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Phase relaxation in disordered semiconductors studied by time-resolved photon echo experiments

U. Siegner, Gert Noll, Ernst Otto Göbel, Serhiy G. Shevel

Published May 21, 1990• 0 citations
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Abstract

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

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Physical review. B, Condensed matter•Aug 15, 1992•66 citations
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].
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
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.
The polarization dependence of the ultrafast nonlinear response of localized excitons in GaAs/AlGaAs quantum wells has been investigated by spectrally resolved, transient four-wave mixing. The role of the excitation-induced dephasing in the delay dependence of the signal is discussed in detail. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay.
The influence of disorder and localization on optical dephasing of excitons in the semiconductor mixed crystals ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Sex{\mathrm{Se}}_{\mathit{x}}Sex​ and Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As has been investigated by means of time-resolved four-wave mixing and photon echo experiments. A dephasing time of several hundreds of picoseconds is found for resonantly excited localized excitons in ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Sex{\mathrm{Se}}_{\mathit{x}}Sex​ while the dephasing time in Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As amounts to only a few picoseconds. In ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Sex{\mathrm{Se}}_{\mathit{x}}Sex​ dephasing results mainly from hopping processes, i.e., exciton-phonon interaction. The contribution of disorder is negligible in terms of phase relaxation in ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Sex{\mathrm{Se}}_{\mathit{x}}Sex​. In contrast, in Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As elastic disorder scattering yields an essential contribution to the dephasing rate. We present a theoretical model, which treats dephasing of optical excitations in a disordered semiconductor, including the influence of disorder as well as exciton-phonon interaction. On the base of this model, the experimentally observed differences in the dephasing behavior of excitons in ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Sex{\mathrm{Se}}_{\mathit{x}}Sex​ and Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As are related to the microscopic structure of the disorder potential and the mechanism of exciton localization.