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International Journal of Modern Physics B

NONLINEAR QUANTUM BEAT SPECTROSCOPY IN SEMICONDUCTORS

K.‐H. Pantke, J. M. Hvam

Published Jan 20, 1994• 43 citations
Publisher

Abstract

We review quantum beats from extended electronic states in bulk semiconductors and multiple quantum well structures obtained by nonlinear spectroscopy. The nonlinear methods are degenerate four-wave mixing, photon echo and nonlinear transmission. The role of the spectral resolution of the nonlinear signal emitted from a four-wave mixing process is discussed in detail. Results obtained by linear methods like fluorescence or transmission are briefly discussed.

DOI
10.1142/s021797929400004x

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We review quantum beats from extended electronic states in bulk semiconductors and multiple quantum well structures obtained by nonlinear spectroscopy. The nonlinear methods are degenerate four-wave mixing, photon echo and nonlinear transmission. The role of the spectral resolution of the nonlinear signal emitted from a four-wave mixing process is discussed in detail. Results obtained by linear methods like fluorescence or transmission are briefly discussed.
The nature of the beat modulations observed in nonlinear four-wave mixing in semiconductors is determined by spectral resolution of the time-integrated four-wave-mixing signals. Beats between close-lying bound-exciton resonances in CdSe are found to be described by macroscopic polarization interferences between two noninteracting two-level systems. Beats between heavy-hole excitons and light-hole excitons in GaAs quantum wells, on the other hand, are described by a three-level system, i.e., as a true quantum interference phenomenon.
We review our recent advances in four-wave mixing spectroscopy of single semiconductor quantum dots using heterodyne spectral interferometry, a novel implementation of transient nonlinear spectroscopy allowing the study of the transient nonlinear polarization emitted from individual electronic transitions in both amplitude and phase. We present experiments on individual excitonic transitions localized in monolayer islands of GaAs/AlAs quantum wells and in self-assembled CdTe/ZnTe quantum dots. We investigate the formation of the photon echo from individual transitions, both with increasing number of transitions in the ensemble, and in the presence of temporal jitter of the energy of a single transition. The detection of amplitude and phase of the signal allows the implementation of a two-dimensional femtosecond spectroscopy, in which mutual coherent coupling of single quantum dot states can observed and quantified.
Multiple frequency quantum beats of a system of the coherently excited quantum confined exciton states in a high-quality semiconductor structure containing a wide InGaAs/GaAs quantum well are experimentally detected by the spectrally resolved pump-probe method. The beat signal is observed both at positive and at negative delays between the pump and probe pulses. Several quantum beat (QB) frequencies are observed in the experiments, which coincide with the interlevel spacings in the exciton system. A theoretical model is developed, which allows one to attribute the QBs at negative delay to the four-wave mixing (FWM) signal detected at the nonstandard direction. The beat signal is strongly enhanced by the interference of the FWM signal with the secondary emission induced by the probe pulse. At positive delays, the QBs are due to the interference of the quantum confined exciton states. The decay time for QBs is of the order of several picoseconds both at positive and negative delays. This is close to the relaxation time of the exciton population that allows one to consider the exciton depopulation as the main mechanism of the coherence relaxation in the system under study.
We show that time-resolved quantum beat spectroscopy in the four-wave mixing (FWM) geometry is a unique tool to investigate the electronic multi-level system associated with spectrally adjacent excitonic resonances. We have studied heavy- and light-hole excitons, excitons associated with different and spatially separated quantum wells, and excitons associated with spatially separated growth islands within the same quantum well. Though the linear spectra are qualitatively similar in all three cases, the respective beating of the time-resolved FWM-signal shows a very different dynamic behaviour in each case. We discuss appropriate electronic multi-level schemes and show that exciton transitions within different quantum wells can be described by independent twolevel systems. In contrast, excitonic transitions associated with different and spatially separated growth islands having different quantum well thickness are not independent but coupled.
Current issues in the study of light-matter interactions are coherence and quantum interference. With ultrafast nonlinear spectroscopy such as transient four-wave mixing (TFWM) the imposed coherence on the optical excitations in e.g. GaAs multiple quantum wells has been studied. In this contribution, we study the influence of inhomogeneous broadening on quantum beats observed by spectrally resolved TFWM. In artificially grown semiconductor structures as e.g. quantum wells, inhomogeneities due to interface-disorder has, up till now, been inevitable. In the experiments, the light-hole exciton (lhx) and the heavy-hole exciton (hhx) in a 100 Å GaAs multiple quantum well are excited simultaneously with 150 fs pulses from a self mode-locked Ti:sapphire laser. The spectral profile is shown in the inset of Fig. 1.