Direct measurement of a non-Hermitian topological invariant in a hybrid light-matter system

Optical spin hall effect in exciton-polariton condensates in lead halide perovskite microcavities

An exciton-polariton condensate is a hybrid light-matter state in the quantum fluid phase. The photonic component endows it with characters of spin, as represented by circular polarization. Spin-polarization can form stochastically for quasi-equilibrium exciton-polariton condensates at parallel momentum vector k|| ∼ 0 from bifurcation or deterministically for propagating condensates at k|| > 0 from the optical spin-Hall effect (OSHE). Here, we report deterministic spin-polarization in exciton-polariton condensates at k|| ∼ 0 in microcavities containing methylammonium lead bromide perovskite (CH3NH3PbBr3) single crystals under non-resonant and linearly polarized excitation. We observe two energetically split condensates with opposite circular polarizations and attribute this observation to the presence of strong birefringence, which introduces a large OSHE at k|| ∼ 0 and pins the condensates in a particular spin state. Such spin-polarized exciton-polariton condensates may serve not only as circularly polarized laser sources but also as effective alternatives to ultracold atom Bose-Einstein condensates in quantum simulators of many-body spin-orbit coupling processes.

Exciton polariton condensation from bound states in the continuum at room temperature

Exciton-polaritons (polaritons) resulting from the strong exciton-photon interaction stimulates the development of novel low-threshold coherent light sources to circumvent the ever-increasing energy demands of optical communications1-3. Polaritons from bound states in the continuum (BICs) are promising for Bose-Einstein condensation owing to their theoretically infinite quality factors, which provide prolonged lifetimes and benefit the polariton accumulations4-7. However, BIC polariton condensation remains limited to cryogenic temperatures ascribed to the small exciton binding energies of conventional material platforms. Herein, we demonstrated room-temperature BIC polariton condensation in perovskite photonic crystal lattices. BIC polariton condensation was demonstrated at the vicinity of the saddle point of polariton dispersion that generates directional vortex beam emission with long-range coherence. We also explore the peculiar switching effect among the miniaturized BIC polariton modes through effective polariton-polariton scattering. Our work paves the way for the practical implementation of BIC polariton condensates for integrated photonic and topological circuits.

Parity-time-symmetric photonic topological insulator

Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.

Topological spin textures in electronic non-Hermitian systems

Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification of observables. However, their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired, where a variety of materials are available, calculations are solidly founded, and accurate spectroscopic techniques can be applied. We demonstrate that, in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities, highly nontrivial topological soliton spin textures appear in momentum space. Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically. Moreover, the distinct topological soliton objects can be deformed to each other, mediated by topological transitions driven by tuning across a critical direction of doped magnetism. These results not only open a solid-state avenue to exotic spin patterns via spin- and angle-resolved photoemission spectroscopy, but also inspire non-Hermitian dissipation engineering of spins in solids.

Electrically Controlling Vortices in a Neutral Exciton-Polariton Condensate at Room Temperature

Manipulating bosonic condensates with electric fields is very challenging as the electric fields do not directly interact with the neutral particles of the condensate. Here we demonstrate a simple electric method to tune the vorticity of exciton-polariton condensates in a strong coupling liquid crystal (LC) microcavity with CsPbBr_{3} microplates as active material at room temperature. In such a microcavity, the LC molecular director can be electrically modulated giving control over the polariton condensation in different modes. For isotropic nonresonant optical pumping we demonstrate the spontaneous formation of vortices with topological charges of +1, +2, -2, and -1. The topological vortex charge is controlled by a voltage in the range of 1 to 10 V applied to the microcavity sample. This control is achieved by the interplay of a built-in potential gradient, the anisotropy of the optically active perovskite microplates, and the electrically controllable LC molecular director in our system with intentionally broken rotational symmetry. Besides the fundamental interest in the achieved electric polariton vortex control at room temperature, our work paves the way to micron-sized emitters with electric control over the emitted light's phase profile and quantized orbital angular momentum for information processing and integration into photonic circuits.

Bound chiral magnonic polariton states for ideal microwave isolation

Bound states in the continuum (BICs) present a unique solution for eliminating radiation loss. So far, most reported BICs are observed in transmission spectra, with only a few exceptions being in reflection spectra. The correlation between reflection BICs (r-BICs) and transmission BICs (t-BICs) remains unclear. Here, we report the presence of both r-BICs and t-BICs in a three-mode cavity magnonics. We develop a generalized framework of non-Hermitian scattering Hamiltonians to explain the observed bidirectional r-BICs and unidirectional t-BICs. In addition, we find the emergence of an ideal isolation point in the complex frequency plane, where the isolation direction can be switched by fine frequency detuning, thanks to chiral symmetry protection. Our results demonstrate the potential of cavity magnonics and also extend the conventional BICs theory through the application of a more generalized effective Hamiltonians theory. This work offers an alternative idea for designing functional devices in general wave optics.

