Exciton-polariton trapping and potential landscape engineering

Dirac Cones and Room Temperature Polariton Lasing Evidenced in an Organic Honeycomb Lattice

Artificial 1D and 2D lattices have emerged as a powerful platform for the emulation of lattice Hamiltonians, the fundamental study of collective many-body effects, and phenomena arising from non-trivial topology. Exciton-polaritons, bosonic part-light and part-matter quasiparticles, combine pronounced nonlinearities with the possibility of on-chip implementation. In this context, organic semiconductors embedded in microcavities have proven to be versatile candidates to study nonlinear many-body physics and bosonic condensation, and in contrast to most inorganic systems, they allow the use at ambient conditions since they host ultra-stable Frenkel excitons. A well-controlled, high-quality optical lattice is implemented that accommodates light-matter quasiparticles. The realized polariton graphene presents with excellent cavity quality factors, showing distinct signatures of Dirac cone and flatband dispersions as well as polariton lasing at room temperature. This is realized by filling coupled dielectric microcavities with the fluorescent protein mCherry. The emergence of a coherent polariton condensate at ambient conditions are demonstrated, taking advantage of coupling conditions as precise and controllable as in state-of-the-art inorganic semiconductor-based systems, without the limitations of e.g. lattice matching in epitaxial growth. This progress allows straightforward extension to more complex systems, such as the study of topological phenomena in 2D lattices including topological lasers and non-Hermitian optics.

Qubit gate operations in elliptically trapped polariton condensates

We consider bosonic condensates of exciton-polaritons optically confined in elliptical traps. A superposition of two non-degenerated p-type states of the condensate oriented along the two main axes of the trap is represented by a point on a Bloch sphere, being considered as an optically tunable qubit. We describe a set of universal single-qubit gates resulting in a controllable shift of the Bloch vector by means of an auxiliary laser beam. Moreover, we consider interaction mechanisms between two neighboring traps that enable designing two-qubit operations such as CPHASE and CNOT gates. Both the single- and two-qubit gates are analyzed in the presence of error sources in the context of polariton traps, such as pure dephasing and spontaneous relaxation mechanisms, leading to a fidelity reduction of the final qubit states and quantum concurrence, as well as the increase of Von Neumann entropy. We also discuss the applicability of our qubit proposal in the context of DiVincenzo's criteria for the realization of local quantum computing processes. Altogether, the developed set of quantum operations would pave the way to the realization of a variety of quantum algorithms in a planar microcavity with a set of optically induced elliptical traps.

Exciton Polaritons in Emergent Two-Dimensional Semiconductors

The "marriage" of light (i.e., photon) and matter (i.e., exciton) in semiconductors leads to the formation of hybrid quasiparticles called exciton polaritons with fascinating quantum phenomena such as Bose-Einstein condensation (BEC) and photon blockade. The research of exciton polaritons has been evolving into an era with emergent two-dimensional (2D) semiconductors and photonic structures for their tremendous potential to break the current limitations of quantum fundamental study and photonic applications. In this Perspective, the basic concepts of 2D excitons, optical resonators, and the strong coupling regime are introduced. The research progress of exciton polaritons is reviewed, and important discoveries (especially the recent ones of 2D exciton polaritons) are highlighted. Subsequently, the emergent 2D exciton polaritons are discussed in detail, ranging from the realization of the strong coupling regime in various photonic systems to the discoveries of attractive phenomena with interesting physics and extensive applications. Moreover, emerging 2D semiconductors, such as 2D perovskites (2DPK) and 2D antiferromagnetic (AFM) semiconductors, are surveyed for the manipulation of exciton polaritons with distinct control degrees of freedom (DOFs). Finally, the outlook on the 2D exciton polaritons and their nonlinear interactions is presented with our initial numerical simulations. This Perspective not only aims to provide an in-depth overview of the latest fundamental findings in 2D exciton polaritons but also attempts to serve as a valuable resource to prospect explorations of quantum optics and topological photonic applications.

