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We report the formation of a ring-shaped array of vortices after injection of angular momentum in a polariton superfluid. The angular momentum is injected by a $\ell= 8$ Laguerre-Gauss beam, whereas the global rotation of the fluid is hindered by a narrow Gaussian beam placed at its center. In the linear regime a spiral interference pattern containing phase defects is visible. In the nonlinear (superfluid) regime, the interference disappears and the vortices nucleate as a consequence of the angular momentum quantization. The radial position of the vortices evolves freely in the region between the two pumps as a function of the density. Hydrodynamic instabilities resulting in the spontaneous nucleation of vortex-antivortex pairs when the system size is sufficiently large confirm that the vortices are not constrained by interference when nonlinearities dominate the system., Comment: 5 pages, 5 figures, submitted to PRL

We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band structure. Close to the Dirac point,we derive an effective Hamiltonian. We find that the local reduced symmetry ($\mathrm{D_{3h}}$) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect., Comment: 5 pages, 3 figures

In a recent preprint (arXiv:1401.1128v1) Cilibrizzi and co-workers report experiments and simulations showing the scattering of polaritons against a localised obstacle in a semiconductor microcavity. The authors observe in the linear excitation regime the formation of density and phase patterns reminiscent of those expected in the non-linear regime from the nucleation of dark solitons. Based on this observation, they conclude that previous theoretical and experimental reports on dark solitons in a polariton system should be revised. Here we comment why the results from Cilibrizzi et al. take place in a very different regime than previous investigations on dark soliton nucleation and do not reproduce all the signatures of its rich nonlinear phenomenology. First of all, Cilibrizzi et al. consider a particular type of radial excitation that strongly determines the observed patterns, while in previous reports the excitation has a plane-wave profile. Most importantly, the nonlinear relation between phase jump, soliton width and fluid velocity, and the existence of a critical velocity with the time-dependent formation of vortex-antivortex pairs are absent in the linear regime. In previous reports about dark soliton and half-dark soliton nucleation in a polariton fluid, the distinctive dark soliton physics is supported both by theory (analytical and numerical) and experiments (both continuous wave and pulsed excitation)., Comment: 4 pages, 2 figures

We investigate the spin dynamics of half-solitons in polariton Bose-Einstein condensates. Half-solitons, which behave as magnetic monopoles, can be accelerated in the presence of the effective magnetic field of the microcavity. We study the generation of DC magnetic currents in a gas of half-solitons. At low densities, the current is suppressed due to the dipolar oscillations. At moderate densities, a magnetic current is recovered as a consequence of the collisions between the carriers. We show a deviation from Ohm's law due to the competition between magnetic dipoles and monopoles.

We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite life time of the condensed particles and energy relaxation. The coupling between the reservoir and the condensate is described with semi-classical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyse the main properties of a condensate described by this hybrid Boltzmann Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first order coherence, dynamic and energetic stability, drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfils the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs it moves at a velocity smaller than the speed of excitations. First order spatial coherence of the condensate is found to decay exponentially in 1D and with a power law in 2D, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite life time of the condensate excitations. We compare these properties with the ones of a condensate described by the popular "diffusive" models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.

We show that the interplay between the structure anisotropy and the energy splitting between the TE and TM modes of a microcavity leads to the appearance of a gauge field for a propagating polariton condensate. This field is analog with a spin-orbit coupling and the field texture can be tuned by rotating the sample and ranges continuously from a Rashba to a monopolar field. In the linear regime, the monopolar field leads to a remarkable focusing effect. In the interacting regime, the effective spin-orbit coupling induces a breakdown of superfluidity. The spatially homogeneous flows become unstable and dynamically evolve into textured ground states such as stripes and domain walls., Comment: 5 pages, 5 figures (Phys. Rev. Lett., in press)

We report on a new mechanism of giant phase modulation. The phenomenon arises when a dispersed photonic mode (slow light) strongly couples to an excitonic resonance. In such a case, even a small amount of optically injected carriers creates a potential barrier for the propagating exciton-polariton which provokes a considerable phase shift. We evidence this effect by fabricating an exciton-polariton Mach-Zehnder interferometer, modulating the output intensity by constructive or destructive interferences controlled by optical pumping of a micrometric size area. The figure of merit for a {\pi} phase shift, defined by the control power times length of the modulated region, is found at least one order of magnitude smaller than slow light photonic crystal waveguides., Comment: 18 pages, 6 figures

