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Journal of the Physical Society of Japan

Dynamical Processes of High Density Single Excitons and Excitonic Molecules in CdSe

Hiroto Kuroda, Shigeo Shionoya

Published Feb 1, 1974• 32 citations
Publisher

Abstract

To study the dynamical processes of high density single excitons and excitonic molecules in CdSe, the time dependences of M, P M and P luminescence lines and the time-resolved absorption spectra of A excitons are measured in the pico-second region at 4.2 K. The exciton absorption peak shifts to the high energy side due to the high density effect, the shift reaching the maximum at 20 ps after the pulse excitation. M line reaches the maximum at 100 ps, P M line at 200 ps and P line at 300∼350 ps. The decay constants are 100, 100 and 350 ps, respectively. The dynamical aspects of the formation of A excitons, the formation of excitonic molecules and the inelastic collisions of single excitons and excitonic molecules are discussed. It is interpreted why the use of the pico-second pulse excitation is essentially important for the realization of the Bose condensation of excitonic molecules.

DOI
10.1143/jpsj.36.476

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Cambridge University Press eBooks•Feb 28, 2000•0 citations
To study the dynamical processes of high density single excitons and excitonic molecules in CdSe, the time dependences of M, P M and P luminescence lines and the time-resolved absorption spectra of A excitons are measured in the pico-second region at 4.2 K. The exciton absorption peak shifts to the high energy side due to the high density effect, the shift reaching the maximum at 20 ps after the pulse excitation. M line reaches the maximum at 100 ps, P M line at 200 ps and P line at 300∼350 ps. The decay constants are 100, 100 and 350 ps, respectively. The dynamical aspects of the formation of A excitons, the formation of excitonic molecules and the inelastic collisions of single excitons and excitonic molecules are discussed. It is interpreted why the use of the pico-second pulse excitation is essentially important for the realization of the Bose condensation of excitonic molecules.
The Bose condensation of many exciton system is observed experimentally for the first time. It is found that excitonic molecules in CdSe exhibit the Bose condensation when the excitation is given at 1.8∼4.2 K by pico-second light pulses from a model-locked neodymium glass laser. This is concluded from the experimental facts that (1) an extremely sharp luminescence line attributed to originate from the k =0 condensed excitonic molecules is observed, (2) this sharp line is accompanied by the side-band on the low energy side and the spectrum is well understood by the theory developed by one of the authors, and (3) this line is produced within a limited range of excitation density which is wider at 1.8 K than at 4.2 K. Some arguments are presented on the importance of the use of the picosecond pulse excitation for the realization of the condensation.
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.
Various optical spectra such as time-resolved luminescence spectra are studied for excitonic molecules in CuCl under two-photon resonance excitation by using picosecond and nanosecond frequency-tunable laser pulses. Two sharp emission lines observed under resonance excitation are ascribed to the radiative decay of “cold” excitonic molecules created directly at k ∼2 k 0 , while the broad emission band on the low energy side of the sharp line to the luminescence of “hot” molecules created through single excitons. The stimulated emission process gives a considerable influence on both the sharp luminescence lines and the hot molecule band, and further on two-photon resonant excitonic Raman lines as well. Discussions are made on the Bose condensation of the excitonic molecules and also on whether the emission under just-resonance excitation is due to Raman scattering or luminescence.
In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.
A picosecond time-resolved four-wave mixing technique is used to study the dephasing of nonlinear optical resonances in CdSe. At low temperature strong coherent, nonlinear signals at the free exciton resonance, at the biexciton resonance, and at the exciton-biexciton transition are observed. The observed correlation traces, i.e. the diffracted intensity versus the delay between the interfering light pulses, yield information on the dephasing process. Dephasing times for excitons as long as 40 ps, decreasing with increasing excitation density and temperature, are observed. A two-level model is applied to describe theoretically the dynamical behavior of the resonances, and to extract their homogeneous broadening, as well as their inhomogeneous broadening.
Condensate Formation in the Bose Gas An important question in connection with the experiments aimed at achieving BEC of a weakly interacting Bose gas with a finite lifetime is the time needed for the formation of the condensate. It is not at all evident that the condensation can always take place within the lifetime of the system. For the case of liquid He, the assumption of equilibrium seems satisfied because 4 He atoms, which do not decay, undergo roughly 10 11 interparticle-scattering events per second, assuming classical hard-sphere scattering. In other boson systems, however, nonequilibrium effects may have a significant effect. For excitons in a semiconductor, the lifetime of the particle may be only a few hundred scattering times. Spin-polarized hydrogen also has a finite lifetime to nonpolarized states [1], and alkali atoms can recombine into molecules [2]. Naively judging from classical behavior, one might assume that hundreds of scattering times may seem more than adequate time to establish equilibrium. The case of Bose condensation is unique, however, since a macroscopic number of particles must enter a single quantum state that by random-scattering processes alone is highly improbable. Therefore we need not assume that the time for Bose condensation is short. Early experiments with orthoexcitons in CU 2 O seemed to indicate that the excitons might not have enough time to condense within their lifetime [3]. As discussed in Subsection 1.4.3, the orthoexciton density increased to approach the BEC boundary given in Eq. (1.18) and highly degenerate Bose-Einstein momentum distributions were observed, but a significant condensate fraction did not appear. Instead the gas increased its temperature to accommodate extra particles, reaching temperatures well above the lattice temperature.