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The emergence of spatial coherence in a confined two-dimensional Bose gas of exciton-polaritons with tuneable interactions offers a unique opportunity to explore the role of interactions in a phase transition in a driven-dissipative quantum system, where both the phase transition and thermalisation are mediated by interactions. We investigate, experimentally and numerically, the phase correlations and steady-state properties of the gas over a wide range of interaction strengths by varying the photonic/excitonic fraction of the polaritons and their density. We find that the first order spatial coherence function exhibits algebraic decay consistent with the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Surprisingly, the exponent of the algebraic decay is inversely proportional to the coherent density of polaritons, in analogy to equilibrium superfluids above the BKT transition, but with a different proportionality constant. Our work paves the way for future investigations of the phenomenon of phase transitions and superfluidity in a driven-dissipative setting, Comment: 11 pages, 6 figures

Dispersion engineering is a powerful and versatile tool that can vary the speed of light signals and induce negative-mass effects in the dynamics of particles and quasiparticles. Here, we show that dissipative coupling between bound electron-hole pairs (excitons) and photons in an optical microcavity can lead to the formation of exciton polaritons with an inverted dispersion of the lower polariton branch and hence a negative mass. We perform direct measurements of the anomalous dispersion in atomically thin (monolayer) WS$_2$ crystals embedded in planar microcavities and demonstrate that the propagation direction of the negative-mass polaritons is opposite to their momentum. Our study introduces a new concept of non-Hermitian dispersion engineering for exciton polaritons and opens a pathway for realising new phases of quantum matter in a solid state., Comment: 16 pages, 13 figures

Exciton-polaritons (polaritons herein) in transition-metal dichalcogenide monolayers have attracted significant attention due to their potential for polariton-based optoelectronics. Many of the proposed applications rely on the ability to trap polaritons and to reach macroscopic occupation of their ground energy state. Here, we engineer a trap for room-temperature polaritons in an all-dielectric optical microcavity by locally increasing the interactions between the WS$_2$ excitons and cavity photons. The resulting confinement enhances the population and the first-order coherence of the polaritons in the ground state, with the latter effect related to dramatic suppression of disorder-induced inhomogeneous dephasing. We also demonstrate efficient population transfer into the trap when optically injecting free polaritons outside of its periphery., Comment: 5 pages, 5 figures

Floquet engineering offers a path to optically-controlled materials, but experimental implementations have frequently relied on femtosecond pulses to achieve the high peak fields required to maximise interactions and obtain a measurable response. The Floquet formalism, however, is based on a continuous, periodic drive. Here we use femtosecond laser pulses to drive the optical Stark effect, a simple realization of Floquet engineering, in monolayer WS2. By monitoring the coherent evolution of the free-induction decay, we show that the system evolves adiabatically, and that the finite duration of the pulses does not introduce any effects beyond Floquet theory. Furthermore, we demonstrate that the induced energy shift follows a linear dependence on instantaneous intensity, even for ultrafast driving fields of fewer than 15 optical cycles.

Atomically-thin transition metal dichalcogenide crystals (TMDCs) hold great promise for future semiconductor optoelectronics due to their unique electronic and optical properties. In particular, electron-hole pairs (excitons) in TMDCs are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, the excitons can hybridise with cavity photons to form exciton polaritons (polaritons herein), which display both ultrafast velocities and strong interactions. The ability to manipulate and trap polaritons on a microchip is critical for future applications. Here, we create a potential landscape for room-temperature polaritons in monolayer WS$_2$, and demonstrate their free propagation and trapping. We show that the effect of dielectric disorder, which restricts the diffusion of WS$_2$ excitons and broadens their spectral resonance, is dramatically reduced in the strong exciton-photon coupling regime leading to motional narrowing. This enables the ballistic transport of WS$_2$ polaritons across tens of micrometers with an extended range of partial first-order coherence. Moreover, the dephasing of trapped polaritons is dramatically suppressed compared to both WS$_2$ excitons and free polaritons. Our results demonstrate the possibility of long-range transport and efficient trapping of TMDC polaritons in ambient conditions., Comment: 8 pages, 4 figures

