Comment on "Topological stability of the half-vortices in spinor exciton-polariton condensates"

We show that recent paper by Flayac et al. [Phys. Rev. B 81, 045318 (2010) and arXiv:0911.1650] is misleading. We demonstrate the existence of static half-quantum vortices in exciton-polariton condensates and calculate the warping of their polarization texture produced by TE-TM splitting of polariton band.Comment: 4 pages, 1 figure. More material was added (in particular, on the current flow)

Vortices in exciton-polariton condensates with polarization splitting

The presence of polarization splitting of exciton-polariton branches in planar semiconductor microcavities has a pronounced effect on vortices in polariton condensates. We show that the TE-TM splitting leads to the coupling between the left and right half-vortices (vortices in the right and left circular components of the condensate), that otherwise do not interact. We analyze also the effect of linear polarization pinning resulted from a fixed splitting between two perpendicular linear polarizations. In this case, half-vortices acquire strings (solitons) attached to them. The half-vortices with strings can be detected by observing the interference fringes of light emitted from the cavity in two circular polarizations. The string affects the fringes in both polarizations. Namely, the half-vortex is characterized by an asymmetric fork-like dislocation in one circular polarization; the fringes in the other circular polarization are continuous, but they are shifted by crossing the string.Comment: 4 pages, 2 figs, Optics of Excitons in Confined Systems 11 (Madrid, 7-11 september 2009

Polarization dynamics of trapped polariton condensates with PT\mathcal{PT}-symmetry

We propose a grated microcavity setup to form trapped polariton condensates with parity-time ($\mathcal{PT}$) symmetry and study their polarization dynamics. The pseudo-conservative dynamics of the Stokes vector in proposed configuration is preserved in the presence of polariton-polariton interaction. In the case of weak gain-dissipation inbalance, as compared to the linear polarization splitting, the polarization Stokes spheres are deformed into ellipsoids. When linear polarization splitting becomes weak, i.e., when $\mathcal{PT}$-symmetry is broken for noninteracting system, the Stokes spheres are transformed into hyperboloids, but the dynamics is still described by closed trajectories, allowing manipulation of the polarization of polariton condensate by changing polarization splitting without losing its coherency.Comment: 6 pages, 2 figure

Stochastic polarization formation in exciton-polariton Bose-Einstein condensates

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 life-time) the average polarization degree is close to zero, whilst above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. We establish the link between second order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.Comment: 4 pages, 3 figure

Quantum theory of polariton weak lasing and polarization bifurcations

The quantum theory of polariton condensation in a trapped state reveals a second-order phase transition evidenced by spontaneous polarization parity breaking in sub-spaces of fixed polariton occupation numbers. The emission spectra of polariton condensate demonstrate the coexistence of the symmetry-conserving condensate state with the linear X polarization and the symmetry-broken, elliptically polarized states in the vicinity of the threshold. As a result, the oscillating linear second-order coherence $g^{(2)}_{xx}(t)$, with $g^{(2)}_{xx}(t)<1$ over some time intervals, is obtained. The spontaneous symmetry breaking is reflected in the second-order cross correlator of circular polarizations. The related build-up of elliptically-polarized weak lasing results also in non-monotonous dependence of the circular second-order coherence on the excitation power and the interaction strength.Comment: 7 pages, 5 figure

Pseudo diamagnetism of four component exciton condensates

We analyze the spin structure of the ground state of four-component exciton condensates in coupled quantum wells as a function of spin-dependent interactions and applied magnetic field. The four components correspond to the degenerate exciton states characterized by $\pm2$ and $\pm1$ spin projections to the axis of the structure. We show that in a wide range of parameters, the chemical potential of the system increases as a function of magnetic field, which manifests a pseudo-diamagnetism of the system. The transitions to polarized two- and one-component condensates can be of the first-order in this case. The predicted effects are caused by energy conserving mixing of $\pm2$ and $\pm1$ excitons.Comment: 4 pages, 2 figure