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arXiv:2310.16166 · Physical review. B./Physical review. B

Quantum theory of polariton weak lasing and polarization bifurcations

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

Published Aug 13, 2024• 1 citation
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Abstract

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 ${g}_{xx}^{(2)}(t)$, with ${g}_{xx}^{(2)}(t)<1$ 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.

DOI
10.1103/physrevb.110.075304

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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.
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.
We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.
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 intrinsic Josephson effect is observed in a two-component polariton condensate in a strained planar microcavity under a resonant pulsed excitation such that only one of the two linearly polarized eigenstates is pumped from the outside. On reaching the threshold density, the polariton-polariton interaction involves a spontaneous breaking of the symmetry between spin-up and spin-down polaritons. As a result, the condensate acquires nearly circular polarization while the pump is strong and then passes to the Josephson oscillation regime since the pump weakens.
Second-order time correlations of polaritons have been measured across the condensation threshold in a CdTe microcavity. The onset of Bose-Einstein condensation is marked by the disappearance of photon bunching, demonstrating the transition from a thermal-like state to a coherent state. Coherence is, however, degraded with increasing polariton density, most probably as a result of self-interaction within the condensate and scatterings with noncondensed excitons and polaritons. Such behavior clearly differentiates polariton Bose condensation from photon lasing.
We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton lifetime), the average polarization degree is close to zero, while above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. It is shown that the polariton-polariton interaction leads to suppression of the linear polarization degree of the condensate due to the self-induced Larmor precession of the pseudospin. We establish the link between the second-order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.