Non-Hermitian chiral degeneracy of gated graphene metasurfaces

Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction of an eigenspace dimensionality at the EP has been investigated mostly in a passive repetitive manner. Here, we propose an electrical and spectral way of resolving chiral EPs and clarifying the consequences of chiral mode collapsing of a non-Hermitian gated graphene metasurface. More specifically, the measured non-Hermitian Jones matrix in parameter space enables the quantification of nonorthogonality of polarisation eigenstates and half-integer topological charges associated with a chiral EP. Interestingly, the output polarisation state can be made orthogonal to the coalesced polarisation eigenstate of the metasurface, revealing the missing dimension at the chiral EP. In addition, the maximal nonorthogonality at the chiral EP leads to a blocking of one of the cross-polarised transmission pathways and, consequently, the observation of enhanced asymmetric polarisation conversion. We anticipate that electrically controllable non-Hermitian metasurface platforms can serve as an interesting framework for the investigation of rich non-Hermitian polarisation dynamics around chiral EPs.

Negative-mass exciton polaritons induced by dissipative light-matter coupling in an atomically thin semiconductor

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) WS₂ crystals embedded in planar microcavities and demonstrate that the propagation direction of the negative-mass polaritons is opposite to their momentum. Our study introduces the concept of non-Hermitian dispersion engineering for exciton polaritons and opens a pathway for realising new phases of quantum matter in a solid state.

Bulk-boundary correspondence in disordered non-Hermitian systems

The bulk-boundary correspondence (BBC) refers to the consistency between eigenvalues calculated under open and periodic boundary conditions. This consistency can be destroyed in systems with non-Hermitian skin effect (NHSE). In spite of the great success of the generalized Brillouin zone (GBZ) theory in clean non-Hermitian systems, the applicability of GBZ theory is questionable when the translational symmetry is broken. Thus, it is of great value to rebuild the BBC for disordered samples, which extends the application of GBZ theory in non-Hermitian systems. Here, we propose a scheme to reconstruct BBC, which can be regarded as the solution of an optimization problem. By solving the optimization problem analytically, we reconstruct the BBC and obtain the modified GBZ theory in several prototypical disordered non-Hermitian models. The modified GBZ theory provides a precise description of the fantastic NHSE, which predicts the asynchronous-disorder-reversed NHSE's directions.

Double-Cavity Modulation of Exciton Polaritons in CsPbBr3 Microwire

The lead halide perovskite has become a promising candidate for the study of exciton polaritons due to their excellent optical properties. Here, both experimental and simulated results confirm the existence of two kinds of Fabry-Pérot microcavities in a single CsPbBr₃ microwire with an isosceles right triangle cross section, and we experimentally demonstrate that confined photons in a straight and a folded Fabry-Pérot microcavity are strongly coupled with excitons to form exciton polaritons. Furthermore, we reveal the polarization characteristic and double-cavity modulation of exciton polaritons emission by polarization-resolved fluorescence spectroscopy. Our results not only prove that the modulation of exciton polaritons emission can occur in this simple double-cavity system but also provide a possibility to develop related polariton devices.

Modulated Rashba-Dresselhaus Spin-Orbit Coupling for Topology Control and Analog Simulations

We show theoretically that Rashba-Dresselhaus spin-orbit coupling (RDSOC) in lattices acts as a synthetic gauge field. This allows us to control both the phase and the magnitude of tunneling coefficients between sites, which is the key ingredient to implement topological Hamitonians and spin lattices useful for simulation perpectives. We use liquid crystal based microcavities in which RDSOC can be switched on and off as a model platform. We propose a realistic scheme for implementation of a Su-Schrieffer-Heeger chain in which the edge states existence can be tuned, and a Harper-Hofstadter model with a tunable contrasted flux for each (pseudo)spin component. We further show that a transverse-field Ising model and classical XY Hamiltonian with tunable parameters can be implemented, opening up prospects for analog physics, simulations, and optimization.

