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Physical Review Research

Hysteresis in linearly polarized nonresonantly driven exciton-polariton condensates

Helgi Sigurðsson

Published Jun 11, 2020• 8 citations
Publisher

Abstract

It is shown that a condensate of microcavity exciton-polaritons exhibits bistability between its two orthogonal linearly polarized components for varying nonresonant excitation power.A non-Hermitian splitting of these components results in two parity-symmetric fixed-point solutions of opposite polarization, making up the hysteresis branches.These solutions correspond to the lowest threshold linearly polarized mode, which dominates at low pump powers, and a cross-polarized mode, which appears due to nonlinear pinning at higher excitation powers.The spin symmetry of the solutions extends the nonresonant bistable operation of polariton condensates to the entire equatorial plane of the Poincaré sphere.The results pave the way towards development of tailored bistable, linearly polarized, coherent sources of light.

DOI
10.1103/physrevresearch.2.023323

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It is shown that a condensate of microcavity exciton-polaritons exhibits bistability between its two orthogonal linearly polarized components for varying nonresonant excitation power.A non-Hermitian splitting of these components results in two parity-symmetric fixed-point solutions of opposite polarization, making up the hysteresis branches.These solutions correspond to the lowest threshold linearly polarized mode, which dominates at low pump powers, and a cross-polarized mode, which appears due to nonlinear pinning at higher excitation powers.The spin symmetry of the solutions extends the nonresonant bistable operation of polariton condensates to the entire equatorial plane of the Poincaré sphere.The results pave the way towards development of tailored bistable, linearly polarized, coherent sources of light.
We study the nonlinear dynamics of spinor exciton-polaritons in resonantly pumped microcavities. Using steady-state analysis and computing eigenfrequencies via Bogoliubov-like linearization, we show that multiple Hopf bifurcations beyond conventional bistability occur within specific power regimes and are not associated with stable solutions of the system. Owing to nonlinear excitonic interactions, these transitions occur at different pump powers during forward and backward pump sweeps, leading to pronounced hysteresis between fixed-point and limit-cycle states. In the spinor regime, multiple limit-cycle branches and associated dynamical hysteresis loops emerge due to the interplay of polarization coupling and spin-dependent nonlinearities. We show how the locations of the bifurcation points can be tuned by the pump frequency and other system parameters. Our results identify synchronization as the organizing principle underlying limit-cycle formation, dynamical hysteresis, and bifurcation cascades in driven spinor exciton-polariton microcavities.
We theoretically investigate a spinor polariton condensate under nonresonant pumping, based on driven-dissipative Gross-Pitaevskii equations coupled to the rate equation of a spin-unpolarized reservoir. We find the homogeneous polariton condensate can transit from the spin-unpolarized phase, where it is linearly polarized, to the spin-polarized phase, where it is elliptically polarized, depending on the cross-spin versus same-spin interactions and the linear polarization splitting. In both phases, we study elementary excitations using Bogoliubov approach, in a regime where the decay rate of total exciton density in reservoir crosses over from the slow to the fast limit. Depending on reservoir parameters, the global-phase mode can be either diffusive or gapped. By contrast, the relative-phase mode always possesses a gapped energy, undamped in the spin-unpolarized phase but weakly damped in the spin-polarized phase. In the spin-unpolarized phase, both modes are linearly polarized despite pumping and decay. However, in the spin-polarized phase, the mode polarization can be significantly affected by the reservoir and depends strongly on the circular polarization degree of the condensate. Interestingly, we demonstrate that the ``ghost'' branch of the Bogoliubov spectrum of the relative-phase mode can be visualized in the photoluminescence emission, distinguishable from that of the global-phase mode and thus allowing for experimental observation, when the spinor polariton condensate is elliptically polarized.
We realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10 μs, 1 s], offering a promising route to spin switches and spin memory elements.
We investigate the influence of transverse-electric–transverse-magnetic (TE–TM) splitting on the nonlinear response and bistability of resonantly driven spinor exciton-polaritons in a spatially homogeneous microcavity system. Using a coupled exciton–photon mean-field model, we find that TE–TM splitting significantly modifies the bistability threshold, hysteresis width, and spin composition of the steady states. In particular, TE–TM splitting counteracts the spin imbalance imposed by elliptically polarized pumping, leading to nearly equal populations of the two spin components and strongly suppressed degree of circular polarization in the steady state. The pump momentum plays a crucial role through its connection to the curvature of the lower polariton dispersion, resulting in distinct nonlinear regimes with different switching thresholds and dynamical responses. The intermediate branch within the hysteresis loop is unstable but may exhibit slow instability growth rates, giving rise to long-lived transient states. These results clarify how TE–TM splitting reshapes bistability and nonlinear spin dynamics in polariton systems and provide insight into the controlling polariton switching behavior through cavity anisotropy and pump parameters.
The spin and intensity of optically trapped polariton condensates are studied under steady-state elliptically polarized nonresonant pumping. Three distinct effects are observed: (1) spin inversion where condensation occurs in the opposite handedness from the pump, (2) spin and intensity hysteresis as the pump power is scanned, and (3) a sharp ``spin collapse'' transition in the condensate spin as a function of the pump ellipticity. We show these effects are strongly dependent on trap size and sample position and are linked to small counterintuitive energy differences between the condensate spin components. Our results, which fail to be fully described within the commonly used nonlinear equations for polariton condensates, show that a more accurate microscopic picture is needed to unify these phenomena in a two-dimensional condensate theory.