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Physical Review B

Nonlinear route to intrinsic Josephson oscillations in spinor cavity-polariton condensates

Sergei S. Gavrilov, Andrey S. Brichkin, Sergey I. Novikov, Sven Höfling, Christian Schneider, Martin Kamp, A. Forchel, V. D. Kulakovskiĭ

Published Dec 9, 2014• 53 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.90.235309

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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.
We address polarization instability in a freely decaying polariton condensate created by 2-ps-long linearly polarized laser pulses in the upper sublevel of the lower-polariton (LP) branch in a GaAs-based microcavity with reduced symmetry. The generated linearly polarized condensate is found to lose its stability at excitation densities above the threshold value: it passes into the regime of inner Josephson oscillations with strongly oscillating circular and diagonal linear polarization degrees, as well as monotonically decreased oscillations in linear polarization accompanied by a gradual increase in the condensate of the low-sublevel component. These phenomena occur with a relatively small decrease in the total polarization and spatial coherence of the spinor condensate. At high LP densities, the LP-LP interaction leads to the nonlinear Josephson effect. All effects are found to be well reproduced by the model based on spinor Gross-Pitaevskii equations. The cause of the instability was clarified by considering a simplified model of the spinor 0D oscillator: it is spin anisotropy of the LP-LP interaction. The threshold density was shown to increase with decreasing difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\alpha}$ of the constants of the interparticle interaction of LPs with identical and opposite spins as ${\ensuremath{\delta}}_{l}/\mathrm{\ensuremath{\Delta}}\ensuremath{\alpha}$, where ${\ensuremath{\delta}}_{l}$ is the LP level splitting. The reduction in the linear polarization is connected with the fact that the LPs escaping from the condensate with oscillating circular polarization carry off more energy than from the linearly polarized one.
We analyze theoretically the phenomena related to the Josephson effect for exciton and polariton condensates, taking into account their specific spin degrees of freedom. We distinguish between two types of Josephson effects: the extrinsic effect, related to the coherent tunneling of particles with the same spin between two spatially separated potential traps, and the intrinsic effect, related to the ``tunneling'' between different spinor components of the condensate within the same trap. We show that the Josephson effect in the nonlinear regime can lead to nontrivial polarization dynamics and produce spontaneous separation of the condensates with opposite polarization in real space.
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.
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 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.
Bosonic condensates of spinless noninteracting particles confined on a ring cannot propagate circular periodic currents once rotation symmetry of the system is broken. However, a persistent current may appear due to interparticle interactions exceeding some critical strength. In this up-critical regime breaking of the symmetry between the clockwise and anticlockwise rotations takes place. We consider this symmetry-breaking scenario in the case of a spinor condensate of exciton polaritons trapped on a ring split by a potential barrier. Due to the intrinsic symmetry of the effective spin-orbit interaction, which stems from the linear splitting between transverse-electric and transverse-magnetic microcavity modes, the potential barrier blocks the circulating current and imposes linear polarization patterns. On the other hand, circularly polarized polaritons form circular currents propagating in opposite directions with equal absolute values of angular momentum. In the presence of interparticle interactions, the symmetry of clockwise and anticlockwise currents can be broken spontaneously. We describe several symmetry-breaking scenarios, which imply either restoration of the global condensate rotation or the onset of the circular polarization in the symmetry-broken state.