Spin Textures of Exciton-Polaritons in a Tunable Microcavity with Large TE-TM Splitting

Strong light-matter coupling in van der Waals materials

In recent years, two-dimensional (2D) van der Waals materials have emerged as a focal point in materials research, drawing increasing attention due to their potential for isolating and synergistically combining diverse atomic layers. Atomically thin transition metal dichalcogenides (TMDs) are one of the most alluring van der Waals materials owing to their exceptional electronic and optical properties. The tightly bound excitons with giant oscillator strength render TMDs an ideal platform to investigate strong light-matter coupling when they are integrated with optical cavities, providing a wide range of possibilities for exploring novel polaritonic physics and devices. In this review, we focused on recent advances in TMD-based strong light-matter coupling. In the foremost position, we discuss the various optical structures strongly coupled to TMD materials, such as Fabry-Perot cavities, photonic crystals, and plasmonic nanocavities. We then present several intriguing properties and relevant device applications of TMD polaritons. In the end, we delineate promising future directions for the study of strong light-matter coupling in van der Waals materials.

Non-Abelian physics in light and sound

Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.

Photochemical Reaction Enabling the Engineering of Photonic Spin-Orbit Coupling in Organic-Crystal Optical Microcavities

The control and active manipulation of spin-orbit coupling (SOC) in photonic systems are fundamental in the development of modern spin optics and topological photonic devices. Here, we demonstrate the control of an artificial Rashba-Dresselhaus (RD) SOC mediated by photochemical reactions in a microcavity filled with an organic single crystal of photochromic phase-change character. Splitting of the circular polarization components of the optical modes induced by photonic RD SOC is observed experimentally in momentum space. By applying an ultraviolet light beam, we control the spatial molecular orientation through a photochemical reaction, and with that we control the energies of the photonic modes. This way, we realize a reversible conversion of spin splitting of the optical modes with different energies, leading to an optically controlled switching between circularly and linearly polarized optical modes in our device. Our strategy of in situ and reversible engineering of SOC induced by a light field provides a promising approach to actively design and manipulate synthetic gauge fields toward future on-chip integration in photonics and topological photonic devices.

Spin-orbit Rabi oscillations in optically synthesized magnetic fields

Rabi oscillation has been proven to be one of the cornerstones of quantum mechanics, triggering substantial investigations in different disciplines and various important applications both in the classical and quantum regimes. So far, two independent classes of wave states in the Rabi oscillations have been revealed as spin waves and orbital waves, while a Rabi wave state simultaneously merging the spin and orbital angular momentum has remained elusive. Here we report on the experimental and theoretical observation and control of spin-orbit-coupled Rabi oscillations in the higher-order regime of light. We constitute a pseudo spin-1/2 formalism and optically synthesize a magnetization vector through light-crystal interaction. We observe simultaneous oscillations of these ingredients in weak and strong coupling regimes, which are effectively controlled by a beam-dependent synthetic magnetic field. We introduce an electrically tunable platform, allowing fine control of transition between different oscillatory modes, resulting in an emission of orbital-angular-momentum beams with tunable topological structures. Our results constitute a general framework to explore spin-orbit couplings in the higher-order regime, offering routes to manipulating the spin and orbital angular momentum in three and four dimensions. The close analogy with the Pauli equation in quantum mechanics, nonlinear optics, etc., implies that the demonstrated concept can be readily generalized to different disciplines.

Full characterization of vector eigenstates in symmetrically confined systems with photonic spin-orbit coupling

The photonic spin-orbit (SO) coupling is a widely investigated effect in optical microcavities leading to various interesting physical phenomena and potential applications. We report the full sets of eigenenergies and eigenstates in a symmetrically confined potential under the effect of SO coupling induced by the transverse-electric transverse-magnetic (TE-TM) splitting, which are derived analytically via the degenerate perturbation theory. We obtained the eigenenergies and the eigenstates from the 1st to the 6th orders of excited manifold, and demonstrate unambiguously that universal rules governing the mode formation exist in such complicated photonic systems, making the modes exhibiting the features of solid and hollow skyrmions as well as spin vortices. We show that these eigenstates can be described by the SO coupled hyperspheres that can be decomposed into a series of higher-order Poincare spheres. Our results significantly extend the area of microcavity spin-optronics to the general theory of eigenvalues in confined systems, and provide an efficient theoretical frame for the information processing using microcavity-based high-dimensional vector states.

