Self-localization of polariton condensates in periodic potentials

Localized gap modes of coherently trapped atoms in an optical lattice

We theoretically investigate one-dimensional localized gap modes in a coherent atomic gas where an optical lattice is formed by a pair of counterpropagating far-detuned Stark laser fields. The atomic ensembles under study emerge as Λ-type three-level configuration accompanying the effect of electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations and the multiple scales method, we derive a nonlinear equation governing the spatial-temporal evolution of the probe-field envelope. We then uncover the formation and properties of optical localized gap modes of two kinds, such as the fundamental gap solitons and dipole gap modes. Furthermore, we confirm the (in)stability regions of both localized gap modes in the respective band-gap spectrum with systematic numerical simulations relying on linear-stability analysis and direct perturbed propagation. The predicted results may enrich the nonlinear horizon to the realm of coherent atomic gases and open up a new door for optical communication and information processing.

Room temperature organic exciton-polariton condensate in a lattice

Interacting Bosons in artificial lattices have emerged as a modern platform to explore collective manybody phenomena and exotic phases of matter as well as to enable advanced on-chip simulators. On chip, exciton–polaritons emerged as a promising system to implement and study bosonic non-linear systems in lattices, demanding cryogenic temperatures. We discuss an experiment conducted on a polaritonic lattice at ambient conditions: We utilize fluorescent proteins providing ultra-stable Frenkel excitons. Their soft nature allows for mechanically shaping them in the photonic lattice. We demonstrate controlled loading of the coherent condensate in distinct orbital lattice modes of different symmetries. Finally, we explore the self-localization of the condensate in a gap-state, driven by the interplay of effective interaction and negative effective mass in our lattice. We believe that this work establishes organic polaritons as a serious contender to the well-established GaAs platform for a wide range of applications relying on coherent Bosons in lattices.

Many studies of polariton condensates have been limited to low temperatures. Here the authors demonstrate ambient polariton condensation in lattices using organic traps that profit from the stability of organic excitons and the large Rabi splitting.

Polariton surface solitons under a resonant pump

We address the formation of stable dissipative surface solitons in the exciton-polariton condensate in a one-dimensional array of microcavity pillars under the action of a localized resonant pump acting in the edge resonator. We show that the localization degree and peak amplitudes of surface solitons can be effectively controlled by the pump frequency and that the allowed energy gap of the periodic structure determines the energy range, where surface solitons can form. One observes bistability at sufficiently large pump amplitudes and a nonlinearity-induced shift of the position of the resonance peak from the allowed energy band of the periodic array into its forbidden energy gap. The growth of the spatial period of the array reduces coupling between pillars and currents from a surface pillar into bulk pillars which leads to the increase of the surface soliton amplitude. Strong expansion into the depth of the array occurs for pump frequencies corresponding to the middle of the allowed energy band. Surface solitons can be excited from the broadband Gaussian noise. Above certain threshold noise levels, solitons from a stable upper branch of the bistability curve are excited while, below threshold, solitons from the lower branch form.

Two-Dimensional Vortex Solitons in Spin-Orbit-Coupled Dipolar Bose–Einstein Condensates

Solitons are self-trapped modes existing in various nonlinear systems. Creating stable solitons in two- and three-dimensional settings is a challenging goal in various branches of physics. Several methods have been developed theoretically and experimentally to achieve this, but few of them can support stable multi-dimensional solitons in free space. Recently, a new scheme using spin-orbit-coupling (SOC) has been proposed to create stable 2D solitons in Bose–Einstein condensates (BECs). This paper reviews recent theoretical progress on creating stable 2D solitons in spinor dipolar BEC with SOC, combined with long-range dipole-dipole interaction (DDI), Zeeman splitting (ZS) and contact nonlinearity, in free space. The continuous family of stable symmetric vortex solitons (SVS), asymmetric vortex solitons (AVS), as well as gap solitons (GS) is found via different settings. Their existence and stability conditions are summarized and discussed in detail. The mobility properties of these types of solitons are also addressed. For SVS, a potential method to manipulate its shape and mobility is investigated. These results are supposed to enrich our understanding of 2D solitons and help create multi-dimensional solitons in experiments.

Bistable Topological Insulator with Exciton-Polaritons

The functionality of many nonlinear and quantum optical devices relies on the effect of optical bistability. Using microcavity exciton-polaritons in a honeycomb arrangement of microcavity pillars, we report the resonance response and bistability of topological edge states. A balance between the pump, loss, and nonlinearity ensures a broad range of dynamical stability and controls the distribution of power between counterpropagating states on the opposite edges of the honeycomb lattice stripe. Tuning energy and polarization of the pump photons, while keeping their momentum constant, we demonstrate control of the propagation direction of the dominant edge state. Our results facilitate the development of practical applications of topological photonics.

Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator - material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes - topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

Multivalley engineering in semiconductor microcavities

We consider exciton-photon coupling in semiconductor microcavities in which separate periodic potentials have been embedded for excitons and photons. We show theoretically that this system supports degenerate ground-states appearing at non-zero inplane momenta, corresponding to multiple valleys in reciprocal space, which are further separated in polarization corresponding to a polarization-valley coupling in the system. Aside forming a basis for valleytronics, the multivalley dispersion is predicted to allow for spontaneous momentum symmetry breaking and two-mode squeezing under non-resonant and resonant excitation, respectively.

Exciton-polariton trapping and potential landscape engineering

Exciton-polaritons in semiconductor microcavities have become a model system for the studies of dynamical Bose-Einstein condensation, macroscopic coherence, many-body effects, nonclassical states of light and matter, and possibly quantum phase transitions in a solid state. These low-mass bosonic quasiparticles can condense at comparatively high temperatures up to 300 K, and preserve the fundamental properties of the condensate, such as coherence in space and time domain, even when they are out of equilibrium with the environment. Although the presence of a confining potential is not strictly necessary in order to observe Bose-Einstein condensation, engineering of 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 exhibited by polaritons, as well as on their tailored confinement. Nanotechnology provides several pathways to achieving polariton confinement, and the specific features and advantages of different methods are discussed in this review. Being hybrid exciton-photon quasiparticles, polaritons can be trapped via their excitonic as well as photonic component, which leads to a wide choice of highly complementary trapping techniques. Here, we highlight the almost free choice of the confinement strengths and trapping geometries that provide powerful means for control and manipulation of the polariton systems both in the semi-classical and quantum regimes. Furthermore, the possibilities to observe effects of the polariton blockade, Mott insulator physics, and population of higher-order energy bands in sophisticated lattice potentials are discussed. Observation of such effects could lead to realization of novel polaritonic non-classical light sources and quantum simulators.

Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling

We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to the repulsive excitonic nonlinearity, such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from the TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in the formation of four distinct families of vortex solitons with topological charges m=±1, all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by the domination of different polarization components are encountered.

Talbot Effect for Exciton Polaritons

We demonstrate, experimentally and theoretically, a Talbot effect for hybrid light-matter waves-an 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 phase-locked 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. Thus, our experiment demonstrates efficient shaping of the two-dimensional flow of coherent exciton polaritons by a one-dimensional "flat lens."

Anderson attractors in active arrays

In dissipationless linear media, spatial disorder induces Anderson localization of matter, light, and sound waves. The addition of nonlinearity causes interaction between the eigenmodes, which results in a slow wave diffusion. We go beyond the dissipationless limit of Anderson arrays and consider nonlinear disordered systems that are subjected to the dissipative losses and energy pumping. We show that the Anderson modes of the disordered Ginsburg-Landau lattice possess specific excitation thresholds with respect to the pumping strength. When pumping is increased above the threshold for the band-edge modes, the lattice dynamics yields an attractor in the form of a stable multi-peak pattern. The Anderson attractor is the result of a joint action by the pumping-induced mode excitation, nonlinearity-induced mode interactions, and dissipative stabilization. The regimes of Anderson attractors can be potentially realized with polariton condensates lattices, active waveguide or cavity-QED arrays.

Spatial and temporal structures in cavities with oscillating boundaries

We review the general features of particles, waves and solitons in dynamical cavities formed by oscillating cavity mirrors. Considered are the dynamics of classical particles in one-dimensional geometry of a dynamical billiard, taking into account the non-elastic collisions of particles with mirrors, the (quasi-energy) states of a single quantum particle in a potential well with periodically oscillating wells, and nonlinear structures, including nonlinear Rabi oscillations, cavity optical solitons and solitons of Bose-Einstein condensates, in dynamical cavities or traps.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki-Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

Polaritonic solitons in a Bose-Einstein condensate trapped in a soft optical lattice

We investigate the ground state (GS) of a collisionless Bose-Einstein condensate (BEC) trapped in a soft one-dimensional optical lattice (OL), which is formed by two counterpropagating optical beams perturbed by the BEC density profile through the local-field effect (LFE). We show that LFE gives rise to an envelope-deformation potential, a nonlocal potential resulting from the phase deformation, and an effective self-interaction of the condensate. As a result, stable photon-atomic (polaritonic) lattice solitons, including an optical component, in the form of the deformation of the soft OL, in a combination with a localized matter-wave component, are generated in the blue-detuned setting, without any direct interaction between atoms. These self-trapped modes, which realize the system's GS, are essentially different from the gap solitons supported by the interplay of the OL potential and collisional interactions between atoms. A transition to tightly bound modes from loosely bound ones occurs with the increase of the number of atoms in the BEC.