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Optics Express

Quantum statistics of polariton condensates in the weak lasing regime

Ziqiu Shao, Alexey Vitalievich Kavokin

Published Nov 29, 2024• 0 citations
Publisher

Abstract

We study theoretically the quantum statistics of exciton-polaritons accumulated in two bosonic condensates linked with a coherent (Josephson) and dissipative channel. The weak lasing regime characterized by spontaneous symmetry breaking has been predicted for this system within the mean field approximation. Here we go beyond the mean field theory and show that the weak lasing regime also manifests itself in dramatic changes in the statistics of both condensates that may be revealed in measurements of the second-order coherence. Namely, the condensates experience a superbunching at large enough external pumping and the cross-correlation reveals an anti-bunching effect at low enough pumping.

DOI
10.1364/oe.545567

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We study theoretically the quantum statistics of exciton-polaritons accumulated in two bosonic condensates linked with a coherent (Josephson) and dissipative channel. The weak lasing regime characterized by spontaneous symmetry breaking has been predicted for this system within the mean field approximation. Here we go beyond the mean field theory and show that the weak lasing regime also manifests itself in dramatic changes in the statistics of both condensates that may be revealed in measurements of the second-order coherence. Namely, the condensates experience a superbunching at large enough external pumping and the cross-correlation reveals an anti-bunching effect at low enough pumping.
In spite of having finite lifetimes exciton-polaritons in microcavities are known to condense at strong enough pumping of the reservoir. We present an analytical theory of such Bose condensates on a set of localized one-particle states: condensation centers. To understand the physics of these arrays one has to supplement the Josephson coupling by the radiative coupling caused by the interference of the light emitted by different centers. Combination of these couplings with the one-site interaction between the bosons leads to a rich nonlinear dynamics. In particular, a new regime of radiation appears. We call it weak lasing: The centers have macroscopic occupations and radiate coherently, but the coupling alone is sufficient for stabilization. The system can have several stable states and switch between them. Moreover, the time reversal symmetry in this regime is, as a rule, broken.
The quantum theory of polariton condensation in a trapped state reveals a second-order phase transition evidenced by spontaneous polarization parity breaking in subspaces of fixed polariton occupation numbers. The emission spectra of a polariton condensate demonstrate the coexistence of a symmetry-conserving condensate state with linear polarization and two symmetry-broken elliptically polarized states in the vicinity of the threshold. As a result, an oscillating linearly polarized second-order coherence gxx(2)(t){g}_{xx}^{(2)}(t)gxx(2)​(t), with gxx(2)(t)<1{g}_{xx}^{(2)}(t)<1gxx(2)​(t)<1 over some time intervals, is obtained. Spontaneous symmetry breaking is reflected in the second-order cross correlator of circular polarizations. A related buildup of elliptically polarized weak lasing also results in nonmonotonous dependence of the circular second-order coherence on excitation power and interaction strength.
A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.
A full quantum theory beyond the mean-field regime is developed for an exciton polariton condensate, to gain a complete understanding of quantum fluctuations. We find analytical solution for the polariton density matrix, showing the polariton nonlinearity causing fast relaxation correlated with the pump so as to yield the condensation at threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian and to a nonclassical distribution beyond the understanding at the level of off-diagonal long-range order. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning and temperature.
We study theoretically the correlation properties of exciton-polaritons in planar microcavities under pulsed excitation. In particular, we analyze the quantum statistics of two pseudo-spin components of an exciton-polariton condensate in the course of its formation. Below the bosonic condensation threshold, the statistics of two components correspond to a chaotic thermal state, while above the threshold, the coherence is built up, and the photons emitted by different spin components of the condensate become anticorrelated. This spin antibunching effect can be evidenced by spin-resolved Hanbury-Brown and Twiss spectroscopy of polariton lasers.
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.