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Journal of Experimental and Theoretical Physics Letters

Dynamics of four-wave mixing on excitons in a quantum optical microcavity

Yulan Fu, M. Willander, Eougenious L. Ivchenko, Andrey A. Kiselev

Published Dec 1, 1996• 5 citations
Publisher

Abstract

A theory of degenerate four-wave mixing in a semiconductor optical cavity with quantum wells is constructed. The nonlinear response of a microcavity can be four to five orders of magnitude stronger than that of an isolated quantum well. For P 2 E -and P 3 -type nonlinearities the damped diffracted signal oscillates with a period determined by the Rabi splitting. For a biexcitonic mechanism of nonlinearity, the signal contains damped overtones of the Rabi splitting and the biexciton binding energy.

DOI
10.1134/1.567250

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A theory of degenerate four-wave mixing in a semiconductor optical cavity with quantum wells is constructed. The nonlinear response of a microcavity can be four to five orders of magnitude stronger than that of an isolated quantum well. For P 2 E -and P 3 -type nonlinearities the damped diffracted signal oscillates with a period determined by the Rabi splitting. For a biexcitonic mechanism of nonlinearity, the signal contains damped overtones of the Rabi splitting and the biexciton binding energy.
A microscopic semi-classical theory for the self-consistent calculation of the nonlinear response field is applied to the exciton–microcavity coupled systems. Our results show that the respective spectral features of the degenerated four wave mixing (DFWM) signal in both the weak (Ω ≤ Γ) and the strong coupling (Ω ≫ Γ) regimes, where Ω is the Rabi splitting and Γ is the width of the modes, can be clearly described with a single framework. In the weak coupling regime, the nonlinear signal is strongest at the bare excitonic resonance, and its enhancement due to cavity effect is remarkable. In the strong coupling regime, our framework very well reproduces the polarization dependent DFWM spectra in a recent experiment.
We theoretically investigate the four-wave mixing (FWM) of a biexciton in a microcavity in the framework of cavity bipolariton. Cavity bipolaritons are stably formed in the strong-coupling regime with an exciton-cavity coupling comparable to the biexciton binding energy. The FWM signal obtained from our bipolariton model, where the biexciton and unbound two-exciton states form a complete system, agrees well with the experimental data [Baars et al., Phys. Rev. B 63, 165311 (2001)]. A strong FWM signal is obtained when a cavity bipolariton is formed by a superposition state of a biexciton and unbound two-cavity-polariton states. We also analyze the dynamics of the formation of biexciton and cavity polaritons by numerically solving the optical master equation in time domain. Efficient excitation of cavity bipolariton requires a specific pulse duration and/or pulse delay so that two-cavity polaritons are formed before the biexciton is excited.
Summary form only given. The role of exciton-exciton scattering in the nonlinear optical response of semiconductor quantum wells is well established. However, an interesting question arising from the system's dimensionality has so far not been addressed. In the quantum theory of scattering in two dimensions, the scattering amplitude behaves non-smoothly and non-perturbatively at low energies. While the exact scattering amplitude vanishes as 1/ln (energy) as energy /spl darr/0, the second Born approximation diverges logarithmically. These properties result from the system's dimensionality and hold for any short-range well-behaved potential. One may ask whether the second Born approximation also fails for exciton-exciton scattering in two-dimensional structures and how this breakdown may be experimentally detected. In this contribution, we address this question within a microscopic theory of frequency-degenerate four-wave-mixing signals from a quantum-well microcavity. Analyzing an experiment reported in with this theory, we argue that the data are already sufficiently sensitive to show the breakdown of the second Born approximation for exciton-exciton scattering.
We present a coherent nonlinear optical study of composite exciton-cavity systems in the strong-coupling regime. Quantum oscillations in a transient four-wave-mixing response show the creation of a coherent superposition state between the two normal modes of the composite system and demonstrate in the time domain the coherent energy exchange between the exciton and cavity. The deep oscillation persists when the cavity resonance is far detuned from the exciton resonance. The result shows that dynamics of the nonlinear response can be in a nonperturbative regime while dynamics of the linear response remains in a perturbative regime.
The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splitting when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons, and the electromagnetic field of the microcavity. An exciton oscillator strength of 4\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ is deduced for 76-\AA{} quantum wells.
We present a model for the nonlinear optical response of quantum wells, which includes biexcitons. We show that within this model, the interaction of two laser pulses, mediated by the nonlinear susceptibility, results in oscillations and in coupling between ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ excitons. This explains the temporal behavior of the differential absorption and four-wave mixing in recent experiments [Phys. Rev. Lett. 68, 349 (1992); 68, 1880 (1992)]. The oscillations have a frequency equal to the biexciton binding energy, and are different from known interference and quantum beat phenomena.