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Journal of Experimental and Theoretical Physics

Excitonic light-absorption and amplification bands in the presence of laser radiation

S. A. Moskalenko, V. G. Pavlov

Published Jul 1, 1997• 0 citations
Publisher

Abstract

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k 0. We assume that the detuning $$\tilde \Delta $$ from resonance between the energy ħω ex (k 0)+L 0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at $$\tilde \Delta = 0$$ the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when $$\tilde \Delta < 0$$ , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k 0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at $$\tilde \Delta \approx 0$$ and depend on the orientation of the vectors q and k 0.

DOI
10.1134/1.558320

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We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k 0. We assume that the detuning Δ~\tilde \Delta Δ~ from resonance between the energy ħω ex (k 0)+L 0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at Δ~=0\tilde \Delta = 0Δ~=0 the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when Δ~<0\tilde \Delta < 0Δ~<0 , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k 0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at Δ~≈0\tilde \Delta \approx 0Δ~≈0 and depend on the orientation of the vectors q and k 0.
The absorption and gain bands of a weak probe signal in the presence of the Bose-Einstein condensation of excitons, which appears under nonequilibrium conditions in a field of coherent laser radiation, are considered. It is shown that the absorption of light is caused by a quantum transition from the ground state of the crystal to the quasiexciton branch of the spectrum. Amplification of the signal occurs as a result of transitions from the quasiexciton branch of the spectrum to the ground state of the crystal.
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.
Nonequilibrium Theory of the Optical Stark Effect in the Excitonic Range of the Spectrum One of the most important applications of the theory of Bose condensation of excitons is the optical Stark effect, or “AC Stark effect, ” first demonstrated for excitons in Cu 2 O [1] and since seen in several semiconductors and semiconductor heterostructures (e.g., Refs. 2-5). This effect is a promising tool for the field of optical communications. One of the major interests in this field is the development of all-optical-switching methods, by which light signals are switched on or off directly by other light signals, just as in electronics, electrical signals switch other electrical signals. At the present, most optical communications systems use electrical signals (e.g., electro-optic or acousto-optic devices) to switch the light signals, which means that the limiting bandwidth of the system is controlled by that of the electrical signals, not the optical bandwidth. The optical Stark effect offers this possibility. When one laser beam impinges on a sample, it can drastically alter the excitonic absorption line shape. Therefore a second beam can see either a transparent or an absorbing medium, depending on the presence of the control beam. This is the optical equivalent of a transistor. The basic effect is shown in Fig. 6.1. When an intense laser is tuned to a photon energy that is just below the excitonic ground state, the exciton ground state is shifted in frequency and the oscillator strength is altered. This leads to a strong reduction in the optical absorption at the original wavelength of the exciton ground state.
Introduction. Polaritons and Semiconductor Microcavities As we have mentioned previously, BEC of excitons or biexcitons and lasing can be seen as two limits of the same theory. Lasing occurs in the case of strong electron-photon coupling (recombination rate fast compared with interparticle-scattering rate) while excitonic BEC occurs in the case of weak electron-photon coupling (recombination rate slow compared with the interparticle-scattering rate.) A laser can be seen as a Bose condensate in which the long-range phase coherence exists in the photon states [1], while in the exciton condensate the coherence exists in the electronic states. This is one of the reasons for some of the confusing debates in the early history of excitonic Bose condensation – in many systems there is not a sharp distinction between an excitonic condensate and supperradiance, i.e., luminescence with enhanced intensity due to stimulated emission [2-4]. In the previous chapters, we have so far considered a laser light source only as a source of excitons by means of quantum transitions. In Chapter 6, the laser radiation was taken into account as a given external factor. This chapter is dedicated to phenomena related to a strong and noticeable exciton-photon interaction, when the light significantly influences the energy spectrum of the high-density excitons [5-9]. As we will see, this leads to many fascinating effects related to instabilities. A strong exciton-photon interaction implies a strong polariton effect, in which photon and exciton states are mixed (as in Fig. 1.3). When this mixing is strong, it is not obvious how to define the ground state of the system.
A comprehensive investigation of the optical properties of excitonic molecules in CuCl films is presented and discussed. The experimental work includes resonant two-photon absorption (TPA), observations of the resonantly excited biexciton emission, and optical pump-and-probe studies. The collision broadening of the TPA implies a collision rate \ensuremath{\sim}${10}^{\ensuremath{-}12}$ sec for the biexcitons, which is sufficiently rapid to establish a quasithermal equilibrium for the particles on a time scale that is short in comparison with the biexciton lifetime and the duration of the laser pump pulse. The biexciton luminescence line shapes obtained with resonant $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=0$ two-photon excitation have been fitted using a Bose-Einstein thermal distribution of biexcitons. The chemical potential obtained from the fits goes to zero as the biexciton density is increased at a fixed lattice temperature or if the lattice temperature is decreased at fixed density. The sharp luminescence features that are observed at high densities and low temperatures with single-beam, two-photon excitation are interpreted as resulting from a Bose-Einstein---condensed state of the biexcitons at twice the wave vector of the laser pumping photons. Further evidence for a condensed state is obtained from optical-probe measurements in which a small number of probe biexcitons is injected into the sample, with and without the presence of a condensed state produced by an intense laser pump beam. The luminescence of these injected probe biexcitons is modified in the presence of the pump beam such that it exhibits the sharp features of the emission from the condensed state. Measurements of optical gain and stimulated emission in the presence of the pump beam show that the redistribution of the probe luminescence does not result from those processes, but must involve a preferential redistribution of the probe particles in momentum space via collisions. Such a redistribution is expected when additional particles are added to a condensed system of bosons.