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arXiv:cond-mat/0607719 · Physical Review B

Parametric oscillation threshold of semiconductor microcavities in the strong coupling regime

Michiel Wouters, Iacopo Carusotto

Published Feb 27, 2007• 86 citations
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Abstract

The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviors is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behavior of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal, and idler frequencies.

DOI
10.1103/physrevb.75.075332

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The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviors is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behavior of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal, and idler frequencies.
Abstract We report the observation of optical bistability in a semiconductor microcavity pumped at the “magic angle” above the parametric oscillation threshold. Experimental evidence is given in the form of a hysteresis cycle of the nonlinear emission as a function of the pump intensity. A model analogous to those developped for triply resonant Optical Parametric Oscillators (OPO) is in good agreement with the experimental findings. In the second part, we study the potential application of the parametric oscillation regime to quantum optics. The quantum correlations between the emitted “signal” and “idler” beams are computed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.
We report an experimental study of the optical bistability in a semiconductor microcavity (MC), consisting of a wedged λ GaAs spacer containing a single 8.5 nm In 0.04 Ga 0.96 As quantum well (QW). Increasing the excitation power, a transition between the normal coupling and the weak coupling regime of the MC modes is observed. At intermediate excitation power the reflectivity spectrum shows the simultaneous presence of three resonances, with a third peak spectrally lying between the two normal modes. Monitoring the reflected signal for different laser energy as a function of the excitation power, we found that optical bistability is observed only at the energy of the third peak. The experimental findings do not agree with transfer matrix calculations based on exciton bleaching, suggesting that more complex nonlinear mechanisms are relevant in the observed bistable behaviour.
We propose a mechanism for achieving optical bistability in semiconductor heterostructures. In contrast to the well-known refractive shift of the Fabry-Perot mode in macroscopic resonators, we consider the bleaching of the exciton Rabi splitting in strong-coupling microcavities and prove that this nonlinear process leads to an optically bistable behavior. Through a model based on the transfer-matrix formalism, we predict the dependence of this effect on specific material parameters and on the nature of the cavity. Numerical calculations are carried out for quantum well embedded cavities and the possibility of room-temperature bistable operation is also discussed. \textcopyright{} 1996 The American Physical Society.
The quantum correlations between the beams generated by polariton pair scattering in a semiconductor microcavity above the parametric oscillation threshold are computed analytically. The influence of various parameters, including the cavity-exciton detuning, the intensity mismatch between the signal and idler beams, and the amount of spurious noise, is analyzed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However, the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons.