Nonequilibrium patterns in open systems are ubiquitous in nature, with examples as diverse as desert sand dunes, animal coat patterns such as zebra stripes, or geographic patterns in parasitic insect populations. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light. The unique features of polaritons in semiconductor microcavities allow us to go one step further and to study Turing patterns in an interacting coherent quantum fluid. We demonstrate formation and control of these patterns. We also demonstrate the promise of these quantum Turing patterns for applications, such as low-intensity ultra-fast all-optical switches.

We present a detailed theoretical study of transverse exciton-polariton patterns in semiconductor quantum well microcavities. These patterns are initiated by directional instabilities (driven mainly by polariton-polariton scattering) in the uniform pump-generated polariton field and are measured as optical patterns in a transverse plane in the far field. Based on a microscopic many-particle theory, we investigate the spatiotemporal dynamics of the formation, selection, and optical control of these patterns. An emphasis is placed on a previously proposed low-intensity, all-optical switching scheme designed to exploit these instability-driven patterns. Simulations and detailed analyses of simplified and more physically transparent models are used. Two aspects of the problem are studied in detail. First, we study the dependencies of the stability behaviors of various patterns, as well as transition time scales, on parameters relevant to the switching action. These parameters are the degree of built-in azimuthal anisotropy in the system and the switching (control) beam intensity. It is found that if the parameters are varied incrementally, the pattern system undergoes abrupt transitions at threshold parameter values, which are accompanied by multiple-stability and hysteresis behaviors. Moreover, during a real-time switching action, the transient dynamics of the system, in particular, the transition time scale, may depend significantly on the proximity of unstable patterns. The second aspect is a classification and detailed analysis of the polariton scattering processes contributing to the pattern dynamics, giving us an understanding of the selection and control of patterns as results of these processes' intricate interplay. The crucial role played by the (relative) phases of the polariton amplitudes in determining the gains and/or losses of polariton densities in various momentum modes is highlighted. As a result of this analysis, an interpretation of the actions of the various processes in terms of concepts commonly used in classical pattern-forming systems is given.

The precise adjustment of the polariton condensate flow under incoherent excitation conditions is an indispensable prerequisite for polariton-based logic gate operations. In this report, an all-optical approach for steering the motion of a polariton condensate using only nonresonant excitation is demonstrated. We create arbitrarily shaped functional potentials by means of a spatial light modulator, which allow for tailoring the condensate state and guiding a propagating condensate along reconfigurable pathways. Additional numerical simulations confirm the experimental observations and elucidate the interaction effects between background carriers and polariton condensates.

The optical spin Hall effect (OSHE) is a transport phenomenon of exciton polaritons in semiconductor microcavities, caused by the polaritonic spin-orbit interaction, that leads to the formation of spin textures. In the semiconductor cavity, the physical basis of the spin orbit coupling is an effective magnetic field caused by the splitting of transverse-electric and transverse-magnetic (TE-TM) modes. The spin textures can be observed in the near field (local spin distribution of polaritons), and as light polarization patterns in the more readily observable far field. For future applications in spinoptronic devices, a simple and robust control mechanism, which establishes a one-to-one correspondence between stationary incident light intensity and far-field polarization pattern, is needed. We present such a control scheme, which is made possible by a specific double-microcavity design.The detection and manipulation of spins is an important part of science, in areas ranging from quantum computing, information, and spintronics 1 , to ubiquitous medical imaging techniques such as Magnetic Resonance Imaging (MRI). Much of the functionality of spin effects rests on the ability to control the spin dynamics through the application of external optical and/or magnetic fields. For example, in MRI spatial gradients of external magnetic fields control the spin precession, and in electron or nuclear spin-based quantum computing logical operations are performed using spatially or time-varying electromagnetic fields (e.g. Ref.1,2 ). Major research efforts have focused on photonic counterparts to magnetic spin systems, including the plasmonic spin Hall effect 3 , and, importantly, wide-ranging investigations of the spin orbit interactions of light 4-8 . All-optical spin systems combine the benefits of magnetic spin systems and their (sometimes relatively simple) spin dynamics with the highly developed technology of optical preparation and detection of polarization states (the optical analogue of spin).A promising semiconductor system is a microcavity containing semiconductor quantum wells, where spin states of exciton-polaritons can be created optically and the TE-TM splitting yields a spin-orbit interaction that can be described by an effective magnetic field. This, in turn, gives rise to a polaritonic spin Hall effect, the so-called optical spin Hall effect (OSHE) 9-14 . Since polaritons with different in-plane wave vectors experience different effective magnetic fields, an isotropic distribution of polaritons on a ring in wave vector space can lead to an anisotropic polarization texture or pattern, both in real (configuration) and wave vector space.Such polarization/spin textures have been found for excitations of linearly and circularly polarized polaritons in Ref.10 and 14 , respectively (structurally similar polarization/spin textures are also present in different physical systems, e.g. 15,16 ). The OSHE in wave vector space corresponds to that seen experimentally in far-field observations, which are particularly important ...

Over the past decade, spontaneously emerging patterns in the density of polaritons in semiconductor microcavities were found to be a promising candidate for all-optical switching. But recent approaches were mostly restricted to scalar fields, did not benefit from the polariton's unique spin-dependent properties, and utilized switching based on hexagon far-field patterns with 60° beam switching (i.e. in the far field the beam propagation direction is switched by 60°). Since hexagon far-field patterns are challenging, we present here an approach for a linearly polarized spinor field, that allows for a transistor-like (e.g., crucial for cascadability) orthogonal beam switching, i.e. in the far field the beam is switched by 90°. We show that switching specifications such as amplification and speed can be adjusted using only optical means.