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arXiv:1706.08450 · Physical review. B./Physical review. B

Quantum exciton-polariton networks through inverse four-wave mixing

T. C. H. Liew, Yuri G. Rubo

Published Jan 10, 2018• 19 citations
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Abstract

We demonstrate the potential of quantum operation using lattices of exciton-polaritons in patterned semiconductor microcavities. By introducing an inverse four-wave mixing scheme acting on localized modes, we show that it is possible to develop nonclassical correlations between individual condensates. This allows a concept of quantum exciton-polariton networks, characterized by the appearance of multimode entanglement even in the presence of realistic levels of dissipation.

DOI
10.1103/physrevb.97.041302

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We demonstrate the potential of quantum operation using lattices of exciton-polaritons in patterned semiconductor microcavities. By introducing an inverse four-wave mixing scheme acting on localized modes, we show that it is possible to develop nonclassical correlations between individual condensates. This allows a concept of quantum exciton-polariton networks, characterized by the appearance of multimode entanglement even in the presence of realistic levels of dissipation.
We develop the theoretical formalism to calculate second-order correlations in dissipative exciton-polariton system and we propose intensity-intensity correlation experiments to reveal the physics of exciton-light coupling in semiconductor microcavities in the Rabi oscillation regime. We predict a counterintuitive behavior of the correlator between upper and lower polariton branches: Due to the decoherence caused by stochastic exciton-photon conversions this correlator is expected to decrease below 1, while the individual second-order coherence of upper and lower polaritons exhibits nonmonotonous bunching.
Exciton polaritons are coupled states of matter and light, originated by the strong interaction between an optical mode and semiconductor excitons. This interaction can be obtained also at a single-particle level, in which case it has been shown that a quantum treatment is mandatory. In this work we study the light-matter entanglement of polaritons from a fully quantum formalism including pumping and dissipation. We find that the entanglement is completely destroyed if the exciton and photon are tuned at the resonance condition, even under very low pumping rates. Instead, the best condition for maximizing entanglement and purity of the steady state is when the exciton and photon are out of resonance and when incoherent pumping exactly compensates the dissipation rate. In the presence of multiple quantum dots coupled to the light mode, matter-light entanglement survives only at larger detuning for a higher number of quantum dots considered.
A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.
Exciton-polaritons, mixed light-matter quasiparticles in semiconductors, have recently shown evidence for Bose-Einstein condensation. Some of the properties of condensates of exciton-polaritons are reviewed in this article. We first discuss the spontaneous appearance of long-range order and the way this can be easily accessed in the case of polariton fluids. We show that the Penrose-Onsager criterion is valid even for such a very special case of condensate. We then describe the experiments that allow observation of topological defects in the fluid: quantized vortices, half vortices, and hyperbolic spin vortices. We demonstrate through the comparison with the gross Pitaevskii equation that the appearance and stability of such vortices are linked with the dissipative nature of the condensate together with the presence of disorder. We then briefly summarize the experiments on superfluid behavior of the polaritons at large-enough densities and expand somewhat more on the dynamical behavior of turbulence in the wake of an obstacle, with the appearance of vortex streets. We finally show that the Bogoliubov transformation has been revealed through four-wave mixing experiments.
We propose a continuous-variable analog of quantum controlled-not gates based on a system of exciton polaritons in semiconductor microcavities. This can be realized by engineering a parametric interaction between control and target polariton modes, which can be varied in time. As an explicit setup we use a system of dipolaritons, which allows for enhancement of parametric interaction by auxiliary classical fields and scalable multigate system realization. We find that high operational fidelity for the proposed gate is achievable for realistic system parameters.