Polariton Condensation in Gap-Confined States of Photonic Crystal Waveguides

The development of patterned multiquantum well heterostructures in GaAs/AlGaAs waveguides has recently made it possible to achieve exciton-polariton condensation in a topologically protected bound state in the continuum (BIC). Polariton condensation was shown to occur above a saddle point of the two-dimensional polariton dispersion in a one-dimensional photonic crystal waveguide. A rigorous analysis of the condensation phenomenon in these systems, as well as the role of the BIC, is still missing. In the present Letter, we theoretically and experimentally fill this gap by showing that polariton confinement resulting from the negative effective mass and the photonic energy gap in the dispersion play a key role in enhancing the relaxation toward the condensed state. In fact, our results show that low-threshold polariton condensation is achieved within the effective trap created by the exciting laser spot, regardless of whether the resulting confined mode is long-lived (polariton BIC) or short-lived (lossy mode). In both cases, the spatial quantization of the polariton condensate and the threshold differences associated to the corresponding state lifetime are measured and characterized. For a given negative mass, a slightly lower condensation threshold from the polariton BIC mode is found and associated to its reduced radiative losses, as compared to the lossy one.

Manipulating nonlinear exciton polaritons in an atomically-thin semiconductor with artificial potential landscapes

Exciton polaritons in atomically thin transition-metal dichalcogenide microcavities provide a versatile platform for advancing optoelectronic devices and studying the interacting Bosonic physics at ambient conditions. Rationally engineering the favorable properties of polaritons is critically required for the rapidly growing research. Here, we demonstrate the manipulation of nonlinear polaritons with the lithographically defined potential landscapes in monolayer WS2 microcavities. The discretization of photoluminescence dispersions and spatially confined patterns indicate the deterministic on-site localization of polaritons by the artificial mesa cavities. Varying the trapping sizes, the polariton-reservoir interaction strength is enhanced by about six times through managing the polariton-exciton spatial overlap. Meanwhile, the coherence of trapped polaritons is significantly improved due to the spectral narrowing and tailored in a picosecond range. Therefore, our work not only offers a convenient approach to manipulating the nonlinearity and coherence of polaritons but also opens up possibilities for exploring many-body phenomena and developing novel polaritonic devices based on 2D materials.

Plexcitonics: plasmon-exciton coupling for enhancing spectroscopy, optical chirality, and nonlinearity

Plexcitonics is a rapidly developing interdisciplinary field that holds immense potential for the creation of innovative optical technologies and devices. This field focuses on investigating the interactions between plasmons and excitons in hybrid systems. In this review, we provide an overview of the fundamental principles of plasmonics and plexcitonics and discuss the latest advancements in plexcitonics. Specifically, we highlight the ability to manipulate plasmon-exciton interactions, the emerging field of tip-enhanced spectroscopy, and advancements in optical chirality and nonlinearity. These recent developments have spurred further research in the field of plexcitonics and offer inspiration for the design of advanced materials and devices with enhanced optical properties and functionalities.

Observation of Zitterbewegung in photonic microcavities

We present and experimentally study the effects of the photonic spin-orbit coupling on the real space propagation of polariton wavepackets in planar semiconductor microcavities and polaritonic analogues of graphene. In particular, we demonstrate the appearance of an analogue Zitterbewegung effect, a term which translates as 'trembling motion' in English, which was originally proposed for relativistic Dirac electrons and consisted of the oscillations of the centre of mass of a wavepacket in the direction perpendicular to its propagation. For a planar microcavity, we observe regular Zitterbewegung oscillations whose amplitude and period depend on the wavevector of the polaritons. We then extend these results to a honeycomb lattice of coupled microcavity resonators. Compared to the planar cavity, such lattices are inherently more tuneable and versatile, allowing simulation of the Hamiltonians of a wide range of important physical systems. We observe an oscillation pattern related to the presence of the spin-split Dirac cones in the dispersion. In both cases, the experimentally observed oscillations are in good agreement with theoretical modelling and independently measured bandstructure parameters, providing strong evidence for the observation of Zitterbewegung.