Elimination of Chirality in Three-Dimensionally Confined Open-Access Microcavities

The emergent optical activity (OA) caused by anisotropic light emitter in microcavities is an important physical mechanism discovered recently, which leads to Rashba-Dresselhaus photonic spin-orbit (SO) coupling. In this study, we report a sharp contrast of the roles of the emergent OA in free and confined cavity photons, by observing the optical chirality in a planar-planar microcavity and its elimination in a concave-planar microcavity, evidenced by polarization-resolved white-light spectroscopy, which agrees well with the theoretical predictions based on the degenerate perturbation theory. Moreover, we theoretically predict that a slight phase gradient in real space can partially restore the effect of the emergent OA in confined cavity photons. The results are significant additions to the field of cavity spinoptronics and provide a novel method for manipulating photonic SO coupling in confined optical systems.

Circularly Polarized Lasing from a Microcavity Filled with Achiral Single-Crystalline Microribbons

Organic circularly polarized (CP) lasers have received increasing attention due to their future photoelectric applications. Here, we demonstrate a CP laser from a pure organic crystal-filled microcavity without any chiral molecules or chiral structures. Benefited from the giant anisotropy and excellent laser gain of organic crystals, optical Rashba-Dresselhaus spin-orbit coupling effect can be induced and is conductive to the CP laser in such microcavities. The maximum dissymmetry factor of the CP lasing with opposite helicities reachs 1.2. Our strategy may provide a new idea for the design of CP lasers towards future 3D laser displays, information storage and other fields.

Circularly polarized electroluminescence from a single-crystal organic microcavity light-emitting diode based on photonic spin-orbit interactions

Circularly polarized (CP) electroluminescence from organic light-emitting diodes (OLEDs) has aroused considerable attention for their potential in future display and photonic technologies. The development of CP-OLEDs relies largely on chiral-emitters, which not only remain rare owing to difficulties in design and synthesis but also limit the performance of electroluminescence. When the polarization (pseudospin) degrees of freedom of a photon interact with its orbital angular momentum, photonic spin-orbit interaction (SOI) emerges such as Rashba-Dresselhaus (RD) effect. Here, we demonstrate a chiral-emitter-free microcavity CP-OLED with a high dissymmetry factor (g_EL) and high luminance by embedding a thin two-dimensional organic single crystal (2D-OSC) between two silver layers which serve as two metallic mirrors forming a microcavity and meanwhile also as two electrodes in an OLED architecture. In the presence of the RD effect, the SOIs in the birefringent 2D-OSC microcavity result in a controllable spin-splitting with CP dispersions. Thanks to the high emission efficiency and high carrier mobility of the OSC, chiral-emitter-free CP-OLEDs have been demonstrated exhibiting a high g_EL of 1.1 and a maximum luminance of about 60000 cd/m², which places our device among the best performing CP-OLEDs. This strategy opens an avenue for practical applications towards on-chip microcavity CP-OLEDs.

Moiré-Induced Optical Nonlinearities: Single- and Multiphoton Resonances

Moiré excitons promise a new platform with which to generate and manipulate hybrid quantum phases of light and matter in unprecedented regimes of interaction strength. We explore the properties in this regime, through studies of a Bose-Hubbard model of excitons coupled to cavity photons. We show that the steady states exhibit a rich phase diagram with pronounced bistabilities governed by multiphoton resonances reflecting the strong interexciton interactions. In the presence of an incoherent pumping of excitons we find that the system can realize single- and multiphoton lasers.

Polarization and Phase Textures in Lattice Plasmon Condensates

Polarization textures of light may reflect fundamental phenomena, such as topological defects, and can be utilized in engineering light beams. They have been observed, for instance, in photonic crystal lasers and semiconductor polariton condensates. Here we demonstrate domain wall polarization textures in a plasmonic lattice Bose-Einstein condensate. A key ingredient of the textures is found to be a condensate phase that varies spatially in a nontrivial manner. The phase of the Bose-Einstein condensate is reconstructed from the real- and Fourier-space images using a phase retrieval algorithm. We introduce a simple theoretical model that captures the results and can be used for design of the polarization patterns and demonstrate that the textures can be optically switched. The results open new prospects for fundamental studies of non-equilibrium condensation and sources of polarization-structured beams.

