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physica status solidi (b)

Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors. III. Response of the Many‐Exciton System on an Externally Driven Light Field

Volkhard May, Frank Boldt, K. Henneberger

Published Oct 1, 1985• 10 citations
Publisher

Abstract

Abstract The nonlinear response of a dense exciton gas in a platelet on an externally driven field is discussed using non equilibrium Green's function technique. A generalized Boltzmann‐equation of excitons containing many‐particle corrections in the diffusion‐, drift‐ and collision‐term is derived. Using a relaxed distribution (Boltzmann‐distribution) and an unrelaxed distribution (macro‐occupation) of ls‐excitons a bistability in exciton density as well as in the transmitted light intensity is obtained for a nearly resonant and stationary applied pump‐field of intensity 0.1 and 10kW/cm2, respectively. The bistability is obtained as a pure excitonic effect below the Mott‐transition.

DOI
10.1002/pssb.2221310222

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physica status solidi (b)•Sep 1, 1992•14 citations
Abstract The nonlinear response of a dense exciton gas in a platelet on an externally driven field is discussed using non equilibrium Green's function technique. A generalized Boltzmann‐equation of excitons containing many‐particle corrections in the diffusion‐, drift‐ and collision‐term is derived. Using a relaxed distribution (Boltzmann‐distribution) and an unrelaxed distribution (macro‐occupation) of ls‐excitons a bistability in exciton density as well as in the transmitted light intensity is obtained for a nearly resonant and stationary applied pump‐field of intensity 0.1 and 10kW/cm2, respectively. The bistability is obtained as a pure excitonic effect below the Mott‐transition.
Abstract The spectral properties of a dense exciton gas are discussed using an exciton self‐energy in second collisional Born approximation with respect to exciton‐exciton interaction. The shift of the continuum edge and the ls exciton as well as the increase of the damping of the ls exciton are calculated linearly in the exciton density. The distribution of ls excitons is assumed to be either a macro‐occupation of the k = 0 state or a Boltzmann distribution with effective temperature varying between 10 and 60 K. A weakening of the level shift is obtained with increasing temperature. In the case of macro‐occupation damping is calculated self‐consistently resulting in a sublinear dependence on density.
The optical spectra of laser-excited semiconductors change with varying laser intensity. Close to exciton or biexciton resonances these optical nonlinearities are, e.g., large enough to obtain optical bistability. The cause for these large nonlinearities are many-body effects in the system of the electron-hole pair excitation. The use of nonequilibrium Green’s functions, or if a quasi-equilibrium exists of thermal Green’s functions, makes it possible to take radiative and Coulomb interactions consistently into account.
Summary form only given. Large-radius excitons in semiconductors suffer strong Coulomb interaction on close approach. This is a distinctive difference in comparison with two-level systems in quantum optics. A mean field theory of interacting excitons in semiconductors leads to purely repulsive interaction, and does not account for spin-dependent polarization mixing and the formation of excitonic molecules (biexcitons). We have developed a theory for the nonlinear optical response, which can account for both. The coherent polarization is driven by exciton-exciton correlation, which can be expressed in terms of spin-dependent retarded memory functions. The effective equation is a generalized Gross-Pitaevskii equation.
An excitonic approach to the ultrafast optical response of confined semiconductors at elevated densities below the Mott transition is presented. The theory is valid from the coherent regime, where coherent excitonic transitions and biexcitons dominate, to the incoherent regime, where excitonic occupations dominate. Numerical simulations of the 1s1s1s exciton dynamics during intense circularly polarized pump pulses in two different Coulomb-interaction regimes are performed for two-dimensional semiconductors: Moderate Coulomb interaction is compared with dominating Coulomb interaction with respect to the light-matter interaction strength. The different many-body contributions are disentangled and it is found, that excitonic Rabi oscillations in the Coulomb-dominated regime are considerably less strong. By also comparing circular and linear excitation in a MoSe2_22​ monolayer, it is found, that linear excitation creates a regime, where excitonic Rabi oscillations are almost completely suppressed.
An exciton-phonon mechanism for producing cavityless optical bistability is suggested. We consider the influence of the oscillating subsystem of a crystal on the absorption process of a laser wave in the region of exciton frequencies. It is shown that exciton-phonon interaction leads to nonlinear dependence of the absorption coefficient on the density of the exciton gas. The increase of absorption with increasing exciton density, however, is possible only in the frequency region on the long-wavelength tail of the exiton band. As a result, the exciton density of the crystal becomes a hysteresis function of external parameters (intensity of the incident wave, temperature, etc.). We calculate the absorption coefficient of excitons and define the frequency and temperature regions where optical bistability may exist. We analyze different relaxation mechanisms of excitons and explain the experimental results of observing optical bistability in different semiconductor crystals.
Abstract A model which allows to treat self‐consistently many‐body exciton effects, including biexciton formation, is proposed for the theoretical description of an excitonic polarization induced by an intense electromagnetic field. In the presence of a pump field the normal spectrum of electromagnetic waves in the vicinity of the nonlinear biexciton resonance is shown to be composed of four polariton branches, where each is the superposition of two photons and two excitons. In the self‐consistent field approximation, the structure of the interconnected, strongly nonlinear exciton and biexciton resonances is studied, including optical Stark shift, multistable behaviour, etc. For a certain range of the exciton interaction parameters at sufficiently strong pump wave the system of excitons and excitonic molecules transforms abruptly to a dense coherent electron–hole “liquid”. Appearance and temporary evolution of an exciton–biexciton system after switching on a pump is also considered.