Collective Oscillations Driven by Correlation in the Nonlinear Optical Regime

Abstract

We present an analytical and numerical study of the coherent exciton polarization including excitonexciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization component and novel ultrafast collective modes. The frequency and damping of the collective modes are determined by the high-frequency properties of the retarded two-exciton correlation function, which includes Coulomb effects beyond the mean-field approximation. The overall time evolution depends on the low-frequency spectral behavior. The collective mode, well separated from the slower coherent density evolution, manifests itself in the coherent emission of a resonantly excited excitonic system, as demonstrated numerically. PACS numbers: 71.35.Lk, 42.50.Md, 78.47. + p Observations of coherent optical phenomena require a sufficiently long dephasing time. Thus, coherent processes such as the Rabi oscillations [1] and form-invariant pulse propagation [2] (also known as self-induced transparency) are well studied both theoretically and experimentally in atomic vapors [3]. In solid-state physics, the nonlinear optical properties of semiconductors are expected to exhibit analogous behavior, especially under resonant excitation of excitons [4,5], where the exciton transition approximates an ideal two-level system. However, there is a distinct difference in semiconductors. At moderate excitation densities, the mobile, large-radius Wannier excitons suffer strong Coulomb interaction on close approach and, at high densities, the collection of excitons dissociates into a neutral plasma.A mean-field theory of the exciton-exciton interaction leads to a purely coherent repulsive interaction, which does not yield a mechanism for dephasing due to the fluctuating effective local field. This level of approximation allows for nonlinear electric field-driven density oscillations, which are termed Rabi oscillations [6][7][8]. A further low-density approximate relation for the density and the polarization leads to a Gross-Pitaevskii equation [9,10] for the exciton dynamics. This yields form-invariant soliton solutions [11][12][13]. Keldysh and Kozlov [14] included correlation in a low-density ensemble of excitons. Here we present an extension of the Gross-Pitaevskii equation to include the correlation effects and explore some fundamental consequences in the ultrafast nonlinear optical processes. The correlation effects are based on our previous theory of exciton correlation in the weak nonlinear optical regime and are contained entirely in a retarded memory function [15,16]. The reactance part of the correlation function provides a renormalization of the coherent interaction and the admittance part provides a dephasing mechanism from exciton-exciton interaction. The latter contribution may be regarded as a nonlocal temporal excitation-induced dephasing [17]. A new finding is the ultrafast collective density oscillations riding on the slow coherent density, both being excited by a short laser pulse...

Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

“…The theory consistently includes all coherent third order (χ (3) ) nonlinearities and the resulting equations of motion are solved in a self-consistent fashion in the optical fields which includes a certain class of higherorder nonlinearities. 30,31,32 Correlations involving more than two excitons and those involving incoherent excitons are neglected. These effects are not expected to qualitatively alter the presented results for the considered coherent exciton densities of ∼ 10 10 cm −2 , especially for excitation well below the exciton resonance.…”

Quantum Field Theory of Exciton Correlations and Entanglement in Semiconductor Structures

“…For example, as it was proposed in Ref. (Ostreich & Sham, 1999), in the case of slowly varying polarization the memory term can be approximated by…”

“…Thus, the memory function can be approximated by (Ostreich & Sham, 1999) In the case of an one-dimensional model for excitons, the authors of Ref. (Ostreich & Sham, 1999) found α = 1.…”

“…(Ostreich & Sham, 1999)). It is possible to show that the number of possible collective modes increases from 0 to 2 with the exciton density increasing (the zero-frequency exponential spectral density Fig.…”

“…The time-dependence of the exciton density in the case of β = 2" (a) and exponential spectral function (b). We have used the parameters for the 3D model of semiconductor from (Ostreich & Sham, 1999): β = 52ω x /3, F(0)=14ω 2 x , ω x = 6.7meV.Thetimeisgiveninunits of 1/ω x and n(0)=0.1. mode corresponds to the Goldstone mode).…”