We consider a spin-1/2 Bose-Einstein condensate prepared initially in a single spin projection. The two channels of excitations existing in such a system (namely density and spin waves) are discussed and we show how pure spin waves can be excited in the presence of local magnetic defects. We analyze the role played by spin excitations on the Landau superfluidity criterion and demonstrate the absence of absolute superfluidity for the antiferromagnetic condensate. In the ferromagnetic case, we identify two critical velocities for the breakdown of superfluidity., Comment: 5 pages, 3 figures

A textbook example of quantum mechanical effects is the coupling of two states through a tunnel barrier. In the case of macroscopic quantum states subject to interactions, the tunnel coupling gives rise to Josephson phenomena including Rabi oscillations, the a.c. and d.c. effects, or macroscopic self-trapping depending on whether tunnelling or interactions dominate. Non-linear Josephson physics, observed in superfluid helium and atomic condensates, has remained inaccessible in photonic systems due to the required effective photon-photon interactions. We report on the observation of non-linear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule etched in a semiconductor microcavity. By varying both the distance between the micropillars forming the molecule and the condensate density in each micropillar, we control the ratio of coupling to interaction energy. At low densities we observe coherent oscillations of particles tunnelling between the two micropillars. At high densities, interactions quench the transfer of particles inducing the macroscopic self-trapping of the condensate in one of the micropillars. The finite lifetime of polaritons results in a dynamical transition from self-trapping to oscillations with pi phase. Our results open the way to the experimental study of highly non-linear regimes in photonic systems, such as chaos or symmetry-breaking bifurcations.

We provide a theoretical description of the polarization pattern and phase singularities experimentally evidenced recently in a condensate of indirect excitons [H. High et al., Nature 483, 584-588 (2012)]. We show that the averaging of the electron and hole orbital motion leads to a comparable spin-orbit interaction for both type of carriers. We demonstrate that the interplay between a radial coherent flux of bright indirect excitons and the Dresselhaus spin-orbit interaction results in the formation of spin domains and of topological defects similar to Skyrmions. We reproduce qualitatively all the features of the experimental data and obtain polarization pattern as in the optical spin Hall effect despite the different symmetry of the spin-orbit interactions.

The optical spin-Hall effect results in the formation of an antisymmetric real space polarization pattern forming spin currents. In this paper, we show that the exciton-polariton parametric scattering allows us to reverse the sign of these currents. We describe the pulsed resonant excitation of a strongly coupled microcavity with a linearly polarized pump at normal incidence. The energy of the pulse is set to be close to the inflexion point of the polariton dispersion and the focusing in real space populates the reciprocal space on a ring. For pumping powers below the parametric scattering threshold, the propagation of the injected polaritons in the effective magnetic field induced by the TE and TM splitting produce the normal optical spin-Hall effect. Keeping the same input polarization but increasing the pump intensity, the parametric scattering towards an idler and a signal state is triggered on the whole elastic circle. The injected particles are scattered toward these states while propagating radially all over the plane, gaining a cross linear polarisation with respect to the pump during the nonlinear process. Eventually, the propagation of the polaritons in the effective field results in the optical spin Hall-effect, but this time with inverted polarization domains., Comment: 6 pages, 3 figures

The dynamics of propagating polariton condensates in one-dimensional microcavities is investigated through time resolved experiments. We find a strong increase in the condensate intensity when it travels through the non-resonantly excited area. This amplification is shown to come from bosonic stimulated relaxation of reservoir excitons into the polariton condensate, allowing for the repopulation of the condensate through non-resonant pumping. Thus, we experimentally demonstrate a polariton amplifier with a large band width, opening the way towards the transport of polaritons with high densities over macroscopic distances., Comment: 5 pages + Supplementary

We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves towards a Wigner crystal., Comment: 5 pages, 4 figures

We show that the polarization domains generated in the linear optical spin-Hall effect by the analog of spin-orbit interaction for exciton-polaritons are associated with the formation of a Skyrmion lattice. In the non-linear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the spin domains and in an abrupt transformation of the Skyrmions into half-solitons, associated with both the focalization of the spin currents and the emergence of a strongly anisotropic emission pattern., Comment: 5 Pages, 3 Figures

