we have demonstrated laser emission from a composite exciton-cavity system in the nonperturbative regime where the collective dipole coupling rate between the excitonic system and the cavity mode is large compared with relevant damping rates. Laser emission in this regime is shown to arise from population inversion of localized excitons. An abrupt change in the lasing threshold is also observed when the composite system undergoes a transition from the nonperturbative to the perturbative regime and is attributed to exciton ionization. These studies represent a significant step toward exploring and understanding lasing processes in the nonperturbative regime and should stimulate further theoretical and experimental efforts in understanding optical interactions in semiconductor microcavities. We wish to acknowledge helpful discussions with H. Carmichael. The work performed at the University of Oregon was supported by AFOSR. 1 C. Weisbuch et al., Phys. Rev. Lett. 69, ; R. Houdre et al., ibid. 73, R. Stanley et al., Phys. Rev. B 53, , and extensive references there. 3 T. Norris et al., Phys. Rev. B 50, ; J. Jacobson et al., Phys. Rev. A 51, H. Wang et al., Phys. Rev. B 51, R. Houdre et al., Phys. Rev. B 52, ; J.-K. Rhee et al., Solid State Commun. 97, F. Jahnke et al., Phys. Rev. Lett. 77, X. Fan et al., Phys. Rev. A 56, Y. Yamamoto private communication ; S.Pauet al., Phys. Rev. A 54, For a review, see E. Hanamura and H. Haug, Phys. Rep., Phys. Lett. 33C, J. Ding et al., Phys. Rev. Lett. 69, ; F. Keller et al., ibid. 75, P. V. Kelkar et al., Phys. Rev. B 56, S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Adv. Phys. 38, The Stokes shift measured by tuning the cavity far away from the exciton resonance is 1.5 nm. 14 H. Wang, M. Jiang, and D. G. Steel, Phys. Rev. Lett. 65, Normal-mode oscillations in transient nonlinear response similar to that shown in Ref. 4 have also been observed, confirming that the composite system is in the nonperturbative regime. 16 Emissions from the outer region of the excitation spot where the exciton density is below n th also contribute as a broad resonance. 17 H. J. Carmichael et al., incavity Quantum Electrodynamics, edited by P. R. Berman Academic, Boston, 1994 ; J. Gripp et al., Phys. Rev. A 54, Y. Zhu et al., Phys. Rev. Lett. 64, Y. Kaluzny et al., Phys. Rev. Lett. 51,

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194 PHYSICAL REVIEW B VOLUME 57, NUMBER APRIL 1998-II Biexcitonic effects in the nonperturbative regime of semiconductor microcavities Xudong Fan and Hailin Wang Department of Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon H. Q. Hou and B. E. Hammons Sandia National Laboratories, Albuquerque, New Mexico Received 10 February 1998 Polarization-dependent transient pump-probe spectroscopy reveals important effects of biexcitonic interactions on coupled optical excitations in semiconductor microcavities. We show that exciton-to-biexciton transitions can result in a significant increase in normal mode splitting of cavity-polaritons, in sharp contrast to effects of nonlinear optical interactions such as band filling that reduce the splitting. A phenomenological model based on Maxwell-Bloch equations is developed to elucidate how biexcitonic effects contribute to cavity-polaritons. S Planar semiconductor microcavities embedded with quantum wells QW have been used as a composite excitoncavity system to investigate excitonic optical interactions in a nonperturbative regime where collective dipole coupling rates between the exciton and the cavity mode are large compared with relevant cavity decay rates and exciton dephasing rates. Resonant optical excitations of the composite system in this regime are characterized by coupled exciton-cavity modes, or cavity polaritons. Extensive studies of semiconductor microcavities have shown normal mode splitting NMS of cavity polaritons in emission and reflection spectra and normal mode oscillation in transient optical responses. 1,2 Motional narrowing of cavity polaritons in a disordered potential has also been investigated recently. 3 Strong coupling between the exciton and the cavity mode in the nonperturbative regime also leads to unusual manifestations of excitonic nonlinear optical interactions. Since NMS between two cavity-polariton branches reflects the collective dipole coupling strength between the exciton and the cavity mode, nonlinear optical processes such as phase space filling that saturate the excitonic transition reduce the magnitude of NMS, 4 while processes such as excitation-induced dephasing EID primarily broaden the cavity-polariton resonance. 5 Biexcitonic interactions are also expected to affect optical excitations in the nonperturbative regime. Biexcitonic effects were shown to be important in understanding coherent nonlinear optical processes such as four-wave mixing of cavity polaritons. 6 A clear physical understanding of how biexcitons contribute to coupled excitations in semiconductor microcavities, however, is still lacking in part because biexcitonic effects cannot be easily incorporated into the widely used semiconductor Bloch equations. 7 In this paper we present experimental and theoretical investigations on unique manifestations of biexcitonic effects in the nonperturbative regime in a microcavity embedded with GaAs QWs. Using polarization-dependent transient pump-probe spectroscopy, we found that biexcitonic interactions can result in a significant increase in NMS of cavity polaritons, in sharp contrast to effects of nonlinear optical interactions such as phase space filling that reduce the NMS. We attribute the observed increase in NMS to coupled excitations associated with the exciton-to-biexciton transition. A phenomenological model based on Maxwell-Bloch equations is also developed to elucidate how biexcitonic effects contribute to optical excitations in semiconductor microcavities. Our result underscores the necessity to include biexcitonic interactions in theoretical descriptions of optical interactions in the nonperturbative regime in semiconductor microcavities and should also impact interpretations of many other nonlinear optical studies in semiconductor microcavities. The microcavity structure used in our study contains four 13-nm GaAs/Al 0.3 Ga 0.7 As QWs placed at the center antinode of a wavelength long cavity. The two Bragg reflectors of the cavity consist of 16 and 22 pairs of Al 0.11 Ga 0.89 As/AlAs, respectively. The heavy-hole hh exciton absorption linewidth is estimated to be 1 nm, indicating that excitons are inhomogeneously broadened. The empty cavity linewidth is 0.25 nm. Additional information on the sample can also be found in earlier studies on laser emission from semiconductor microcavities. 8 Transient pump-probe studies were performed in the reflection geometry and with output from a mode-locked Ti:Sapphire laser with a pulse duration of 150 fs and a repetition rate of 82 MHz. All measurements were carried out at 10 K. Figure 1 shows as dashed-lines reflection spectra of the sample obtained at low excitation limit. The NMS observed is 2.6 nm. Note that the linewidth for the upper higherenergy cavity polariton is considerably greater than that for the lower cavity polariton even though the cavity is at or very near the hh exciton absorption line center. The asymmetric linewidth, which has also been observed in numerous earlier studies, is likely the result of an asymmetric inhomogeneous line shape or motional narrowing in a QW with interface disorders. 3 Effects of light-hole excitons may also play an important role. Reflection spectra when the sample is pre-excited by a resonant pump pulse are shown as solid lines in Fig. 1. When the pump-and-probe pulses have the same circular polarization, a large reduction in the NMS due to bleaching of the excitonic transition occurs as shown in Fig. 1 a. Significant broadening of the cavity-polariton resonance due to EID is /98/57 16 / /$ R The American Physical Society