Optically Driven Rotation of Exciton-Polariton Condensates

The rotational response of quantum condensed fluids is strikingly distinct from rotating classical fluids, especially notable for the excitation and ordering of quantized vortex ensembles. Although widely studied in conservative systems, the dynamics of rotating open-dissipative superfluids such as exciton-polariton condensates remains largely unexplored, as it requires high-frequency rotation while avoiding resonantly driving the condensate. We create a rotating polariton condensate at gigahertz frequencies by off-resonantly pumping with a rotating optical stirrer composed of the time-dependent interference of two frequency-offset, structured laser modes. Acquisition of angular momentum exceeding the critical 1ℏ/particle is directly measured, accompanied by the deterministic nucleation and capture of quantized vortices with a handedness controlled by the pump rotation direction. The demonstration of controlled optical rotation of a spontaneously formed polariton condensate enables new opportunities for the study of open dissipative superfluidity, ordering of non-Hermitian quantized vortex matter, and topological states in a highly nonlinear, photonic platform.

Single-Photon Source in a Topological Cavity

The introduction of topological physics into the field of photonics has led to the development of photonic devices endowed with robustness against structural disorder. While a range of platforms have been successfully implemented demonstrating topological protection of light in the classical domain, the implementation of quantum light sources in photonic devices harnessing topologically nontrivial resonances is largely unexplored. Here, we demonstrate a single photon source based on a single semiconductor quantum dot coupled to a topologically nontrivial Su-Schrieffer-Heeger (SSH) cavity mode. We provide an in-depth study of Purcell enhancement for this topological quantum light source and demonstrate its emission of nonclassical light on demand. Our approach is a promising step toward the application of topological cavities in quantum photonics.

Optically trapped room temperature polariton condensate in an organic semiconductor

The strong nonlinearities of exciton-polariton condensates in lattices make them suitable candidates for neuromorphic computing and physical simulations of complex problems. So far, all room temperature polariton condensate lattices have been achieved by nanoimprinting microcavities, which by nature lacks the crucial tunability required for realistic reconfigurable simulators. Here, we report the observation of a quantised oscillating nonlinear quantum fluid in 1D and 2D potentials in an organic microcavity at room temperature, achieved by an on-the-fly fully tuneable optical approach. Remarkably, the condensate is delocalised from the excitation region by macroscopic distances, leading both to longer coherence and a threshold one order of magnitude lower than that with a conventional Gaussian excitation profile. We observe different mode selection behaviour compared to inorganic materials, which highlights the anomalous scaling of blueshift with pump intensity and the presence of sizeable energy-relaxation mechanisms. Our work is a major step towards a fully tuneable polariton simulator at room temperature.

Enhancing Ground-State Population and Macroscopic Coherence of Room-Temperature WS_{2} Polaritons through Engineered Confinement

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.

Kardar-Parisi-Zhang universality in a one-dimensional polariton condensate

Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces¹ and of interfaces in bacterial colonies², and spin transport in quantum magnets^3-6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space-time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar-Parisi-Zhang (KPZ) equation⁷. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence^8-17. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws^18,19, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantum systems.

Strongly correlated electron-photon systems

An important goal of modern condensed-matter physics involves the search for states of matter with emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at heterointerfaces, precise alignment of low-dimensional materials and the use of extreme pressures. Here we highlight a paradigm based on controlling light-matter interactions, which provides a way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of phenomena. Photon-mediated superconductivity, cavity fractional quantum Hall physics and optically driven topological phenomena in low dimensions are among the frontiers discussed in this Perspective, which highlights a field that we term here 'strongly correlated electron-photon science'.

Spontaneous symmetry breaking and the dynamics of three interacting nonlinear optical resonators with gain and loss

The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and their dynamical stability are considered in detail. Spontaneous symmetry breaking is found and it is shown that this bifurcation results in the formation of asymmetric states. It is also found that the oscillating states can occur in the system in a certain range of parameters. The results of the analysis of the stationary states are confirmed by direct numerical simulations. The possibility of switching between different states is also demonstrated by numerical experiments.

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

Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterized by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant—fractional spectral winding. Our work represents an essential step toward realization of non-Hermitian topological phases in a condensed matter system.