Monopoles are magnetic charges, point-like sources of magnetic field. Contrary to electric charges they are absent in Maxwell's equations and have never been observed as fundamental particles. Quantum fluids such as spinor Bose-Einstein condensates have been predicted to show monopoles in the form of excitations combining phase and spin topologies. Thanks to its unique spin structure and the direct optical control of the fluid wavefunction, an ideal system to experimentally explore this phenomenon is a condensate of exciton-polaritons in a semiconductor microcavity. We use this system to create half-solitons, non-linear excitations with mixed spin-phase geometry. By tracking their trajectory, we demonstrate that half-solitons behave as monopoles, magnetic charges accelerated along an effective magnetic field present in the microcavity. The field-induced spatial separation of half-solitons of opposite charges opens the way to the generation of magnetic currents in a quantum fluid., Comment: 19 pages, includes Supplmentary Information

The impact of a random disorder potential on the dynamical properties of Bose Einstein condensates is a very wide research field. In microcavities, these studies are even more crucial than in the condensates of cold atoms, since random disorder is naturally present in the semiconductor structures. In this chapter, we consider a stable condensate, defined by a chemical potential, propagating in a random disorder potential, like a liquid flowing through a capillary. We analyze the interplay between the kinetic energy, the localization energy, and the interaction between particles in 1D and 2D polariton condensates. The finite life time of polaritons is taken into account as well. In the first part, we remind the results of [G. Malpuech et al. Phys. Rev. Lett. 98, 206402 (2007).] where we considered the case of a static condensate. In that case, the condensate forms either a glassy insulating phase at low polariton density (strong localization), or a superfluid phase above the percolation threshold. We also show the calculation of the first order spatial coherence of the condensate versus the condensate density. In the second part, we consider the case of a propagating non-interacting condensate which is always localized because of Anderson localization. The localization length is calculated in the Born approximation. The impact of the finite polariton life time is taken into account as well. In the last section we consider the case of a propagating interacting condensate where the three regimes of strong localization, Anderson localization, and superfluid behavior are accessible. The localization length is calculated versus the system parameters. The localization length is strongly modified with respect to the non-interacting case. It is infinite in the superfluid regime whereas it is strongly reduced if the fluid flows with a supersonic velocity., Comment: chapter for a book "Exciton Polaritons in Microcavities: New Frontiers" by Springer (2012), the original publication is available at http://www.springerlink.com

Half-integer topological defects in polariton condensates can be regarded as magnetic charges, with respect to built-in effective magnetic fields present in microcavities. We show how an integer topological defect can be separated into a pair of half-integer ones, paving the way towards flows of magnetic charges: spin currents or magnetricity. We discuss the corresponding experimental implementation within microwires (with half-solitons) and planar microcavities (with half-vortices)., Comment: 18 Pages, 8 figures, submitted to New Journal of Physics (special issue)

We analyzed multimode Josephson junctions with exciton-polaritons (polaritonic Josephson junctions) when several coupling mechanisms of fundamental and excited states are present. The applied method is based on Keldysh-Green function formalism and takes into account polariton pseudospin. We found that mean value of circular polarization degree in intrinsic Josephson oscillations and microscopic quantum self-trapping follow an oscillator behavior whose renormalizes due to intermode interactions. The effect of an additional transfer of particles over junction barrier occurring in multimode approximation in combination with common Josephson tunneling is discussed in regime of dynamical separation of two polarizations., Comment: 12 pages, 4 figures

Until now, the generation of an excitonic reservoir in a cavity polariton system under quasi-resonant pumping has always been neglected. We show that in microcavities having a small Rabi splitting (typically GaAs cavities with a single quantum well), this reservoir can be efficiently populated by polariton-phonon scattering. We consider the influence of the exciton reservoir on the energy shifts of the resonantly pumped polariton modes. We show that the presence of this reservoir effectively reduces the spin anisotropy of the polariton-polariton interaction, in agreement with recent experimental measurements, where the multistability of cavity polaritons has been analyzed, Comment: 7 pages, 6 figures

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations.

