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Physical review. B, Condensed matter

Influence of Coulomb interaction on the photon echo in disordered semiconductors

D. Bennhardt, P. Thomas, A. Weller, Markus Lindberg, S. W. Koch

Published Apr 15, 1991• 32 citations
Publisher

Abstract

The photon-echo signal in disordered semiconductors is treated including the electron-hole Coulomb attraction. The amplitude of the spontaneous photon echo is calculated up to third order in the external-field amplitude using the semiconductor Bloch equations. Several idealized situations are analyzed showing the significance of a critical correlation of the polarization dynamics in the two time intervals preceding and following the second excitation pulse. Strong photon-echo decay is predicted for short-range disorder without Coulomb interaction. The inclusion of electron-hole attraction leads to a stabilization of the echo signal. For the case of long-range disorder with Coulomb interaction, we predict slow decay in the diffusive limit.

DOI
10.1103/physrevb.43.8934

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•May 21, 1990•0 citations
The photon-echo signal in disordered semiconductors is treated including the electron-hole Coulomb attraction. The amplitude of the spontaneous photon echo is calculated up to third order in the external-field amplitude using the semiconductor Bloch equations. Several idealized situations are analyzed showing the significance of a critical correlation of the polarization dynamics in the two time intervals preceding and following the second excitation pulse. Strong photon-echo decay is predicted for short-range disorder without Coulomb interaction. The inclusion of electron-hole attraction leads to a stabilization of the echo signal. For the case of long-range disorder with Coulomb interaction, we predict slow decay in the diffusive limit.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
The phase relaxation of optically excited electronic states can be studied in fourwave mixing experiments where three excitation pulses at t = 0, t =t21, and t = T, respectively, interact via the third-order polarization of the medium to generate a nonlinear signal whose intensity depends on the dephasing time T2. For inhomogeneously broadened optical transitions the signal will be emitted as a time delayed photon echo pulse at t = T + t21 provided the pulse duration is short compared with T2. The echo amplitude decays as exp(−4t21/T2).1
The coherent optical response of semiconductor quantum wells is studied theoretically using the multiband semiconductor Bloch equations which include coupling of the heavy- and light-hole bands as well as many-body Coulomb effects. For the case of a two-pulse excitation scheme it is shown how the different rotational symmetries of heavy- and light-hole bands induce a strong polarization dependence of the signal in the photon echo direction. The selection rules are based on the Kane-Luttinger theory while the transition amplitudes are obtained by numerically solving the multiband semiconductor Bloch equations. In addition, the influence of valence-band mixing effects on the optical Stark effect is demonstrated.