Strain induced localization to delocalization transition on a Lieb photonic ribbon lattice

Ribbon lattices are kind of transition systems in between one and two dimensions, and their study is crucial to understand the origin of different emerging properties. In this work, we study a Lieb ribbon lattice and the localization-delocalization transition occurring due to a reduction of lattice distances (compression) and the corresponding flat band deformation. We observe how above a critical compression ratio the energy spreads out and propagates freely across the lattice, therefore transforming the system from being a kind of insulator into a conductor. We implement an experiment on a photonic platform and show an excellent agreement with the predicted phenomenology. Our findings suggest and prove experimentally the use of compression or mechanical deformation of lattices to switch the transport properties of a given system.

Motional narrowing, ballistic transport, and trapping of room-temperature exciton polaritons in an atomically-thin semiconductor

Monolayer transition metal dichalcogenide crystals (TMDCs) hold great promise for semiconductor optoelectronics because their bound electron-hole pairs (excitons) are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, excitons can hybridise with cavity photons to form exciton polaritons, which inherit useful properties from their constituents. The ability to manipulate and trap polaritons on a microchip is critical for applications. Here, we create a non-trivial potential landscape for polaritons in monolayer WS₂, and demonstrate their trapping and ballistic propagation across tens of micrometers. We show that the effects of dielectric disorder, which restrict the diffusion of WS₂ excitons and broaden their spectral resonance, are dramatically reduced for polaritons, leading to motional narrowing and preserved partial coherence. Linewidth narrowing and coherence are further enhanced in the trap. Our results demonstrate the possibility of long-range dissipationless transport and efficient trapping of TMDC polaritons in ambient conditions.

Van der Waals heterostructure polaritons with moiré-induced nonlinearity

Controlling matter-light interactions with cavities is of fundamental importance in modern science and technology¹. This is exemplified in the strong-coupling regime, where matter-light hybrid modes form, with properties that are controllable by optical-wavelength photons^2,3. By contrast, matter excitations on the nanometre scale are harder to access. In two-dimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form⁴, enabling the generation of correlated electron gases in the lattice potentials^5-9. Excitons confined in moiré lattices have also been reported^10,11, but no cooperative effects have been observed and interactions with light have remained perturbative^12-15. Here, by integrating MoSe₂-WS₂ heterobilayers in a microcavity, we establish cooperative coupling between moiré-lattice excitons and microcavity photons up to the temperature of liquid nitrogen, thereby integrating versatile control of both matter and light into one platform. The density dependence of the moiré polaritons reveals strong nonlinearity due to exciton blockade, suppressed exciton energy shift and suppressed excitation-induced dephasing, all of which are consistent with the quantum confined nature of the moiré excitons. Such a moiré polariton system combines strong nonlinearity and microscopic-scale tuning of matter excitations using cavity engineering and long-range light coherence, providing a platform with which to study collective phenomena from tunable arrays of quantum emitters.

Propagative Oscillations in Codirectional Polariton Waveguide Couplers

We report on novel exciton-polariton routing devices created to study and purposely guide light-matter particles in their condensate phase. In a codirectional coupling device, two waveguides are connected by a partially etched section that facilitates tunable coupling of the adjacent channels. This evanescent coupling of the two macroscopic wave functions in each waveguide reveals itself in real space oscillations of the condensate. This Josephson-like oscillation has only been observed in coupled polariton traps so far. Here, we report on a similar coupling behavior in a controllable, propagative waveguide-based design. By controlling the gap width, channel length, or propagation energy, the exit port of the polariton flow can be chosen. This codirectional polariton device is a passive and scalable coupler element that can serve in compact, next generation logic architectures.

Topological edge states of nonequilibrium polaritons in hollow honeycomb arrays

We address topological currents in polariton condensates excited by uniform resonant pumps in finite honeycomb arrays of microcavity pillars with a hole in the center. Such currents arise under combined action of the spin-orbit coupling and Zeeman splitting, which breaks the time-reversal symmetry and opens a topological gap in the spectrum of the structure. The most representative feature of this structure is the presence of two interfaces, inner and outer ones, where the directions of topological currents are opposite. Due to the finite size of the structure, polariton-polariton interactions lead to coupling of the edge states at the inner and outer interfaces, which depends on the size of the hollow region. Moreover, switching between currents can be realized by tuning the pump frequency. We illustrate that currents in this finite structure can be stable and study bistability effects arising due to the resonant character of the pump.

