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Physical Review Letters

Strongly Driven Exciton Resonances in Quantum Wells: Light-Induced Dressing versus Coulomb Scattering

Cristiano Ciuti, Carlo Piermarocchi, Vincenzo Savona, Peter E. Selbmann, P. Schwendimann, A. Quattropani

Published Feb 21, 2000• 16 citations
Publisher

Abstract

The nonequilibrium dynamics of a two-dimensional electron-hole gas is studied in the regime of strong and resonant pumping of the exciton resonance. The Coulomb collision rates are consistently determined by taking into account the light-induced coherence of the two-band system that leads to a dressing of the carrier spectral functions. The light dressing dramatically reduces the Coulomb scattering efficiency. Results are presented for Rabi oscillations in the time domain and dynamical Stark splitting in the pump-probe absorption spectra.

DOI
10.1103/physrevlett.84.1752

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•Nov 24, 2006•2 citations
The nonequilibrium dynamics of a two-dimensional electron-hole gas is studied in the regime of strong and resonant pumping of the exciton resonance. The Coulomb collision rates are consistently determined by taking into account the light-induced coherence of the two-band system that leads to a dressing of the carrier spectral functions. The light dressing dramatically reduces the Coulomb scattering efficiency. Results are presented for Rabi oscillations in the time domain and dynamical Stark splitting in the pump-probe absorption spectra.
The role of Coulomb scattering is studied in the coherent transients of strongly driven exciton resonances in semiconductor quantum wells. Coulomb scattering is treated within the second Born approximation and the light-induced dressing of the electron–hole gas is consistently included. The light dressing is found to decrease the Coulomb collision efficiency and therefore the field-driven dynamics is close to the Hartree-Fock case. Indeed, Coulomb relaxation and dephasing are not strong enough to prevent a dynamical Stark splitting in the pump–probe absorption spectra.
Optical interband excitonic absorption of semiconductor quantum wells (QW’s) driven by a coherent pump field is investigated on the basis of semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW’s. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron–hole pairs in the QW structure is low, the pump field induces an Autler–Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron–hole pairs is increased, the split contrast (the ratio between the maximum and the minimum values) is decreased, because the exciton effect is suppressed at higher densities owing to the many-body screening.
Exciton Rabi oscillations and Rabi splitting differ significantly from their atomic counterparts in part because Coulomb interactions between excitons strongly influence the exciton Rabi frequency.' While both exciton Rabi oscillations and Rabi splitting were demonstrated recently in quantum wells (QWs),'.l experimental investigation of how exciton-exciton interactions affect these coherent optical Q~OCCSS~S has been hindered bya number of complications. In time-domain studies, the Rabi frequencyvaries with time due to the changing electric field strength. In typ ical spectral domain studies, a spectrally-broad probe pulse is spectrally resolved after its transmission through the sample. The resulting pump-probe spectra are difficult to interpret due to the presence of coherent spectral oscillations and a sensitive dependence on the pump-probe delay. In this paper we report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field bed theoretical models.' Pump-probe experiments were performed on a 130 A GaAs1AlGa.k multiple QW sample at 10 K. Figure I shows results of pump-probe meas
A theoretical study of excitonic Rabi oscillations in semiconductor quantum wells is presented. Fundamental differences between excitonic Rabi oscillations and optical Rabi oscillations in ideal atomic or molecular 2-level systems are due to the existence of the continuous 1-particle spectrum in solids (energy bands) and the resulting strong effects of the Coulomb interaction, such as the attractive electron-hole interaction and the repulsive exchange interaction. In spite of these fundamental differences, Rabi-like oscillations of the excited electron-hole densities are computed for the case of resonant optical pumping of excitons. We compare our theoretical results with our recent experimental observation of excitonic Rabi oscillations.
A many-body analysis of spectral hole burning and light-induced band renormalization in the gain region of an initially inverted semiconductor is presented. The results are based on the numerical solution of the semiconductor Bloch equations, specialized to the case of noncopropagating pump-and-probe light fields. These equations account for coherent pump-probe scattering and include the Coulomb correlation between charge carriers. They also contain optical dephasing and carrier-carrier scattering rates that are computed within the random-phase approximation.
I report on the effect of a moderate excess electron population on nonlinearities in modulation-doped CdTe quantum wells. I show that the electron population does not qualitatively affect the nature of correlations between excitons. In this respect, I bring strong evidence of the existence of unbound and bound (stable) two-exciton states in the presence of electrons and charged excitons (trions). In time-resolved pump and probe experiment, they lead to the observation of electromagnetically induced transparency and optical Stark shift of the exciton resonance. Rabi flopping of excitons within a sea of electrons is also clearly evidenced through ac Stark splitting and gain without inversion. The quantum coherence is more robust to electron induced dephasing than what would have been expected. I demonstrate third and higher-order exciton correlations in the presence of electrons, which manifest, for increasing exciton densities, through the blue-shift of counter-polarized exciton resonance, the red-shift of the biexciton resonance and the exciton to biexciton crossover. I also evidence correlated behavior of excitons and trions under excitation which manifests itself by crossed trion-exciton effects. I observe a wealth of phenomena encompassing bleaching, crossed bleaching, induced-absorption and energy shifts of the resonances. Significant differences are found between the nonlinear optical effects induced by an exciton and a trion population. Electron scattering with electron and exciton is shown to strongly broaden the high energy tail of exciton and trion resonance lineshapes. Variations of electron density result in a clear modification of both resonance lineshapes. The dynamics of the formation of trions is also studied. I propose a two-channel mechanism for their formation; they are formed through bi- and tri-molecular processes. This implies that both negatively and positively charged excitons coexist in a quantum well, even in the absence of excess carriers. The model is applied to a time-resolved photoluminescence experiment performed on a very high quality InGaAs quantum well sample, in which the photoluminescence contributions at the energy of the trion, exciton and at the band edge can be clearly separated and traced over a broad range of times and densities. The unresolved discrepancy between the theoretical and experimental radiative decay time of the exciton in a doped semiconductor is explained.