Polygonal patterns of confined light

We propose a technique for the generation of polygonal optical patterns in real space using a combined effect of the spin-orbit interaction and confinement of light in the plane of a dielectric optical microcavity. The spin-orbit interaction emerging from the splitting in transverse electric (TE) and transverse magnetic (TM) optical modes of the microcavity gives rise to oscillations in space of propagating macroscopic wave packets of polarized photons. Confined in a harmonic potential, the latter follow closed trajectories of a polygonal form. We demonstrate the possibility of excitation by a continuous wave resonant optical pumping of polygonal optical patterns with a controllable (both even and odd) number of vertices.

Nontrivial band geometry in an optically active system

Optical activity, also called circular birefringence, is known for two hundred years, but its applications for topological photonics remain unexplored. Unlike the Faraday effect, the optical activity provokes rotation of the linear polarization of light without magnetic effects, thus preserving the time-reversal symmetry. In this work, we report a direct measurement of the Berry curvature and quantum metric of the photonic modes of a planar cavity, containing a birefringent organic microcrystal (perylene) and exhibiting emergent optical activity. This experiment, performed at room temperature and at visible wavelength, establishes the potential of organic materials for implementing non-magnetic and low-cost topological photonic devices.

Realization of all-optical vortex switching in exciton-polariton condensates

Vortices are topological objects representing the circular motion of a fluid. With their additional degree of freedom, the vorticity, they have been widely investigated in many physical systems and different materials for fundamental interest and for applications in data storage and information processing. Vortices have also been observed in non-equilibrium exciton-polariton condensates in planar semiconductor microcavities. There they appear spontaneously or can be created and pinned in space using ring-shaped optical excitation profiles. However, using the vortex state for information processing not only requires creation of a vortex but also efficient control over the vortex after its creation. Here we demonstrate a simple approach to control and switch a localized polariton vortex between opposite states. In our scheme, both the optical control of vorticity and its detection through the orbital angular momentum of the emitted light are implemented in a robust and practical manner.

Orbital angular momentum bistability in a microlaser

Light's orbital angular momentum (OAM) is an unbounded degree of freedom emerging in helical beams that appears very advantageous technologically. Using chiral microlasers, i.e., integrated devices that allow generating an emission carrying a net OAM, we demonstrate a regime of bistability involving two modes presenting distinct OAM (ℓ=0 and ℓ=2). Furthermore, thanks to an engineered spin-orbit coupling of light in these devices, these modes also exhibit distinct polarization patterns, i.e., circular and azimuthal polarizations. Using a dynamical model of rate equations, we show that this bistability arises from polarization-dependent saturation of the gain medium. Such a bistable regime appears very promising for implementing ultrafast optical switches based on the OAM of light. As well, it paves the way for the exploration of dynamical processes involving phase and polarization vortices.

Two-Dimensional Topological Polariton Laser

We provide proof-of-principle illustration of lasing in a two-dimensional polariton topological insulator. Topological edge states may arise in a structured polariton microcavity under the combined action of spin-orbit coupling and Zeeman splitting in the magnetic field. Their properties and lifetime are strongly affected by gain. Thus, gain concentrated along the edge of the insulator can counteract intrinsic losses in such a selective way that the topologically protected edge states become amplified, while bulk modes remain damped. When gain is compensated by nonlinear absorption the metastable nonlinear edge states are formed. Taking a triangular structure instead of an infinite edge we observed persistent topological currents accompanied by the time-periodic oscillations of the polariton density.

Transverse instability of dark solitons in spin-orbit coupled polariton condensates

We consider dark solitons and their stability in spin-orbit coupled polariton condensates. The system supports spinor solitons of two types: conventional (symmetric) dark solitons and asymmetric half-dark solitons. They demonstrate essentially different behavior upon variation of the strength of spin-orbit coupling. One-dimensional spin-orbit coupled dark solitons are usually unstable, while half-dark solitons can be stable. Two-dimensional dark solitons at early stages of the development of transverse instabilities turn into asymmetric snaking patterns and later into sets of vortex-antivortex solitons with notably different shapes. Depending on the sign of spin-orbit coupling, two distinct instability scenarios are possible for such solitons, in which vortices in one component correspond to vortices or antivortices in other component. The decay of two-dimensional half-dark solitons results in the formation of half-vortex chains.