Topological insulators are a class of electronic materials exhibiting robust edge states immune to perturbations and disorder. This concept has been successfully adapted in photonics, where topologically nontrivial waveguides and topological lasers were developed. However, the exploration of topological properties in a given photonic system is limited to a fabricated sample, without the flexibility to reconfigure the structure in-situ. Here, we demonstrate an all-optical realization of the orbital Su-Schrieffer-Heeger (SSH) model in a microcavity exciton-polariton system, whereby a cavity photon is hybridized with an exciton in a GaAs quantum well. We induce a zigzag potential for exciton polaritons all-optically, by shaping the nonresonant laser excitation, and measure directly the eigenspectrum and topological edge states of a polariton lattice in a nonlinear regime of bosonic condensation. Furthermore, taking advantage of the tunability of the optically induced lattice we modify the intersite tunneling to realize a topological phase transition to a trivial state. Our results open the way to study topological phase transitions on-demand in fully reconfigurable hybrid photonic systems that do not require sophisticated sample engineering., Comment: 7 pages, 4 figures

Collective (elementary) excitations of quantum bosonic condensates, including condensates of exciton polaritons in semiconductor microcavities, are a sensitive probe of interparticle interactions. In anisotropic microcavities with momentum-dependent TE-TM splitting of the optical modes, the excitations dispersions are predicted to be strongly anisotropic, which is a consequence of the synthetic magnetic gauge field of the cavity, as well as the interplay between different interaction strengths for polaritons in the singlet and triplet spin configurations. Here, by directly measuring the dispersion of the collective excitations in a high-density optically trapped exciton-polariton condensate, we observe excellent agreement with the theoretical predictions for spinor polariton excitations. We extract the inter- and intra-spin polariton interaction constants and map out the characteristic spin textures in an interacting spinor condensate of exciton polaritons.

We report the observation of low-energy, low-momenta collective oscillations of an excitonpolariton condensate in a round "box" trap. The oscillations are dominated by the dipole and breathing modes, and the ratio of the frequencies of the two modes is consistent with that of a weakly interacting two-dimensional trapped Bose gas. The speed of sound extracted from the dipole oscillation frequency is smaller than the Bogoliubov sound, which can be partly explained by the influence of the incoherent reservoir. These results pave the way for understanding the effects of reservoir, dissipation, energy relaxation, and finite temperature on the superfluid properties of exciton-polariton condensates and other two-dimensional open-dissipative quantum fluids., Comment: 13 pages, 15 figures

Optical trapping and manipulation of microcavity exciton polaritons rely on effective potentials induced by the interaction of polaritons with a reservoir of high energy excitonic particles injected by an off-resonant optical pump. Here, we experimentally investigate possible mechanisms responsible for reshaping of these effective potentials in the low-density exciton-polariton regime. We infer the spatial distribution of the reservoir from the spatially resolved energy of exciton-polariton emission measured at zero momentum (zero kinetic energy). Power-dependent shape analysis of the potential barrier induced by a focused continuous wave laser pump shows a monotonic decrease of the barrier width with increasing excitation power, which is attributed to the local heating of the sample at the pump spot. In addition, we observe the significant influence of the reservoir on the zero-momentum emission tens of micrometers away from the laser pump spot, which is in line with the previously reported enhanced transport of high-momentum excitonic polaritons from the bottleneck region. Our work presents evidence for a complex spatial reshaping of the reservoir with the pump power, contrary to the common assumption of a static reservoir distribution fixed by the intensity profile of the pump., Comment: There was a substantial error in the analysis of the experimental data presented in the paper. The figures as well as the conclusions of the manuscript are incorrect and should not be cited

Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an optically-induced "box" trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behaviour is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a non-equilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir., Comment: 11 pages, 5 figures

