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International Journal of Modern Physics B

NONBOSON TREATMENT OF EXCITONIC NONLINEARITY IN OPTICALLY EXCITED MEDIA

Nguyen Ba An

Published May 10, 1991• 1 citation
Publisher

Abstract

The present article shortly reviews some recent results in the study of excitonic nonlinearity in optically excited media using a nonboson treatment for many-exciton systems. After a brief discussion of the exciton nonbosonity the closed commutation relations are given for exciton operators which hold for any exciton density and type. The nonboson treatment is then applied to the problems of intrinsic optical bistability and nonlinear polariton yielding quite interesting and new effects, e.g. new shapes of hysteresis loops of intrinsic optical bistability or anomalies of polariton dispersion.

DOI
10.1142/s0217979291000584

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The present article shortly reviews some recent results in the study of excitonic nonlinearity in optically excited media using a nonboson treatment for many-exciton systems. After a brief discussion of the exciton nonbosonity the closed commutation relations are given for exciton operators which hold for any exciton density and type. The nonboson treatment is then applied to the problems of intrinsic optical bistability and nonlinear polariton yielding quite interesting and new effects, e.g. new shapes of hysteresis loops of intrinsic optical bistability or anomalies of polariton dispersion.
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The interplay of exciton statistics and Coulomb interactions in the optical response of semiconductors is studied by derivation of an effective Hamiltonian written in terms of exciton operators, starting with a two-band model. Statistical effects are incorporated through the nonboson commutation relations of exciton operators, which contain an exciton-size-dependent parameter q that may vary from q = 0 (boson statistics) through q ≪ 1 (Wannier excitons) to q = 2 (Frenkel excitons or Pauli statistics). A unified Green’s function expression for χ(3) that applies to excitons of an arbitrary nature is derived.
Turbulence and chaos in a semiconductor crystal? These are just some of the intriguing predictions of nonlinear optics with coherent excitons. In this chapter we discuss some aspects of nonlinear coherent optics with the participation of the excitons, photons, and biexcitons. As in many nonlinear systems, these effects arise because of feedback mechanisms, i.e., the light impinging on the system affects the electronic states, which in turn affect the dielectric constant of the medium through which the light passes. These effects are closely related to the phenomena of self-organization [1-8] and optical bistability [7-10] and self-pulsations and the appearance of chaos [2-6]. The cooperative nonlinear coherent processes in optical systems have recently attracted much attention [7-20]. These investigations have stimulated the development of new mathematical methods [21-31] and have opened up possibilities for many new applications. The theoretical and the experimental investigations in these directions give rise to the theory of solitons [32∧2] and lead to the new developments in the optics of ultrashort pulses [43-58]. Ultrafast phenomena such as self-induced transparency and nutation are related to the propagation of solitons and pulse trains, whereas the transient stages of the ultrashort lightpulse penetration in the media are described by area theorems. These coherent ultrafast phenomena typically take place during intervals of time less than the relaxation time, i.e., femtoseconds to picoseconds in typical solids. Collisions and incoherent scattering processes destroy the coherent evolution of the excited particles. But if coherent macroscopic states of the excitons, photons, and biexcitons have been formed because of spontaneous or induced BEC, in this case one can consider their time evolution over intervals of time much greater than the relaxation time.
We present a fully-quantum-mechanical theory of the intracavity interaction of coherent light with semiconductors. Interaction is assumed to occur via excitons. Using a master-equation approach we include such effects as exciton-lattice and exciton-exciton interactions. In the two cases of high and low exciton densities, steady-state analysis reveals bistability and hysteresis in the system. Bistability of a dispersive and absorptive nature in both exciton number and output intensity, dependent on input intensity is found. The bistability displayed in the high-density case agrees qualitatively with the experimental curves obtained by Gibbs et al. for GaAs. As yet the low-density bistability has not been experimentally observed.
We realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10 μs, 1 s], offering a promising route to spin switches and spin memory elements.