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Physical Review B

Real-time analysis of the optical response of cavity bipolaritons: Four-wave mixing and dynamics of formation

Hisaki Oka, Hajime Ishihara

Published Nov 14, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.78.195314

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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.
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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.
We theoretically investigate entangled-photon generation via a biexciton in a planar microcavity. Owing to strong exciton-photon coupling, the biexciton in the cavity produces a bound two-cavity-polariton state (cavity bipolariton). Entangled photons are generated by the cascade decay of the cavity bipolariton. We propose a novel scheme for highly efficient entangled-photon generation by controlling the cavity bipolariton states. It is shown that highly efficient generation can be achieved when a weak cavity bipolariton, formed by a biexciton and unbound cavity polaritons, is realized.
We studied the population and coherence dynamics of a biexciton in a planar CuCl microcavity. We developed a time-resolved two-photon polarization spectroscopy technique, by which we extracted the population dynamics of the biexciton even when the biexciton was spectrally overlapped with the lower cavity polariton. The observed lifetime of the cavity biexciton in the weak-coupling regime was much shorter than that of a bare CuCl thin film without a cavity, which directly demonstrates cavity enhancement of the radiative decay rate of the biexciton. The cavity enhancement originates from the hybridization of the unbound two-cavity-polariton state to the biexciton wave function by the biexciton-cavity coupling. By comparing the population and coherence decay curves of the biexciton, we found that the coherence of the cavity biexciton was limited by the radiative population decay.
The coherent dynamics of an optically driven exciton--photon--bipolariton system is studied in bulk CdS. Applying backward-scattering four-wave mixing (FWM) spectroscopy, we analyze the two-photon polarization associated with excitonic molecules and determine the dephasing time ${T}_{2}\ensuremath{\simeq}4.8 \mathrm{ps}.$ We demonstrate that the molecule-mediated FWM signal persists at positive time delays even in the ${\ensuremath{\chi}}^{(3)}$ limit, due to the spatial pinning of coherent polaritons induced by the second pulse. By generalizing the bipolariton model to uniaxial semiconductors, we calculate ${\ensuremath{\tau}}_{\mathrm{rad}}^{\mathrm{XX}}\ensuremath{\simeq}2.8 \mathrm{ps},$ justify the T2=2T1{T}_{2}{=2T}_{1}T2​=2T1​ limit, and prove the bipolariton representation for excitonic molecules in CdS.