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Physical Review Letters

From Coherently Excited Highly Correlated States to Incoherent Relaxation Processes in Semiconductors

W. Schäfer, R. Lövenich, Neil A. Fromer, D. S. Chemla

Published Jan 8, 2001• 30 citations
Publisher

Abstract

Recent theories of highly excited semiconductors are based on two formalisms, referring to complementary experimental conditions, the real-time nonequilibrium Green's function techniques and the coherently controlled truncation of the many-particle problem. We present a novel many-particle theory containing both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first rigorous solution concerning formation and decay of four-particle correlations in semiconductors. They are in excellent agreement with experimental data.

DOI
10.1103/physrevlett.86.344

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In order to optimize opto-electronic applications of semiconductor nanostructures, a deep understanding of optical nonlinearities is essential.One fundamental method currently used within this field of research is ultrafast optical spectroscopy.This work presents a theoretical study of optical nonlinearities in semiconductor quantum wells in the coherent time regime.The theory is based on the equations of motion for the coherent exciton and biexciton transition amplitudes.These equations are derived using two different ways: Heisenberg equations of motion in combination with the dynamics-controlled truncation theory and alternatively the non-equilibrium Green´s function technique. For the coherent regime both approaches are equivalent and can be used to formulate a coupled set of equations for the coherent excitation dynamics that is correct up to the third order in the optical field.In contrast to the dynamics-controlled truncation theory the non-equilibrium Green´s function technique allows the inclusion of incoherent scattering processes into the description.The theory is evaluated to describe pump and probe as well as four-wave-mixing experiments with ZnSe quantum wells.Numerical calculations for the coherent control of the macroscopic polarization andthe dependence of transient four-wave-mixing on the light-polarization and intensity are both in good agreement with experiments.In order to correctly describe elevated excitation conditions for the latter investigation, the theory is self-consistently extended such that the included excitonic and biexcitonic nonlinearities contribute up to arbitrary order in the optical field.

•Jan 1, 2005•1 citation
Recent theories of highly excited semiconductors are based on two formalisms, referring to complementary experimental conditions, the real-time nonequilibrium Green's function techniques and the coherently controlled truncation of the many-particle problem. We present a novel many-particle theory containing both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first rigorous solution concerning formation and decay of four-particle correlations in semiconductors. They are in excellent agreement with experimental data.
Recent conceptual advances in the theory of physics of highly excited semiconductors are based on two formalisms, the real-time non-equilibrium Green's function techniques and the coherently controlled truncation of the many-particle problems. These approaches apply to completely different but complementary experimental conditions. We present a novel many-particle theory, which contains both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first numerical rigorous solutions of the four-particle problem in a semiconductor. They are in excellent agreement with experimental data.
Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.
We study theoretically electron transients in semiconductor alloys excited by light pulses shorter than 100 fs and tuned above the absorption edge during and shortly after the pulse, when disorder scattering is dominant. We use nonequilibrium Green functions employing the field-dependent self-consistent Born approximation. The propagators and the particle correlation function are obtained by a direct numerical solution of the Dyson equations in differential form. For the purely elastic scattering in our model system the solution procedures for the retarded propagator and for the correlation function can be decoupled. The propagator is used as an input in calculating the correlation function. Numerical results combined with a cumulant expansion permit one to separate in a consistent fashion the dark and the induced parts of the self-energy. The dark behavior reduces to propagation of strongly damped quasiparticles; the field induced self-energy leads to an additional time nonlocal coherence. The particle correlation function is formed by a coherent transient and an incoherent back-scattered component. The particle number is conserved only if the field induced coherence is fully incorporated. The transient polarization and the energy balance are also obtained and interpreted.
We present a theory of ultrafast time-resolved pump and probe spectroscopy in semiconductor microcavities. The numerical solutions are in excellent agreement with experimental data. An analytical study based on the Weisskopf-Wigner approximation gives physical insight into the transient optical nonlinearities of semiconductor microcavites. It is able to explain the physical origin of the unusual transient shifts and asymmetric-excitation-induced dephasing observed experimentally. This theory demonstrates that the nonperturbative regime provides a unique tool for measuring the spectrum of four-particle correlations.
This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.
In order to optimize opto-electronic applications of semiconductor nanostructures, a deep understanding of optical nonlinearities is essential.One fundamental method currently used within this field of research is ultrafast optical spectroscopy.This work presents a theoretical study of optical nonlinearities in semiconductor quantum wells in the coherent time regime.The theory is based on the equations of motion for the coherent exciton and biexciton transition amplitudes.These equations are derived using two different ways: Heisenberg equations of motion in combination with the dynamics-controlled truncation theory and alternatively the non-equilibrium Green´s function technique. For the coherent regime both approaches are equivalent and can be used to formulate a coupled set of equations for the coherent excitation dynamics that is correct up to the third order in the optical field.In contrast to the dynamics-controlled truncation theory the non-equilibrium Green´s function technique allows the inclusion of incoherent scattering processes into the description.The theory is evaluated to describe pump and probe as well as four-wave-mixing experiments with ZnSe quantum wells.Numerical calculations for the coherent control of the macroscopic polarization andthe dependence of transient four-wave-mixing on the light-polarization and intensity are both in good agreement with experiments.In order to correctly describe elevated excitation conditions for the latter investigation, the theory is self-consistently extended such that the included excitonic and biexcitonic nonlinearities contribute up to arbitrary order in the optical field.