Exciton-polaritons (polaritons herein) offer a unique nonlinear platform for studies of collective macroscopic quantum phenomena in a solid state system. Shaping of polariton flow and polariton confinement via potential landscapes created by nonresonant optical pumping has gained considerable attention due to the degree of flexibility and control offered by optically-induced potentials. Recently, large density-dependent energy shifts (blueshifts) exhibited by optically trapped polaritons at low densities, below the bosonic condensation threshold, were interpreted as an evidence of strong polariton-polariton interactions [Nat. Phys. 13, 870 (2017)]. In this work, we further investigate the origins of these blueshifts in optically-induced circular traps and present evidence of significant blueshift of the polariton energy due to reshaping of the optically-induced potential with laser pump power. Our work demonstrates strong influence of the effective potential formed by an optically-injected excitonic reservoir on the energy blueshifts observed below and up to the polariton condensation threshold and suggests that the observed blueshifts arise due to interaction of polaritons with the excitonic reservoir, rather than due to polariton-polariton interaction., Comment: 10 pages, 8 figures

We demonstrate, experimentally and theoretically, controlled loading of an exciton-polariton vortex chain into a 1D array of trapping potentials. Switching between two types of vortex chains, with topological charges of the same or alternating sign, is realised by means of appropriate shaping of an incoherent pump beam that drives the system to the regime of bosonic condensation. In analogy to spin chains, these vortex sequences realise either a "ferromagnetic" or an "anti-ferromagnetic" order, whereby the role of spin is played by the orbital angular momentum. The "ferromagnetic" ordering of vortices is associated with the formation of a persistent chiral current. Our results pave the way for controlled creation of nontrivial distributions of orbital angular momentum and topological order in a periodic exciton-polariton system., Comment: 5 pages, 4 figures

We develop a simple yet powerful technique to study Bogoliubov-Cherenkov radiation by producing a pulsed atom laser from a strongly confined Bose-Einstein condensate. Such radiation results when the atom laser pulse falls past a Bose-Einstein condensate at high-hypersonic speeds, modifying the spatial profile to display a characteristic twin jet structure and a complicated interference pattern. The experimental observations are in excellent agreement with mean-field numerical simulations and an analytic theory. Due to the highly hypersonic regime reached in our experiment, this system offers a highly controllable platform for future studies of condensed-matter analogs of quantum electrodynamics at ultrarelativistic speeds., Comment: 14 pages 9 figures. v4 changes: \v{C}herenkov changed to Cherenkov

We demonstrate generation of chiral modes -- vortex flows with fixed handedness in exciton-polariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically-induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system's parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). Our method can be extended to generate high-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies, which could find application in integrated optoelectronics., Comment: 6 pages, 6 figures

Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system., Comment: 18 pages, 5 figures

Diabolical points (degeneracies) can naturally occur in spectra of two-dimensional quantum systems and classical wave resonators due to simple symmetries. Geometric Berry phase is associated with these spectral degeneracies. Here, we demonstrate a diabolical point and the corresponding Berry phase in the spectrum of hybrid light-matter quasiparticles -- exciton-polaritons in semiconductor microcavities. It is well known that sufficiently strong optical pumping can drive exciton-polaritons to quantum degeneracy, whereby they form a macroscopically populated quantum coherent state similar to a Bose-Einstein condensate. By pumping a microcavity with a spatially structured light, we create a two-dimensional quantum billiard for the exciton-polariton condensate and demonstrate a diabolical point in the spectrum of the billiard eigenstates. The fully reconfigurable geometry of the potential walls controlled by the optical pump enables a striking experimental visualisation of the Berry phase associated with the diabolical point. The Berry phase is observed and measured by direct imaging of the macroscopic exciton-polariton wavefunctions., Comment: 7 pages, 4 figures

We demonstrate, experimentally and theoretically, a Talbot effect for hybrid light-matter waves -- exciton-polariton condensate formed in a semiconductor microcavity with embedded quantum wells. The characteristic 'Talbot carpet' is produced by loading the exciton-polariton condensate into a microstructured one dimensional periodic array of mesa traps, which creates an array of sources for coherent polariton flow in the plane of the quantum wells. The spatial distribution of the Talbot fringes outside the mesas mimics the near-field diffraction of a monochromatic wave on a periodic amplitude and phase grating with the grating period comparable to the wavelength. Despite the lossy nature of the polariton system, the Talbot pattern persists for distances exceeding the size of the mesas by an order of magnitude., Comment: 6 pages, 3 figures