Electrically tunable Berry curvature and strong light-matter coupling in liquid crystal microcavities with 2D perovskite

The field of spinoptronics is underpinned by good control over photonic spin-orbit coupling in devices that have strong optical nonlinearities. Such devices might hold the key to a new era of optoelectronics where momentum and polarization degrees of freedom of light are interwoven and interfaced with electronics. However, manipulating photons through electrical means is a daunting task given their charge neutrality. In this work, we present electrically tunable microcavity exciton-polariton resonances in a Rashba-Dresselhaus spin-orbit coupling field. We show that different spin-orbit coupling fields and the reduced cavity symmetry lead to tunable formation of the Berry curvature, the hallmark of quantum geometrical effects. For this, we have implemented an architecture of a photonic structure with a two-dimensional perovskite layer incorporated into a microcavity filled with nematic liquid crystal. Our work interfaces spinoptronic devices with electronics by combining electrical control over both the strong light-matter coupling conditions and artificial gauge fields.

Annihilation of exceptional points from different Dirac valleys in a 2D photonic system

Topological physics relies on Hamiltonian’s eigenstate singularities carrying topological charges, such as Dirac points, and – in non-Hermitian systems – exceptional points (EPs), lines or surfaces. So far, the reported non-Hermitian topological transitions were related to the creation of a pair of EPs connected by a Fermi arc out of a single Dirac point by increasing non-Hermiticity. Such EPs can annihilate by reducing non-Hermiticity. Here, we demonstrate experimentally that an increase of non-Hermiticity can lead to the annihilation of EPs issued from different Dirac points (valleys). The studied platform is a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Non-Hermiticity is provided by polarization-dependent losses. By increasing the non-Hermiticity degree, we control the position of the EPs. After the intervalley annihilation, the system becomes free of any band singularity. Our results open the field of non-Hermitian valley-physics and illustrate connections between Hermitian topology and non-Hermitian phase transitions.

The authors study a liquid crystal microcavity with polarization-dependent absorption, a source of non-Hermiticity. The transition in the Hermitian topology of the spin-orbit coupling makes possible the annihilation of exceptional points.

A non-Hermitian optical atomic mirror

Explorations of symmetry and topology have led to important breakthroughs in quantum optics, but much richer behaviors arise from the non-Hermitian nature of light-matter interactions. A high-reflectivity, non-Hermitian optical mirror can be realized by a two-dimensional subwavelength array of neutral atoms near the cooperative resonance associated with the collective dipole modes. Here we show that exceptional points develop from a nondefective degeneracy by lowering the crystal symmetry of a square atomic lattice, and dispersive bulk Fermi arcs that originate from exceptional points are truncated by the light cone. From its nontrivial energy spectra topology, we demonstrate that the geometry-dependent non-Hermitian skin effect emerges in a ribbon geometry. Furthermore, skin modes localized at a boundary show a scale-free behavior that stems from the long-range interaction and whose mechanism goes beyond the framework of non-Bloch band theory. Our work opens the door to the study of the interplay among non-Hermiticity, topology, and long-range interaction.

Manipulating polariton condensates by Rashba-Dresselhaus coupling at room temperature

Spin-orbit coupling plays an important role in the spin Hall effect and topological insulators. Bose-Einstein condensates with spin-orbit coupling show remarkable quantum phase transition. In this work we control an exciton polariton condensate – a macroscopically coherent state of hybrid light and matter excitations – by virtue of the Rashba-Dresselhaus (RD) spin-orbit coupling. This is achieved in a liquid-crystal filled microcavity where CsPbBr₃ perovskite microplates act as the gain material at room temperature. Specifically, we realize an artificial gauge field acting on the CsPbBr₃ exciton polariton condensate, splitting the condensate fractions with opposite spins in both momentum and real space. Besides the ground states, higher-order discrete polariton modes can also be split by the RD effect. Our work paves the way to manipulate exciton polariton condensates with a synthetic gauge field based on the RD spin-orbit coupling at room temperature.

Engineered spin-orbit coupling can induce novel quantum phases in a Bose-Einstein condensate, however such demonstrations have been limited to cold atom systems. Here the authors realize a exciton-polarion condensate with tunable spin-orbit coupling in a liquid crystal microcavity at room temperature.

Spin-orbit-coupled exciton-polariton condensates in lead halide perovskites

Spin-orbit coupling (SOC) is responsible for a range of spintronic and topological processes in condensed matter. Here, we show photonic analogs of SOCs in exciton-polaritons and their condensates in microcavities composed of birefringent lead halide perovskite single crystals. The presence of crystalline anisotropy coupled with splitting in the optical cavity of the transverse electric and transverse magnetic modes gives rise to a non-Abelian gauge field, which can be described by the Rashba-Dresselhaus Hamiltonian near the degenerate points of the two polarization modes. With increasing density, the exciton-polaritons with pseudospin textures undergo phase transitions to competing condensates with orthogonal polarizations. Unlike their pure photonic counterparts, these exciton-polaritons and condensates inherit nonlinearity from their excitonic components and may serve as quantum simulators of many-body SOC processes.