Generation of optical vortices by exciton polaritons in pillar semiconductor microcavities

We propose a scheme to generate optical vortices through exciting exciton polariton vortices by a Gaussian beam in a pillar microcavity. With coupled Gross-Piteavskii equations we find that the structure of the exciton polariton vortices and antivortices shows a strong dependence on the microcavity radius, pump geometry, and nonlinear exciton-exciton interaction. Due to the nonlinear exciton-exciton interaction the strong Gaussian beam cannot excite more exciton polariton vortices or antivortices with respect to the weak one. The calculation demonstrates that the weak Gaussian beam can excite vortex-antivortex pairs, vortices with high total orbital angular momentum, and superposition states of vortex and antivortex with high total opposite orbital angular momentum. The pump geometry for the Gaussian beam to excite these vortex structures is analyzed in detail, which shows a potential application for generating optical vortex beams.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Spin Order and Phase Transitions in Chains of Polariton Condensates

We demonstrate that multiply coupled spinor polariton condensates can be optically tuned through a sequence of spin-ordered phases by changing the coupling strength between nearest neighbors. For closed four-condensate chains these phases span from ferromagnetic (FM) to antiferromagnetic (AFM), separated by an unexpected crossover phase. This crossover phase is composed of alternating FM-AFM bonds. For larger eight-condensate chains, we show the critical role of spatial inhomogeneities and demonstrate a scheme to overcome them and prepare any desired spin state. Our observations thus demonstrate a fully controllable nonequilibrium spin lattice.

Paramagnetic resonance in spin-polarized disordered Bose-Einstein condensates

We study the pseudo-spin density response of a disordered two-dimensional spin-polarized Bose gas to weak alternating magnetic field, assuming that one of the spin states of the doublet is macroscopically occupied and Bose-condensed while the occupation of the other state remains much smaller. We calculate spatial and temporal dispersions of spin susceptibility of the gas taking into account spin-flip processes due to the transverse-longitudinal splitting, considering microcavity exciton polaritons as a testbed. Further, we use the Bogoliubov theory of weakly-interacting gases and show that the time-dependent magnetic field power absorption exhibits double resonance structure corresponding to two particle spin states (contrast to paramagnetic resonance in regular spin-polarized electron gas). We analyze the widths of these resonances caused by scattering on the disorder and show that, in contrast with the ballistic regime, in the presence of impurities, the polariton scattering on them is twofold: scattering on the impurity potential directly and scattering on the spatially fluctuating condensate density caused by the disorder. As a result, the width of the resonance associated with the Bose-condensed spin state can be surprisingly narrow in comparison with the width of the resonance associated with the non-condensed state.

Twist of generalized skyrmions and spin vortices in a polariton superfluid

We study the spin vortices and skyrmions coherently imprinted into an exciton-polariton condensate on a planar semiconductor microcavity. We demonstrate that the presence of a polarization anisotropy can induce a complex dynamics of these structured topologies, leading to the twist of their circuitation on the Poincaré sphere of polarizations. The theoretical description of the results carries the concept of generalized quantum vortices in two-component superfluids, which are conformal with polarization loops around an arbitrary axis in the pseudospin space.

Injection of Orbital Angular Momentum and Storage of Quantized Vortices in Polariton Superfluids

We report the experimental investigation and theoretical modeling of a rotating polariton superfluid relying on an innovative method for the injection of angular momentum. This novel, multipump injection method uses four coherent lasers arranged in a square, resonantly creating four polariton populations propagating inwards. The control available over the direction of propagation of the superflows allows injecting a controllable nonquantized amount of optical angular momentum. When the density at the center is low enough to neglect polariton-polariton interactions, optical singularities, associated with an interference pattern, are visible in the phase. In the superfluid regime resulting from the strong nonlinear polariton-polariton interaction, the interference pattern disappears and only vortices with the same sign are persisting in the system. Remarkably, the number of vortices inside the superfluid region can be controlled by controlling the angular momentum injected by the pumps.