Exciton-polaritons in semiconductor microcavities have advanced to become a model system for studying dynamical Bose-Einstein condensation, macroscopic coherence, many-body effects, nonclassical states of light and matter, and possibly quantum phase transitions in a solid state. Being low mass bosons, these light-matter quasiparticles can condense at comparably high temperatures up to 300K, while preserving fundamental properties such as coherence in space and time domain even when they are out of equilibrium with the environment. Although the presence of an in-plane polariton confinement potential is not strictly necessary in order to observe condensation of polaritons, engineering the polariton confinement is a key to controlling, shaping and directing the flow of polaritons. Prototype polariton-based optoelectronic devices rely on ultrafast photon-like velocities and strong nonlinearities, as well as on tailored confinement. Nanotechnology provides several pathways to achieving such a confinement, and the specific features and advantages of the different techniques are discussed in this paper. As hybrid exciton-photon quasiparticles, polaritons can be trapped via their excitonic as well as their photonic component, which leads to a wide choice of highly complementary techniques. Here we highlight the almost free choice of trapping geometries and depths of confinement that provides a powerful tool for control and manipulation of polariton systems both in semi-classical and quantum domain. Furthermore, the possibility to observe effects of polariton blockade, Mott insulator physics, and population of higher-order bands in sophisticated lattice potentials is discussed. The observation of such effects will signify the opportunity for the realization of novel polaritonic non-classical light sources and quantum simulators.

We study the loading of a nonequilibrium, dissipative system of composite bosons -- exciton polaritons -- into a one dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and confirm that polariton-phonon scattering is a key energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.

We study, theoretically and numerically, the onset and development of modulational instability in an incoherently pumped spatially homogeneous polariton condensate. Within the framework of mean-field theory, we identify regimes of modulational instability in two cases: 1) Strong feedback between the condensate and reservoir, which may occur in scalar condensates, and 2) Parametric scattering in the presence of polarization splitting in spinor condensates. In both cases we investigate the instability induced textures in space and time including non-equilibrium dynamics of phase dislocations and vortices. In particular we discuss the mechanism of vortex destabilization and formation of spiraling waves. We also identify the presence of topological defects, which take the form of half-vortex pairs in the spinor case, giving an "eyelet" structure in intensity and dipole type structure in the spin polarization. In the modulationally stable parameter domains, we observe formation of the phase defects in the process of condensate formation from an initially spatially incoherent low-density state. In analogy to the Kibble-Zurek type scaling for nonequilibrium phase transitions, we find that the defect density scales with the pumping rate., Comment: 13 pages, 9 figures, revised manuscript sent to Phys. Rev. B

Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (i.e., non-Hermitian) quantum system: it requires constant pumping of energy and continuously decays releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localisation, and dynamical properties. Using a spatially-structured optical pump, we create a chaotic exciton-polariton billiard. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies -- exceptional points. These are known to cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption, and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the nontrivial topological modal structure exclusive to non-Hermitian systems. We also observe the mode switching and topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way for studies of non-Hermitian quantum dynamics of exciton-polaritons, which can lead to novel functionalities of polariton-based devices., Comment: 8 pages, 4 figures

We investigate, theoretically and numerically, the spin dynamics of a two-component exciton-polariton condensate created and sustained by non-resonant spin-polarized optical pumping of a semiconductor microcavity. Using the open-dissipative mean-field model, we show that the existence of well defined phase-locked steady states of the condensate may lead to efficient switching and control of spin (polarization) states with a non-resonant excitation. Spatially inhomogeneous pulsed excitations can cause symmetry breaking in the pseudo-spin structure of the condensate and lead to formation of non-trivial spin textures. Our model is universally applicable to two weakly coupled polariton condensates, and therefore can also describe the behaviour of condensate populations and phases in 'double-well' type potentials.

