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Physical review. B, Condensed matter

Density bistability in an interacting electron-hole system in coherently excited semiconductors

Takuya Iida, Yukio Hasegawa, H. Higashimura, M. Aihara

Published Apr 15, 1993• 23 citations
Publisher

Abstract

An electron-hole system in a direct-gap semiconductor that is coherently excited by a high-intensity laser is investigated. The stationary state of the system in the presence of laser field is described by Bogolyubov quasiparticles. Using a mean-field approximation, we derive a set of basic equations including electron-electron, hole-hole, and electron-hole screened Coulomb interactions. The screening effects are incorporated self-consistently on the basis of a quasistatic random-phase approximation. The stationary state has a fixed chemical potential and is controlled by the frequency of the laser field. By numerical analysis of the basic equations, we show that a resonatorless bistability occurs; that is, an electron-hole pair-density bistability with respect to the excitation energy is shown to be caused by many-body effects via the screened Coulomb interaction. We clarify how the stationary state changes its entity depending on the frequency and intensity of the laser field, and how such a characteristic behavior is observed in optical spectra of probe light.

DOI
10.1103/physrevb.47.9328

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An electron-hole system in a direct-gap semiconductor that is coherently excited by a high-intensity laser is investigated. The stationary state of the system in the presence of laser field is described by Bogolyubov quasiparticles. Using a mean-field approximation, we derive a set of basic equations including electron-electron, hole-hole, and electron-hole screened Coulomb interactions. The screening effects are incorporated self-consistently on the basis of a quasistatic random-phase approximation. The stationary state has a fixed chemical potential and is controlled by the frequency of the laser field. By numerical analysis of the basic equations, we show that a resonatorless bistability occurs; that is, an electron-hole pair-density bistability with respect to the excitation energy is shown to be caused by many-body effects via the screened Coulomb interaction. We clarify how the stationary state changes its entity depending on the frequency and intensity of the laser field, and how such a characteristic behavior is observed in optical spectra of probe light.
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.
Nonlinear optical properties of laser-excited semiconductors are discussed, and the applications to optical bistability and optical logic are reviewed. The physical origin of the nonlinearities is analyzed in terms of the many-body interactions in the system of electron-hole pairs, causing effects such as plasma screening of the Coulomb interaction, band-gap renormalization, and band filling. Theoretical results for absorption and refractive-index spectra are compared to experimental data obtained for room-temperature GaAs and other semiconductors. The experimental and theoretical results for dispersive optical bistability in semiconductors are summarized, and recent experiments on optical logic gating and pattern recognition are discussed.
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 availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
Within the framework of a simple numerical model, we investigate the optical properties of a laser-excited direct-band-gap semiconductor (CdS) in the case when both free and bound electron-hole pairs are present. At low temperatures the ionization of excitons proceeds via a first-order phase transition, which is closely related to the Mott transition, and we argue that in direct-band-gap semiconductors it is not suppressed by the electron-hole liquid condensation, as it is in indirect-band-gap materials. The existence of the two corresponding ionization phases with different optical properties is shown to result in optical bistability (OB), which is quite similar to the increasing-absorption (resonatorless) OB but has some peculiarities of its own. Our model also predicts another optical manifestation of this ionization phase transition---the possibility of absorption oscillations at resonant excitation of excitons.
We theoretically investigate the influence of dynamic Coulomb interaction on optical bistability and Rabi oscillations in a driven two-level semiconductor quantum dot system under laser irradiation. Using density matrix equations derived from the Coulomb-interaction model proposed by Lu et al. [Phys. Rev. A 103, 043504 (2021)], we obtain analytical solutions for population inversion under the rotating wave approximation. Our analysis shows that the Coulomb interaction induces optical bistability, governed by a cubic equation. The thresholds and the shapes of the hysteresis loops are tunable and can be controlled by various parameters, including electron density, confinement potential, detuning, and dephasing. Additionally, our numerical simulations demonstrate the potential for achieving high-efficiency population inversion and predicting bifurcation and anharmonic regimes in Rabi oscillations under monochromatic excitation.