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Theory of photon echoes in disordered semiconductors

D. Bennhardt, P. Thomas, A. Weller

Published May 21, 1990• 0 citations
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Abstract

Photon echo experiments can be used to study the interaction of optical excitations with other quasiparticles on a short time scale. Two short laser pulses impinge on the sample with a time separation τ. The sample then emits a photon echo at time 2τ. The decay of the photon echo amplitude with τ can be attributed to dephasing interactions.

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Physical Review Letters•Feb 1, 1990•129 citations
Photon echo experiments can be used to study the interaction of optical excitations with other quasiparticles on a short time scale. Two short laser pulses impinge on the sample with a time separation τ. The sample then emits a photon echo at time 2τ. The decay of the photon echo amplitude with τ can be attributed to dephasing interactions.
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
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].
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 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.
Time-resolved demonstration of picosecond photon echoes due to intrinsic optical excitations of a semiconductor is presented. Phase relaxation times up to several hundred picoseconds are found for excitons localized by chemical disorder in CdSx{\mathrm{CdS}}_{\mathrm{x}}CdSx​${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ mixed crystals. These long dephasing times are attributed to reduced scattering of the localized excitons as compared to free excitons. Dephasing is identified as due to energy relaxation of the excitons.