Motivated by the recent experiment [Wright et al., Phys. Rev. A 88, 063633 (2013)], we investigate formation of vortices in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean field model, we study the dissipative dynamics of the condensate with parameters matched to the experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of the vortex excitations in the stirred toroidal condensate and compare our results with the experimental observations., Comment: 7 pages 5 figures

We consider a quantum well embedded in a zero-dimensional microcavity with a sub-wavelength grated mirror, where the x-linearly polarized exciton mode is strongly coupled to the cavity photon, while y-polarized excitons remain in the weak coupling regime. Under incoherent optical or electric pumping, we demonstrate polariton bistability associated with parametric scattering processes. Such bistability is useful for constructing polaritonic devices with optical or electrical incoherent pumping., Comment: 5 pages, 3 figures

We study formation and stabilization of vortex rings in atomic Bose-Einstein condensates. We suggest a novel approach for generating and trapping of vortex rings by 'optical tweezers'--two blue-detuned optical beams forming a toroidal void in the bulk of a magnetically or optically confined condensate cloud. We demonstrate that matter-wave vortex rings trapped within the void are energetically and dynamically stable. Our theoretical findings suggest the possibility for generation, stabilization, and nondestructive manipulation of quantized vortex rings in experimentally feasible trapping configurations., Comment: 5 pages, 5 figures

We predict the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic in-plane potentials. Our theory shows that, under the condition of continuous off-resonant pumping and losses associated with polariton decay, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We reveal that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the applied potential, in sharp contrast to the conservative condensates of ultracold alkali atoms., Comment: 5 pages, 5 figures

We present a general theory of spin-to-orbital angular momentum (AM) conversion of light in focusing, scattering, and imaging optical systems. Our theory employs universal geometric transformations of nonparaxial optical fields in such systems and allows for direct calculation and comparison of the AM conversion efficiency in different physical settings. Observations of the AM conversions using local intensity distributions and far-field polarimetric measurements are discussed., Comment: 17 pages, 8 figures

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally., Comment: 8 pages, 3 figures

We show, both theoretically and experimentally, that high-numerical-aperture (NA) optical microscopy is accompanied by strong spin-orbit interaction of light, which translates fine infomation about the specimen to the polarization degrees of freedom of light. An 80nm gold nano-particle scattering the light in the focus of a high-NA objective generates angular momentum conversion which is seen as a non-uniform polarization distribution at the exit pupil. We demonstrate remarkable sensitivity of the effect to the position of the nano-particle: Its subwavelength displacement produces the giant spin-Hall effect, i.e., macro-separation of spins in the outgoing light. This brings forth a far-field optical nanoprobing technique based on the spin-orbit interaction of light., Comment: 4 pages, 4 figures, to appear in Phys. Rev. Lett.

We study the macroscopic quantum self-trapping effect in a mixture of Bose-Einstein condensate and a large number of quantum degenerate fermions, trapped in a double-well potential with a variable separation between the wells. The large number of fermions localized in each well form quasi-static impurities that affect the dynamics of the bosonic cloud. Our semi-analytical analysis based on a mean-field model shows that main features of macroscopic quantum self trapping in a pure bosonic system are radically modified by the influence of fermions, with both the onset of self-trapping and properties of the self-trapped state depending on the fermion concentration as well as on the type of inter-species interaction. Remarkably, repulsive inter-species interaction leads to population inversion of the bosonic energy levels in the trapping potential and hence to the inversion of symmetry of the macroscopic wavefunction. Realistic physical estimates are given based on experimental parameters for a $^{40}$K-$^{87}$Rb system., Comment: 8 pages, 8 figures, submitted to PRA

We present a model of a cw atom laser based on a system of coupled GP equations. The model incorporates continuous Raman outcoupling, pumping and three-body recombination. The outcoupled field has minimal atomic density fluctuations and is locally monochromatic., Comment: 10 pages, 8 eps figures, typos fixed