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Journal of the Physical Society of Japan

Emission Spectrum from the Bose-Condensed Excitonic Molecules

Masahiro Inoue, Eiichi Hanamura

Published Oct 1, 1976• 28 citations
Publisher

Abstract

The emission spectrum is given for radiative decay of the excitonic molecules in the Bose-condensed state at finite temperature which is described in the framework of the Bogoliubov approximation. We take into account the final state interaction of an exciton created in the radiative process with the environment of the Bose-condensed excitonic molecules. The emission spectrum is characterized by a sharp line due to the radiative decay of the Bose-condensed excitonic molecules and the side band at lower energy side due to the process associated with the excitation of the Bose-condensed system. The polariton effect on the emission spectrum is also discussed.

DOI
10.1143/jpsj.41.1273

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The emission spectrum is given for radiative decay of the excitonic molecules in the Bose-condensed state at finite temperature which is described in the framework of the Bogoliubov approximation. We take into account the final state interaction of an exciton created in the radiative process with the environment of the Bose-condensed excitonic molecules. The emission spectrum is characterized by a sharp line due to the radiative decay of the Bose-condensed excitonic molecules and the side band at lower energy side due to the process associated with the excitation of the Bose-condensed system. The polariton effect on the emission spectrum is also discussed.
The influence of the radiative decay of excitonic molecules on a possible quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecule's is examined with respect to the radiative renormalization of the excitonic molecule energy (excitonic molecule Lamb shift). For the excitonic molecule wave function, a Schrödinger equation which contains polariton effects is derived and analyzed. Both the inverse excitonic molecule radiative lifetime γ m and the biexciton Lamb shift Δ m depend strongly on the total excitonic molecule momentum K. The energy renormalization Δ m (K) leads to the excitonic molecule effective mass modification and can result in a camel-back structure at K = 0, which opposes a BEC of excitonic molecules at K = 0. Introduction Observations of a quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecules (EM) have been attempted [1, 2, 3] following its theoretical prediction [4, 5] (for reviews see, e.g. [6, 7]). Recent approaches [8, 9] with high-precision techniques renewed the interest in this phenomenon. Traditionally, one tries to detect BEC of the EMs in luminescence. In the new approach the appearance of coherence in the thermal system of the EMs has been tested by means of four-wave mixing and treated as a fundamental manifestation of BEC. (See the paper by Hasuo et al . in this book.) Both optical methods for the BEC detection imply that the optical transition to the corresponding intermediate exciton (IE) state is dipole-active. In this case the EM state is unstable against optical decay with a “giant” oscillator strength [6].
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.
Polariton effect quenches not only the possibility of Bose-Condensation but also of the self-induced transparency of single direct excitons . Here, as to bi-excitons which are not suffered from this negative effect due to polariton, we propose the direct and coherent excitation of Bose-condensed bi-excitons by giant two-photon absorption due to bi-excitons. Then we discuss the possibility of superradiance of Bose-condensed bi-excitons created by this method and the possibility of self-induced transparency associated with giant two-photon transition due to these bi-excitons.
The exciton absorption and emission bands in the presence of Bose-Einstein condensation (BEC) of excitons, induced by the coherent laser radiation is considered. The laser radiation creates the coherent macroscopic polarization of the crystal, which is described as a virtual BEC of excitons. The energy spectrum of the elementary excitations as well as the probabilities of the quantum transitions depend essentially on the frequency detuning (Delta) -. The nonequilibrium occupation numbers of out-of-condensate excitons nexq arising in the presence of virtual BEC influence on the forms of absorption and emission bands.
It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas and is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. The stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field is established. The possible observable effects of the Bose condensate and the interaction of light with the Bose-Einstein condensate of excitons is studied. The appearance of the Bose condensate in a broad range of the densities significantly changes the spectrum of the coupled excitons and photons. The dielectric theory of polaritons which accounts for the new excitation spectrum predicts a number of interesting phenomena.
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.