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Physical review. B, Condensed matter

Coherent exciton-photon dynamics in semiconductor microcavities:The influence of inhomogeneous broadening

Giovanni Bongiovanni, Andrea Mura, Francesco Quochi, Steffen Gurtler, Jean Louis Staehli, F. Tassone, Ross P. Stanley, U. Oesterlé, R. Houdré

Published Mar 15, 1997• 56 citations
Publisher

Abstract

We investigate a GaAs/(Ga,Al)As Fabry-P\'erot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4--5-meV width, and an 0.7-meV-wide Fabry-P\'erot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.

DOI
10.1103/physrevb.55.7084

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We investigate a GaAs/(Ga,Al)As Fabry-P'erot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4--5-meV width, and an 0.7-meV-wide Fabry-P'erot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.
Time-integrated and spectrally resolved degenerate-four-wave mixing experiments at liquid helium temperature on the heavy- hole exciton resonance of a wedged (In,Ga)As/GaAs quantum well Bragg structure reveal a strong dependence of the dynamic and amplitude of the coherent nonlinear optical response in dependence on sample position. In the vicinity of the Bragg resonance the signal amplitude depends on both the rapid dephasing due to enhanced superradiant decay of the excitons and on the constructive interference of the signal amplitude in the backward Bragg reflection direction. We find that even in the presence of moderate inhomogeneous broadening of the excitonic resonance the superradiant decay dominates the excitonic nonlinearity at Bragg resonance. Our experimental results can be fairly well described by solutions based on the semiconductor Maxwell-Bloch equations taking disorder into account.
We investigate the four-wave mixing response of semiconductor quantum wells having a predominantly inhomogeneous broadening of the exciton states. The influence of the biexcitons on the nonlinear emission, in proximity to the lowest exciton resonance, is studied. Using about 1 ps long pulses, we show that biexcitons are created for all excitation energies lying within the broadened exciton absorption line, and that their binding energy does not depend on the exciton energy. Reducing the temporal width of cross-linearly polarized incident laser fields to about 0.1 ps, we observe a drastic changeover from a prompt response to a photon echo, and quite interesting beating phenomena, visible in time-integrated as well as in time-resolved experiments, appear. Our observations compare well with the numerical solutions of the optical Bloch equations for a five-level scheme. The influence of the inhomogeneous broadening on the beating phenomena is discussed.
Recently, cavity quantum electrodynamic (QED) effects in semiconductor microcavities have been of considerable interest since, in the weak-coupling regime they play an important role in selectively increasing spontaneous emission into the lasing mode of vertical-cavity surface-emitting lasers (VCSEL’s) [1,2], enabling low-threshold, high speed, and high efficiency. In a strong-coupling regime, the normal modes of the coupled system are superpositions of the exciton and cavity modes. Hence the impulsively excited system will evolve in time with the energy oscillating between the exciton and cavity modes. This is known as a vacuum-Rabi oscillation (VRO), with a frequency of Ω=d¯⋅E¯/@@h, where d¯ is the transition dipole moment of atoms and E¯ the vacuum-field strength. Of course, VRO are observable only when the cavity lifetime and exciton dephasing time are long enough compared to VRO period. Recently, Weisbuch et al. [3] have reported an observation of the normal-mode vacuum Rabi splitting in 2-D-exciton/planar-DBR microcavities. The observed splittings were as large as 6 meV in reflection and transmission spectra, implying 690-fs vacuum Rabi oscillations.
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. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.