The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.

We demonstrate that the tunable potential introduced by a surface acoustic wave on a homogeneous polariton condensate leads to fragmentation of the condensate into an array of wires which move with the acoustic velocity. Reduction of the spatial coherence of the condensate emission along the surface acoustic wave direction is attributed to the suppression of coupling between the spatially modulated condensates. Interparticle interactions observed at high polariton densities screen the acoustic potential, partially reversing its effect on spatial coherence.

We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding antivortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO.

Real-and momentum-space spectrally resolved images of microcavity polariton emission in the regime of condensation are investigated under nonresonant excitation using a laser source with reduced intensity fluctuations on the time scale of the exciton lifetime. We observe that the polariton emission consists of many macroscopically occupied modes. Lower-energy modes are strongly localized by the spatial polaritonic potential disorder on a scale of a few microns. Higher-energy modes have finite k vectors and are delocalized over 10-15 m. All the modes exhibit long-range spatial coherence comparable to their size. We provide a theoretical model describing the behavior of the system with the results of the simulations in good agreement with the experimental observations. We show that the multimode emission of the polariton condensate is a result of its nonequilibrium character, the interaction with the local polaritonic potential, and the reduced intensity fluctuations of the excitation laser.

The transmission of a pump laser resonant with the lower polariton branch of a semiconductor microcavity is shown to be highly dependent on the degree of circular polarization of the pump. Spin dependent anisotropy of polariton-polariton interactions allows the internal polarization to be controlled by varying the pump power. The formation of spatial patterns, spin rings with high degree of circular polarization, arising as a result of polarization bistability, is observed. A phenomenological model based on spin dependent Gross-Pitaevskii equations provides a good description of the experimental results. Inclusion of interactions with the incoherent exciton reservoir, which provides spin-independent blueshifts of the polariton modes, is found to be essential. Nonlinear interactions in optical systems result in a variety of important phenomena such as frequency conversion, parametric oscillation, bistability, pattern formation and self-organization. In this context hybrid lightmatter particles, polaritons, which form due to strong exciton-photon coupling in semiconductor microcavities (MCs), attract much attention [1]. In this case strong nonlinear interactions due to the excitonic component of polaritons lead to stimulated polariton-polariton scattering and optical parametric oscillation [2,3], bistability [4,5] and superfluidity [6,7]. Bose-Einstein condensation of polariton quasi-particles has also been reported [8]. It is notable that compared to weakly coupled light/matter microcavity systems, polariton nonlinear interactions are several orders of magnitude stronger [1].A further distinguishing feature of polariton systems arises from their spin properties. In particular, polaritons with parallel spins repel, whereas polaritons with opposite spins attract. Such interactions provide blueshifts and redshifts respectively of the energies of coherent polariton modes. This anisotropy in spin properties results in polarization bistability and multistability predicted recently [9]. Polariton polarization bistability has also been predicted to lead to the formation of spatial spin rings of high degree of circular polarization (DCP) [11]. These non-linear spin properties and spatial patterns may lead to novel optical/spin-based devices such as fast optical modulators, spin switches [11,12] and polariton logic elements (polariton neurons) [10], operating at high picosecond speeds and very low pump powers.In the present work we investigate bistability of spin-up and spin-down polariton fields as a function of the intensity and polarization of an external pump beam. As a result of spin dependent polariton-polariton interactions [9] we are able to switch abruptly the internal polariton DCP by 40-50% by tuning the pump power. Despite strong photonic disorder we demonstrate the formation of spatial ring patterns of high DCP, a result of the bistable threshold-like behavior of the DCP for spatially nonuniform excitation [11]. The pump power behavior and the similar bistability thresholds for spin-up and spindown coherent po...