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Physical review. B, Condensed matter

Exciton-dephasing kinetics after coherent pulse excitation

O. M. Schmitt, L. Bányai, H. Haug

Published Dec 15, 1999• 11 citations
Publisher

Abstract

A system of coherently excited weakly interacting excitons is investigated with respect to its coherent and incoherent dynamics. Both the mean-field terms and the scattering terms are calculated on a microscopic level including the contribution of the anomalous functions. In this framework, the transition from coherent to incoherent excitons is studied. At high excitation densities near the critical density for a Bose-Einstein condensation a pronounced slowing down of the dephasing is obtained.

DOI
10.1103/physrevb.60.16506

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Quantum Electronics and Laser Science Conference•Jan 1, 2002•0 citations
A system of coherently excited weakly interacting excitons is investigated with respect to its coherent and incoherent dynamics. Both the mean-field terms and the scattering terms are calculated on a microscopic level including the contribution of the anomalous functions. In this framework, the transition from coherent to incoherent excitons is studied. At high excitation densities near the critical density for a Bose-Einstein condensation a pronounced slowing down of the dephasing is obtained.
The dephasing and condensation kinetics of bosonic excitons after coherent pulse excitation is studied in the vicinity of a Bose-Einstein condensation (BEC). For a system of excitons interacting with acoustic phonons various excitation conditions are investigated. Significant qualitative changes of the polarization dephasing in the vicinity of the BEC are discussed. Furthermore the kinetics of excitons, interacting via a two particle interaction, is studied. Both the bosonic mean-field terms and the scattering terms are calculated on a microscopic level. As in the phonon-model the dephasing rate of the exciton–exciton scattering diminishes considerably in the vicinity of the BEC. All results are suited as experimentally observable signatures of an excitonic BEC.
Photo-excited excitons, i.e. closely bound electron-hole pairs, are in the low-density regime approximately bosons. For sufficiently low temperatures and sufficiently high densities of the exciton gas, a nonequilibrium phase transition in the form of a Bose-Einstein condensation (BEC) can be expected. Various levels of the description of the kinetics of relaxation and condensation due to the coupling of the excitons to a cold reservoir of acoustic phonons are discussed. For noninteracting excitons a rate equation approach with the exciton Boltzmann equation can be used. For interacting excitons the nonmarkovian quantum kinetics is required for the description of the BEC in order to incorporate the changes of the energy spectrum during the condensation self-consistently. Finally colored Langevin fluctuations can be used to calculate the phase diffusion of the condensate.
The time-dependent correlation function of the order parameter of Bose-Einstein condensation is calculated for a dilute interacting exciton gas cooled by a cold phonon bath. This calculation is achieved by combining two theoretical concepts: (i) a non-Markovian quantum kinetics, which is necessary in order to include the changing single-particle spectrum during the condensation self-consistently, and (ii) the stochastic non-Markovian Langevin fluctuations which are connected with the dissipative scattering integrals. A linearization around the mean quantum kinetics is used in order to determine the order parameter's fluctuations around its mean value. Similarly as in the laser theory the linewidth or the coherence time of the coherent order parameter amplitude is determined. The results show a clear reduction of the linewidth of the coherent exciton amplitude as the system cools down in time through the threshold of the Bose-Einstein condensation. The observation of this line narrowing by nonlinear optical spectroscopy would give a direct indication of the temporal build-up of an exciton condensate in a semiconductor.
Coherent Rayleigh scattering and incoherent luminescence are studied by femtosecond upconversion under resonant excitation as a function of exciton density in GaAs quantum wells. Comparing samples with different well widths allows to establish the relation between inhomogeneous broadening and the shape of resonant Rayleigh scattering. We find an excellent agreement between experiment and a classical model. In samples with moderate inhomogeneous broadening we provide evidence for the transition from coherent to incoherent emission. The comparison with excitonic dephasing times T2 obtained from four-wave-mixing experiments demonstrates that the incoherent exciton population rises within T2/2, at any exciton density when changed by more than an orders of magnitude. The experimental results confirm very clearly the concept predicting that the coherent polarization made up by localized excitons decays into an incoherent exciton population under conservation of the number of excited quanta.
We study the dynamics of a two-component Bose-Einstein condensate (BEC) of 174 Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description.
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.