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Exciton correlations within an electron gas

J. Berney

Published Nov 24, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.5075/epfl-thesis-3726

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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.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
Summary form only given. Since the original discovery of the excitonic optical Stark effect, substantial progress has been made in the understanding of this ultrafast nonlinear optical effect. Recently, a red shift of the excitonic absorption line has been reported using low intensity excitation detuned 4.5 meV below the 1s-heavy-hole (hh) resonance and cross-circularly-polarized pulses. This was attributed to higher-order Coulomb correlations, interpretable as bound and unbound two-exciton states and memory effects. For co-circularly polarized pulses the well-known blue shift was found. Here we present a related effect occurring in the higher-intensity regime. Standard pump-probe experiments were performed on high-quality 8.5 nm-thick In/sub 0.04/Ga/sub 0.96/As multiple quantum well (MQW) samples.
The intensity dependence of pump-induced excitonic absorption changes is studied in high-quality In0.04Ga0.96As{\mathrm{In}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{As}In0.04​Ga0.96​As quantum wells for different detunings and polarization configurations. For resonant excitation with increasing pump intensity a saturation of both the exciton bleaching and the induced absorption due to two-exciton resonances is observed, whereas for pumping below the exciton a characteristic polarization dependence of higher-order contributions to the optical Stark effect is found. Microscopic calculations including Coulomb correlations show that the experimental observations can be described by the coherent dynamics of single- and two-exciton resonances up to fifth order in the optical field.
The nonlinear optical response of quantum well excitons is investigated experimentally using polarization resolved four wave mixing, optical-pump optical-probe, and optical-pump Terahertz-probe spectroscopy. The four-wave mixing data reveal clear signatures of coherent biexcitons which concur with straight-forward polarization selection rules at the Γ point. The type-I samples show the well-established time-domain beating signatures in the transients as well as the corresponding spectral signatures clearly. The latter are also present in type-II samples; however, the smaller exciton and biexciton binding energies in these structures infer longer beating times which, in turn, are accompanied by faster dephasing of the type-II exciton coherences. Furthermore, the THz absorption following spectrally narrow, picosecond excitation at energies in the vicinity of the 1s exciton resonance are discussed. Here, the optical signatures yield the well-established redshifts and blueshifts for the appropriate polarization geometries in type-I quantum well samples also termed “AC Stark Effect”. The THz probe reveals intriguing spectral features which can be ascribed to coherent negative absorption following an excitation into a virtual state for an excitation below the 1s exciton resonance. Furthermore, the scattering and ionization of excitons is discussed for several excitation geometries yielding control rules for elastic and inelastic quasiparticle collisions.
This dissertation presents investigations of fundamental optical nonlinearities in semi-conductor microstructures. Two distinct effects are studied. In the first part the excitonic optical Stark effect in InGaAs and GaAs multiple quantum-well structures is investigated by means of pump-probe spectroscopy. For nonresonant excitation below the excitonic transition the direction of the shift of the resonance depends on the polarization of the pump and probe pulses. In particular, for anti-circular polarization a surprising red-shift is observed. For resonant excitation, induced absorption energetically above and below the exciton transition and bleaching of the resonance is found. Experiments using both resonant and nonresonant excitation reveal the importance of bound and unbound two-exciton states in absorption changes of the 1s heavy-hole exciton resonance. It is found that higher-order Coulomb contributions determine the intensity as well as the time dependence of the differential excitonic absorption. In addition, the influence of light-hole excitons is analyzed. It is shown that the direction of the optical Stark shift for nonresonant excitation depends also sensitively on the heavy-hole to light-hole splitting and the detuning of the pump pulse. For very high pump intensities and nonresonant excitation the absorption is split when a circularly polarized pump and a linearly polarized probe beam are used. For co-circular excitation traces of hyper-Raman gain are observed. In the second part of this dissertation, the nonlinear optical response of semiconductor microcavities in the nonperturbative regime is studied in resonant single-beam transmission and pump-probe experiments. In both types of experiment, a pronounced third transmission peak lying spectrally between the two normal modes is observed. Its dependence on the probe intensity, pump intensity, pump-probe delay, exciton-cavity detuning and pump detuning is investigated. For single-beam transmission, the energy of the third peak parallels the position of the cavity resonance. It is more pronounced for circularly polarized excitation and lasts longer than the two normal modes. For pump-probe experiments, the third peak increases with decreasing probe intensity and increasing pump intensity. Its energy is close to the low-energy side of the pump spectrum and virtually unaffected by the cavity-exciton detuning. The appearance of the third peak requires temporal overlap of pump and probe pulses. The origin of this complex nonlinearity is the quantum nature of light, which induces intraband polarizations in the presence of a coherent driving field and a finite carrier density. It is found that the coupling of the intraband polarizations via guided modes to the polarization of the fundamental longitudinal mode is responsible for the third transmission peak. A fully quantized theory reproduces the experimental observations.
Optical control of the spin coherence of quantum well electrons by short laser pulses with circular or linear polarization is studied experimentally and theoretically. For that purpose the coherent electron spin dynamics in a nnn-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved pump-probe Kerr rotation, using resonant excitation of the negatively charged exciton (trion) state. The amplitude and phase shifts of the electron spin beat signal in an external magnetic field, that are induced by laser control pulses, depend on the pump-control delay and polarization of the control relative to the pump pulse. Additive and nonadditive contributions to pump-induced signal due to the control are isolated experimentally. These contributions can be well described in the framework of a two-level model for the optical excitation of the resident electron to the trion.