We consider half-integer topological defects in a spinor Bose-Einstein condensate of exciton-polaritons. We show that they accelerate under the effect of an in-plane effective magnetic field, like regular electric charges in the electric field. The trajectories of these analogues of magnetic monopoles are derived analytically and checked by numerical simulations. We show that these "magnetic charges" propagate at large in-plane velocities and remain stable up to a critical magnetic field, thanks to the unique spin-anisotropy of polariton interactions., Comment: 4 pages, 4 figures

We propose a new system for the study of event horizons and black holes - a Bose-Einstein condensate of exciton-polaritons. Hawking radiation from a closed horizon in 2D is observed in numerical experiments. We simulate inter-Universe and intra-Universe wormholes capitalizing on the spinor nature of polariton condensates and on the spin dependence of polariton-polariton interactions., Comment: 4 pages, 4 figures

We analyse the interaction of exciton and exciton-polariton condensates in semiconductor microcavity with a coherent acoustic wave. An analytical solution for the dispersion of excitations of coupled condensate-phonon system is found in the approximation of k-independent interactions. Accounting for k-dependence results in a stronger modification of the dispersion, and even in the appearance of the "roton instability" region.

We propose two schemes of a novel spin-optronic device, optical analog of Datta and Das spin transistor for the electrons. The role of ferromagnetic contacts is played by one-dimensional polariton channels with strong TE-TM splitting. A symmetric 2D trap plays a role of the non-magnetic active region. The rotation of the polarization of the pulse in this region can be achieved either due to its interaction with a spatially confined polariton condensate created resonantly by a circular polarized laser, either due to the splitting between the two linear polarizations of the excitons, controlled electrically by use of metallic gate., Comment: 4 pages, submitted to Phys. Rev. B as brief report

We analyze theoretically the role of the exciton-phonon interactions in phenomena related to the Josephson effect between two spatially separated exciton and exciton-polariton condensates. We consider the role of the dephasing introduced by phonons in such phenomena as Josephson tunneling, self-trapping and spontaneous polarization separation. In the regime of cw pumping we find a remarkable bistability effect arising from exciton- exciton interactions as well as regimes of self- sustained regular and chaotic oscillations., Comment: 10 pages, Submitted to Phys. Rev. B

We investigate theoretically the optical properties of Nano-Wires (NWs) with cross sections having either discrete or cylindrical symmetry. The material forming the wire is birefringent, showing a different dielectric response in the plane and along the axis of the wire, which is typically the case for wires made of wurtzite materials, such as ZnO or GaN. We look for solutions of Maxwell`s equations having the proper symmetry. The dispersions and the linewidths versus angle of incident light for the modes having high momentum in the cross-section plane, so called whispering gallery modes, are calculated. We put a special emphasis on the case of hexagonal cross sections. The energy positions of the modes for a set of azimuthal quantum numbers are shown. We demonstrate the dependence of the energy splitting between TE and TM modes versus birefringence. The polarization conversion from TE to TM with increase of the axial wave vectoris discussed for both cylindrical and discrete symmetry., Comment: 9 pages, 10 figures

We propose the scheme of a novel spin-optronic device, optical analog of Datta and Das spin transistor for the electrons. The role of the ferromagnetic-nonmagnetic contact is played by a spatially confined cavity polariton BEC. The condensate is responsible for the appearance of effective magnetic field which rotates the spin state of a propagating pulse of polaritons allowing to tune the transmittivity of the device., Comment: 5 pages, 3 figures

We propose a new theoretical formalism which describes the Bose Einstein condensation of weakly interacting bosons with finite life time interacting with a thermal bath. We show that if a quasi-thermal distribution function of particles is achieved, the elementary excitations of the condensate show a linear spectrum characteristic of a superfluid, with a renormalized sound velocity with respect to the equilibrium case.

Bose Einstein condensation of exciton-polaritons has recently been reported in homogeneous structures only affected by random in-plane fluctuations. We have taken advantage of the ubiquitous defects in semiconductor microcavities to reveal the spontaneous dynamical condensation of polaritons in the quantised levels of a trap. We observe condensation in several quantized states, taking their snapshots in real and reciprocal space. We show also the effect of particle interactions for high occupations numbers, revealed by a change in the confined wave function toward the Thomas Fermi profile., Comment: 15 pages, 4 figures

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given., Comment: Theoretical paper on polariton-polariton scattering in planar microcavities. The new version contains a slightly modified abstract and a revised introduction. Typos have been corrected wherever spotted. 16 pages

We observe the build up of strong (~50%) spontaneous vector polarisation in emission from a GaN-based polariton laser excited by short optical pulses at room temperature. The Stokes vector of emitted light changes its orientation randomly from one excitation pulse to another, so that the time-integrated polarisation remains zero. This behaviour is completely different to any previous laser. We interpret this observation in terms of the spontaneous symmetry breaking in a Bose-Einstein condensate of exciton-polaritons.

