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Theory of the Third-Order Nonlinear Optical Response of Exciton–Microcavity Coupled System

Hajime Ishihara, Tomonari Amakata, K. Cho

Published Dec 1, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1002/(sici)1521-396x(199812)170:2<301::aid-pssa301>3.0.co;2-m

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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.
A theory of degenerate four-wave mixing (DFWM) in the low density excitation limit at the semiconductor band edge is developed on the basis of the bosonic representation of the electron-hole Hamiltonian. By accounting for the exciton-exciton interactions of the lowest order we arrive at the practical few-level density matrix description of the third-order excitonic nonlinearity. The developed theory accounts phenomenologically for the phase space filling, and excitation induced dephasing effects and well reproduces the results of the recent DFWM experiments in high- and low-fineness microcavity. We show that polarization-sensitive four-wave mixing measurements enable to discriminate the contributions to the DFWM signal from the exciton-exciton interactions of different symmetry.
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.
Summary form only given. Using a full microscopic many-body theory, based on the dynamics-controlled truncation (DCT) formalism, we compute four-wave mixing spectra of thin semiconductor quantum well microcavities within the lowest-order nonlinear regime (/spl chi//sup (3)/-regime). Specifically, we focus on heavy-hole 1s excitons and corresponding two-exciton correlations (coherent biexcitons and two-exciton continuum correlations). Within this approach, the linear optical response corresponding to hh-excitons with given absorption lineshapes are inputs to the calculation of the nonlinear FWM spectra.
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.
Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes–Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton–cavity system at resonance. Injecting two photons into the cavity, we demonstrate a larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.
Recently, several research groups have reported investigations of vacuum-field Rabi splittings (VRS) in the linear response of strongly coupled semiconductor microcavities [1-4]. We have previously reported on the dynamics of time-domain vacuum Rabi oscillations, which are most easily understood in the framework of cavity exciton-polaritons, in which the in-plane momentum k|| is conserved [2], so that at each k|| a single cavity mode interacts with only a single mode of the electromagnetic field (Jaynes-Cummings model). In high Q semiconductor microcavities, the strong coupling between two-dimensional excitons and planar distributed- Bragg-reflector cavity modes results in several-meV splittings observable in the reflectivity or absorption spectrum. In the low excitation regime, the VRS is independent of light intensity incident on the cavity, since the vacuum-Rabi frequency exceeds the externally-driven Rabi frequency (in which case the Jaynes-Cummings model is equivalent to the linear dispersion of the coupled exciton-cavity system). As the incident light intensity is increased, two different effects may be expected to contribute to the nonlinear response. First, as long as the excitonic absorption is equivalent to a two-level system, higher-lying states of the Jaynes-Cummings ladder might be observable. Second, at high intensity phase-space filling and Coulomb screening of the exciton states results in a reduced oscillator strength which leads to a reduced VRS; this effect has no analogue in the case of atom-cavity systems. In this paper, we apply several ultrafast nonlinear techniques to investigate the nonlinear response of semiconductor microcavities.