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Physical review. B, Condensed matter

Proposed method for measuring the dephasing relaxation constant of excitonic molecules

T. Takagahara

Published Apr 1, 1984• 4 citations
Publisher

Abstract

Theoretical considerations of a method to measure the dephasing relaxation constant ${\ensuremath{\Gamma}}_{M}$ of excitonic molecules are presented. The proposed method is based on the principle of the two-photon free-induction decay and makes use of an appropriate combination of polarizations of the incident light beams to eliminate the contribution from the excitonic polariton. It is demonstrated that the correlation trace of the signal is sensitive to the value of ${\ensuremath{\Gamma}}_{M}$ and that a determination of ${\ensuremath{\Gamma}}_{M}$ from the experiments is quite feasible.

DOI
10.1103/physrevb.29.4160

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Theoretical considerations of a method to measure the dephasing relaxation constant \ensuremathΓM{\ensuremath{\Gamma}}_{M}\ensuremathΓM​ of excitonic molecules are presented. The proposed method is based on the principle of the two-photon free-induction decay and makes use of an appropriate combination of polarizations of the incident light beams to eliminate the contribution from the excitonic polariton. It is demonstrated that the correlation trace of the signal is sensitive to the value of \ensuremathΓM{\ensuremath{\Gamma}}_{M}\ensuremathΓM​ and that a determination of \ensuremathΓM{\ensuremath{\Gamma}}_{M}\ensuremathΓM​ from the experiments is quite feasible.
Nonlinear optical methods to determine the transverse relaxation constants of excitonic molecules making use of two-photon echo and a new type of excited state photon echo are proposed. The two-photon echo is a seventh order nonlinear effect at the lowest and one needs three pulses to observe it, while the excited state photon echo is a fifth order nonlinear effect and requires four pulses. In these nonlinear optical methods we can satisfy the phase matching condition rather easily due to the large dispersion of excitonic polaritons. We can determine directly the transverse relaxation constants associated with the excitonic molecule from the correlation trace of the two-photon echo and the excited state photon echo.
Picosecond relaxation processes of excitons, including dephasing processes, are systematically studied in CuCl, CdSe and GaAs/AlAs MQW (multi-quantum well structures) by observing time-resolved induced absorption, luminescence and non-degenerate four-wave mixing. By studying the transient induced absorption from the exciton (polariton) state to the excitonic molecule state, time-resolved energy distribution of excitons in CuCl is determined (Fig.1).1) Another technique, i.e. time-resolved luminescence measurement, is applied to excitons in CdSe and GaAs/AlAs MQW (Figs.2 and 3).2,3) By analyzing the above-mentioned experiments the distribution of excitons in the two-dimensional energy-time coordinates is successfully determined. Thus, energy relaxation processes of excitons are clearly visualized. Prior to energy relaxation, coherently generated excitons are considered to be dephased. Phase relaxation of excitons in CuCl is directly measured for the first time in the picosecond time domain by means of time-resolved non-degenerate four-wave mixing (Fig.4).4) These new techniques will be demonstrated and the dephasing as well as energy relaxation mechanism of excitons and excitonic polaritons will be discussed. In the above experiments characteristics of a picosecond tunable optical parametric oscillator pumped by a mode-locked Nd3+:YAG laser as well as a picosecond tunable dye laser synchronously pumped by a mode-locked ion laser are complementarily utilized.
A theoretical study of the time-integrated signal of thermalized luminescence excited by a pair of phase-locked light pulses shows that the idea of coherent control should be efficient for measuring the total dephasing rates of high-energy excitonic transitions. This approach can be used for studying both the homogeneously and inhomogeneously broadened systems, which is highly important in studies of the semiconductor quantum dots. It is found that the method of coherent control makes it possible not only to obtain information about the relaxation constants but also to make conclusions about the statistical properties of frequency distributions of the excitonic transitions responsible for broadening the optical spectra.
The mechanisms of exciton coherence relaxation in GaAs quantum wells in the linear mode have been experimentally investigated. An experimental technique has been developed for measuring the total phase relaxation rate, rates of reversible and temperature-irreversible excitonic phase relaxation, and the radiative decay rate Γ R of excitonic polarization. The experimental values of Γ R for a quantum well of specified thickness, obtained for a series of samples, have a spread not larger than 15%. This accuracy made it possible to estimate the shape of the dependence of Γ R on the well thickness L Z . It is experimentally found that Γ R is temperature-independent up to 80 K.
Quantum-well exciton superradiance and exciton cavity polarization formation both require a substantial spatial coherence area in order to become the dominant exciton field interaction. In both interaction processes the quantum-well (in-plane) momentum is conserved. Momentum scattering, which is due, e.g., to interaction with a phonon reservoir, quickly localizes an initially delocalized exciton and randomizes the excitation momentum. We take a close look at how momentum scattering influences measurements of excitonic superradiance and of exciton cavity polariton splitting. An important conclusion is that, in general, measurements of the emitted light do not correspond to the evolution of the system as a whole. Therefore, e.g., the measured decay rates do not correspond to the true decay rate of the system.