We propose a novel spin-optronic device based on the interference of polaritonic waves traveling in opposite directions and gaining topological Berry phase. It is governed by the ratio of the TE-TM and Zeeman splittings, which can be used to control the output intensity. Because of the peculiar orientation of the TE-TM effective magnetic field for polaritons, there is no analogue of the Aharonov- Casher phase shift existing for electrons., Comment: 4 pages

The non-local dielectric response theory is extended to describe oblique reflection of light from quantum wells subjected to the magnetic field. This allows us to calculate the dispersion and polarization of the exciton-polariton modes in semiconductor microcavities in the presence of a magnetic field normal to the plane of the structure. We show that due to the interplay between the exciton Zeeman splitting and TE-TM splitting of the photon modes, four polariton dispersion branches are formed with a polarization gradually changing from circular in the exciton-like part to linear in the photon-like part of each branch. Faraday rotation in quantum microcavities is shown to be strongly enhanced as compared with the rotation in quantum wells., Comment: 19 pages, 5 figures

We show theoretically that entangled photon pairs can be produced on demand through the biexciton decay of a quantum dot strongly coupled to the modes of a photonic crystal. The strong coupling allows to tune the energy of the mixed exciton-photon (polariton) eigenmodes, and to overcome the natural splitting existing between the exciton states coupled with different linear polarizations of light. Polariton states are moreover well protected against dephasing due to their lifetime ten to hundred times shorter than that of a bare exciton. Our analysis shows that the scheme proposed can be achievable with the present technology.

This comment has been withdrawn by the authors due to crucial error., Comment: This comment has been withdrawn

We report the calculation of cavity exciton-polariton phase diagram which takes into account the presence of realistic structural disorder. Polaritons are modelled as weakly interacting two-dimensional bosons. We show that with increasing density polaritons first undergo a quasi-phase transition towards a Bose glass: the condensate is localized in at least one minimum of the disorder potential, depending on the value of the chemical potential of the polariton system. A further increase of the density leads to a percolation process of the polariton fluid which gives rise to a Kosterlitz-Thouless phase transition towards superfluidity. The spatial representation of the condensate wavefunction as well as the spectrum of elementary excitations are obtained from the solution of the Gross-Pitaevskii equation for all the phases., Comment: 4 pages, 3 figures

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., Comment: 4 pages, 3 figures

We present the general kinetic formalism for the description of spin and energy relaxation of the cavity polaritons in the framework of the Born-Markov approximation. All essential mechanisms of polaritons redistribution in reciprocal space together with final state bosonic stimulation are taken into account, from our point of view. The developed theory is applied to describe our experimental results on the polarization dynamics obtained in the polariton parametric amplifier geometry (pumping at so-called magic angle). We have experimentally confirmed that the anisotropy of the polariton-polariton interaction is responsible for the build up of the cross-linear polarisation of the signal. The long-living linear polarization is observed at zero detuning. Under elliptical pumping, we have directly measured in the time domain and modelled the effect of self-induced Larmor precession., Comment: 21 pages, 4 figures, accepted to Semiconductors

We report a strong experimental evidence of the optical anisotropy in a CdTe-based microcavity: the polarization of light is pinned to one of the crystallographic axes independently on the polarization of the excitation. The polarization degree depends strongly on the excitation power, reaching almost 100 % in the stimulated regime. The relaxation time of the polarization is about 1 ns. We argue that all this is an effect of a splitting of the polariton doublet at k=0. We consider different sources for the splitting and conclude that the most likely one is optical birefringence in the mirrors and/or the cavity., Comment: 15 pages, 2 figures, accepted in Solid State Communications

A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wavefunction and it is shown how this operator evolves from purely fermionic, in case of a small QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively., Comment: Extensively expanded revision, 14 pages, 12 figures, submitted to Phys. Rev. B

It is shown theoretically that Bose condensation of spin-degenerated exciton-polaritons results in spontaneous buildup of the linear polarization in emission spectra of semiconductor microcavities. The linear polarization degree is a good order parameter for the polariton Bose condensation. If spin-degeneracy is lifted, an elliptically polarized light is emitted by the polariton condensate. The main axis of the ellipse rotates in time due to self-induced Larmor precession of the polariton condensate pseudospin. The polarization decay time is governed by the dephasing induced by the polariton-polariton interaction and strongly depends on the statistics of the condensed state., Comment: 11 pages, 1 figure