We present a theory of the linear and nonlinear optical characteristics of the insulating phase of the Falicov-Kimball model within the self-consistent mean-field approximation. The Coulomb attraction between the itinerant d-electrons and the localized f -holes gives rise to a built-in coherence between the d-and f -states, which breaks the inversion symmetry of the underlying crystal, leading to: (1) electronic ferroelectricity, (2) ferroelectric resonance, and (3) a nonvanishing susceptibility for second-harmonic generation. As experimental tests of such a built-in coherence in mixed-valent compounds we propose measurements of the static dielectric constant, the microwave absorption spectrum, and the dynamic second-order susceptibility.

We calculate the linear and nonlinear optical properties of the Falicov-Kimball model for a mixedvalent system within the self-consistent mean-field approximation. Second-harmonic generation can only occur if the mixed-valent state has a built-in coherence between the itinerant d-electrons and the localized f -holes. By contrast, second-harmonic generation cannot occur for solutions of the model with f -site occupation as a good quantum number. As an experimental test of coherence in mixed-valent compounds we propose a measurement of the dynamic second-order susceptibility.The Falicov-Kimball We report here the nonlinear optical responses of these two classes of solutions. Solutions of the model with a built-in coherence can sustain second-harmonic generation. Solutions with classical f -electron site distributions cannot. Therefore, we propose the measurement of the second-order susceptibility of a mixed-valent compound as a test to distinguish between these theories. The existence of such second-harmonic generation due to coherence in the ground state would, of course, be of interest in its own right as a manifestation of strong electron correlation.Four-Wave-Mixing (FWM) spectroscopy has become a powerful tool for studying coherence in semiconductor systems [6]. In a three-beam FWM experiment, two incoming beams of wavevectors k 1 and k 2 set up a transient polarization grating. The third incoming beam of wavevector k 3 diffracts off the grating to produce the outgoing signal in the direction k 4 = k 3 + k 2 − k 1 . Being a third-order process, FWM is allowed in media with or without inversion symmetry. We pose the question: what happens if the state being probed already has a polarization built into it instead of being created artificially by optical pumping? An example of such a system is the self-consistent mean-field (SCMF) solution of the FK model resulting in the Bose-Einstein condensation of d-f excitons.As shown below, the built-in polarization leads to a nonlinear optical response to second order in the exter-1

We present a systematic theory of Coulomb interaction effects in the nonlinear optical processes in semiconductors using a perturbation series in the exciting laser field. The third-order dynamical response consists of phase-space filling correction, mean-field exciton-exciton interaction, and two-exciton correlation effects expressed as a force-force correlation function. The theory provides a unified description of effects of bound and unbound biexcitons, including memory-effects beyond the Markovian approximation. Approximations for the correlation function are presented.Comment: RevTex, 35 pages, 10 PostScript figs, shorter version submitted to Physical Review

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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...