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Physica Scripta

Far from equilibrium evolution in highly excited semiconductors with a consistent treatment of the photon field

E. Heiner, W. Kleinig

Published Mar 1, 1993• 1 citation
Publisher

Abstract

Evolution equations of a laser-excited direct gap two-band semiconductor in the transient stage have been derived by using the first principle Liouville-von Neumann equation and the statistical projection operator method. To be more general, the photon field is described in a quantum mechanical manner. Quantum effects of the electron-photon coupoling as well as charge carrier Coulomb screening and dissipation are involved. The evolution of the time dependent coherent photon state is investigated. It results in additionally evolution equations. Numerical solutions of these systems are cast out for realistic parameters and are compared with previous results.

DOI
10.1088/0031-8949/47/3/015

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Evolution equations of a laser-excited direct gap two-band semiconductor in the transient stage have been derived by using the first principle Liouville-von Neumann equation and the statistical projection operator method. To be more general, the photon field is described in a quantum mechanical manner. Quantum effects of the electron-photon coupoling as well as charge carrier Coulomb screening and dissipation are involved. The evolution of the time dependent coherent photon state is investigated. It results in additionally evolution equations. Numerical solutions of these systems are cast out for realistic parameters and are compared with previous results.
The evolution of a highly excited exciton-electron-hole-pair system in the athermal stage is examined in a first principle theory by use of a time-dependent projection operator technique. The expectation values of excitons and electrons are cast out under the assumption of a Gaussian pulse shape in a theory, suitable for the description of transient properties. The linear response with respect to a white probe pulse is investigated by a Green's function technique, being an extension of the Kubo formalism for reference systems far off equilibrium. This formalism results in a correct description of the time-dependent behavior of effects like blue-shift and bleaching of exciton levels.
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.
A generalized Bloch-Maxwell formulation for laser-field-coupled semiconductors is derived from a two-band model which includes direct Coulomb interactions. The momentum-dependent, microscopic, electron-hole equations of motion in the time-dependent Hartree-Fock approximation and neglecting interband exchange interactions form the starting point for the formulation. A self-consistent set of coupled equations in four dynamical variables for the medium, together with the electric-field amplitude coupled through the Maxwell wave equation in a semiclassical approximation, are obtained to lowest order in the coherent Coulomb exchange interaction and the density-of-states distribution. Intrinsic optical bistability is predicted in a steady state due to a carrier density-dependent redshift of the band edge due explicitly to coherent Coulomb exchange. Integration of the dynamical equations for conditions which correspond to the ultrafast time regime exhibit intrinsic adiabatic inversion, adiabatic following, anomalous Rabi cycling, and unique, as well as fast, optical switching, all of which depend upon the coherent Coulomb exchange interaction.
Generalized Bloch equations for laser-excited semiconductors are derived applying quantum-mechanical projection-operator techniques. The equations include phase-space filling and the many-body Coulomb effects. The coherent part of the equations is evaluated for the regime of ultrafast-pump-probe excitation and shown to reduce to the inhomogeneously broadened two-level Bloch equations for the different momentum states if the proper Coulomb enhancement in the density of states is taken into account. For the high-excitation quasithermal regime a generalization of the Elliott formula for the absorption spectrum is derived which is valid not only for bulk semiconductors, but also for quantum-well structures and other systems with reduced spatial dimensions.
The basic results of theoretical nonperturbative analysis of spontaneous and stimulated emission from two-band excited intrinsic semiconductor interacting with a single mode of radiation field in a lossless micro-cavity are presented. The self-consistent dynamics of the coupled system ''semiconductor + single mode radiation field", accompanied with spontaneous and stimulated emission was investigated as dependent of the initial level of the excitation of semiconductor in the presence initially of the physical field vacuum. Calculations have been carried out with the help of the commutation version of the evolution method without introducing explicitly the phonon mechanisms. The initial non-equilibrium electron and hole populations in the bands have been supposed to be created by ultra-short laser pulses and described by the Fermi-Dirac quasi-equilibrium distributions with the given chemical potentials. The interaction between the electron-hole subsystem and the mode field has been adopted to be switched on suddenly. The calculations have shown that depending on the initial excitation level of electron-hole subsystem three states of the mode field are realized: the equilibrium Bose-Einstein photon distribution with nonzero chemical potential; the quasi-equilibrium distribution with the average number of photons equal to unit and accompanied with their fluctuations, and finally, the state of photon avalanche. The first regime takes the place when the coefficient of the light amplification is negative. Then, the equilibrium between the electron-hole subsystem and arising photons exists until the average number reaches the unit. For negative and =1 the equilibrium still exists but is accompanied with field fluctuations. Finally, when the steady growth arises the lower but stable values are established
Abstract Equations for the reduced density operator are evaluated. Investigating the subdynamics of nonrelevant observables a resolvent formulation is obtained selfconsistently for the screening part of the evolution superoperator. Utilizing the diagonal representation for the time‐dependent mean field term of the Hamiltonian, a selfconsistent concrete calculation of the screened potential is possible in the high density limit of the nonequilibrium. The result is an extension of the well known RPA‐formula for nonequilibrium two‐band systems of Fermions. An extension to the semimarkovian approximation is counted for.