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Topical Meeting on Optical Bistability (OB)

Quantum Theory of Optical Excitonic Bistability

Crispin W. Gardiner, Moira L. Steyn‐Ross

Published Jan 1, 1983• 0 citations
Publisher

Abstract

A fully quantum mechanical formulation of the electron-hole-exciton-light system is developed following the work of Hanamura. In this formulation 1. The excitons are described by the "bosonisation transformation of Marumori et al. In this method exciton bose operators are introduced to describe electron-hole pairs, and anti symmetrisation effects are taken account of by a unitary transformation of the system operators, which introduces extra nonlinearities into the hamiltonian. This means that exclusion principle effects at high exciton densities are fully accounted for. The theory is formulated for Wannier (non-localised) excitons.

DOI
10.1364/obi.1983.thb28

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A fully quantum mechanical formulation of the electron-hole-exciton-light system is developed following the work of Hanamura. In this formulation 1. The excitons are described by the "bosonisation transformation of Marumori et al. In this method exciton bose operators are introduced to describe electron-hole pairs, and anti symmetrisation effects are taken account of by a unitary transformation of the system operators, which introduces extra nonlinearities into the hamiltonian. This means that exclusion principle effects at high exciton densities are fully accounted for. The theory is formulated for Wannier (non-localised) excitons.
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.
Abstract Optical bistability (OB) is a phenomenon that describes a light induced phase transition in the non-equilibrium state. It is vital for all-optical computing and communication, serving as the basis for switches, logic gates, transistors, and memory. By enabling two stable light states, OB allows storage and fast switching, making high-speed, energy-efficient data processing possible. In this work we study the phenomenon in a two-band semiconductor in an optical cavity. Starting from a many-body Hamiltonian of optically generated electrons, holes and light-semiconductor interaction and Coulomb electron–electron, hole–hole and electron–hole interactions, we obtain the optical Bloch equations, in the mean field approximation, where relaxation is included phenomenologically. We obtain expressions for particle density, excitonic pair density and output intensity as non-linear functions of input light intensity. All these quantities show bistable behaviour, with two stable phases, and hysteresis in the non-equilibrium state. Equilibrium is ensured by introducing damping terms for the particle density amplitude, excitonic density amplitude, and cavity photon amplitude phenomenologically. The electron–hole pairs increase with light intensity, shows bistable features and then disappears with further increase in the input light intensity. The bistable behaviour becomes pronounced as we pass from low Coulomb interaction strengths to high Coulomb interaction strengths between electrons and holes. For sub-bandgap excitations, the output light versus incident light shows a complex behaviour.
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.
The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.
Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.
We derive a bosonized Hamiltonian for a semiconductor quantum well with a light field by a new bosonization method taking exactly into account the composite-particle effects of excitons. Then we apply the bosonized Hamiltonian to the four-wave-mixing (FWM) processes. The obtained Hamiltonian describes two-boson states corresponding to bound and unbound two-exciton states and guarantees exclusion of unphysical states, which cannot exist in the fermionic space due to the Pauli exclusion principle. Calculated results of the FWM signals are in good agreement with the experimental ones, and therefore, the bosonized Hamiltonian turns out to be able to describe two-exciton correlations effectively.