Singly quantized vortices have already been observed in many systems, including the superfluid helium, Bose-Einstein condensates of dilute atomic gases, and condensates of exciton-polaritons in the solid state. Two-dimensional superfluids carrying spin are expected to demonstrate a different type of elementary excitations referred to as half-quantum vortices, characterized by a p rotation of the phase and a p rotation of the polarization vector when circumventing the vortex core. We detect half-quantum vortices in an exciton-polariton condensate by means of polarization-resolved interferometry, real-space spectroscopy, and phase imaging. Half-quantum vortices coexist with single-quantum vortices in our sample.

From a theoretical point of view, we discuss a variety of phenomena linked to the spin and polarization degree of freedom of exciton-polaritons in semiconductor microcavities. We start with linear optical effects including the optical spin Hall effect, formation of polarization vortices and ballistic propagation of polarized exciton-polaritons. Next, the interplay between spin-dependent dynamics and Bose condensation in the 2D system of microcavity polaritons is addressed. Theoretically, this many-body system of interacting particles is described by the spinor Gross-Pitaevskii equations. These equations provide a description of the time evolution of polarized polariton fields under different conditions of optical excitation as well as an understanding of the phenomena of superfluidity, multistability and hysteresis via renormalization of the dispersion of elementary excitations. The comprehension of polarization-sensitive dynamics can be made through the introduction of several effective fields of different nature acting on the polariton pseudospin. The theory of parametric scattering of exciton-polaritons is presented, using the second quantization formalism. It is found that the combination of nonlinearity and various mechanisms of spin reorientation leads to self-organization and the formation of polarized patterns such as polarization crosses, vortices and rings. The manipulation of polariton spins can lead to various applications in signal processing, including the construction of optical logic gates and spin memory elements; the creation of spin currents; and the control of polarized signal propagation in the microcavity plane. The concept of polariton neurons is discussed in this connection.

New effects of polarization multistability and polarization hysteresis in a coherently driven polariton condensate in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is of 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.

We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatiallytrapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two ellipticallypolarized (up to 95% circularly-polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100-fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.Condensation of exciton-polaritons (polaritons) spontaneously breaks the global phase symmetry [1][2][3][4][5]. Owing to their easy optical interrogation, high-speed (ps) interactions, and macroscopic coherence (over hundreds of microns) [6], polariton condensates are excellent candidates to probe and exploit for sensing [7,8], spinoptronics [9][10][11], new optoelectronic devices [12][13][14], and quantum simulators [15]. The driven-dissipative multicomponent polariton system can undergo additional bifurcations and condense into states which are not eigenstates of the single-particle Hamiltonian, but many-body states with reduced symmetry [16,17]. Thus, we should expect that two-component exciton-polariton condensates can also show spontaneous symmetry breaking bifurcations in their polarization state. Spin studies of microcavity polaritons have been of great interest in recent years [18][19][20][21][22][23][24][25][26][27][28][29]. However, spontaneous symmetry-breaking bifurcation of spin has not been observed before.Here, we demonstrate spontaneous magnetization in an exciton-polariton condensate, as a direct result of bifurcations in the spin degree of freedom. Utilizing an optically trapped geometry, condensates spontaneously emerge in either of two discrete spin-polarized states that are stable for many seconds, > 10 10 longer than their formation time. These states emit highly circularly-polarized coherent light (up to 95%) and have opposite circular polarizations. The condensate stochastically condenses in a left-or right-circularly polarized state, with an occurrence likelihood that can be controlled by the ellipticity * ho278@cam.ac.uk † jjb12@cam.ac.uk of the nonresonant pump. The two spin-polarized states can be initialized and switched from one state to another with weak resonant optical pulses. Our system has potential applications in sensing, optical spin memories and spin switches, and it can be implemented for studying long-range spin interactions in polariton condensate lattices. This article is structured as follows: in Section I we review trapped polariton condensates and the current understanding of polarization in untrapped polariton condensates. In Section ...