Nonlinear higher-order polariton topological insulator

We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with a kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome array. Corner states coexist with densely packed edge states but are well isolated from them in energy. Nonlinear corner states persist even in the presence of perturbations in a corner microcavity pillar.

Demonstration of a polariton step potential by local variation of light-matter coupling in a van-der-Waals heterostructure

The large oscillator strength of excitons in transition metal dichalcogenide layers facilitates the formation of exciton-polariton resonances for monolayers and van-der-Waals heterostructures embedded in optical microcavities. Here, we show, that locally changing the number of layers in a WSe₂/hBN/WSe₂ van-der-Waals heterostructure embedded in a monolithic, high-quality-factor cavity gives rise to a local variation of the coupling strength. This effect yields a polaritonic stair case potential, which we demonstrate at room temperature. Our result paves the way towards engineering local polaritonic potentials at length scales down to atomically sharp interfaces, based on purely modifying its real part contribution via the coherent light-matter coupling strength g.

Optical Control of Couplings in Polariton Condensate Lattices

We demonstrate deterministic control of the nearest and next-nearest neighbor coupling in the unit cell of a square lattice of microcavity exciton-polariton condensates. We tune the coupling in a continuous and reversible manner by optically imprinting potential barriers of variable height, in the form of spatially localized incoherent exciton reservoirs that modify the particle flow between condensates. By controlling the couplings in a 2×2 polariton cluster, we realize ferromagnetic, antiferromagnetic, and paired ferromagnetic phases and demonstrate the potential scalability of the system.

Multi-orbital tight binding model for cavity-polariton lattices

In this work we present a tight-binding model that allows to describe with a minimal amount of parameters the band structure of exciton-polariton lattices. This model based on s and p non-orthogonal photonic orbitals faithfully reproduces experimental results reported for polariton graphene ribbons. We analyze in particular the influence of the non-orthogonality, the inter-orbitals interaction and the photonic spin-orbit coupling on the polarization and dispersion of bulk bands and edge states.

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.

Rotating patterns in polariton condensates in ring-shaped potentials under a bichromatic pump

We consider a polariton condensate in a microcavity driven by a bichromatic resonant pump formed by two vortical laser beams carrying different topological charges. The system is additionally confined in a ring-shaped potential. We show that in this system, steadily rotating nonlinear localized modes can be excited, whose angular rotation frequency is determined by optical frequencies and topological charges of the pump beams. When pump frequencies approach eigenfrequencies of the modes of the ring potential, resonant growth of peak amplitude of the excited states occurs. Repulsive polariton-polariton interactions lead to tilting of the resonance curves and appearance of bistability of rotating patterns.

Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons

Phase frustration in periodic lattices is responsible for the formation of dispersionless flatbands. The absence of any kinetic energy scale makes flatband physics critically sensitive to perturbations and interactions. We report on the experimental investigation of the nonlinear response of cavity polaritons in the gapped flatband of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and abrupt edges, a signature of the frozen propagation of switching fronts. This type of gap soliton belongs to the class of truncated Bloch waves, and has only been observed in closed systems up to now. Here, the driven-dissipative character of the system gives rise to a complex multistability of the flatband nonlinear domains. These results open up an interesting perspective regarding more complex 2D lattices and the generation of correlated photon phases.

Room temperature exciton-polariton condensate in an optically-controlled trap

We report experimental studies on the optical properties of an exciton polariton condensate confined in an optically defined trap at room temperature. As a result of the parabolic profile of the optical trap, the polariton condensate redistributes itself in simple harmonic oscillator states, forming an analog of the gravity pendulum. We observed the coexistence of two harmonic oscillator modes in a single trap, which were confirmed to be confined modes connected by longitudinal optical (LO) phonons using Raman spectroscopy. Clear features of mode competition behaviors were observed for these two harmonic oscillators when the injection rate of polaritons was varied. The observed mode competition was successfully simulated by a three-level rate equation model. In addition, as a result of the bosonic stimulation in the trap region, up to ∼88% of the injected polaritons were successfully trapped when polariton lasing takes place.

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.

Direct Transfer of Light's Orbital Angular Momentum onto a Nonresonantly Excited Polariton Superfluid

Recently, exciton polaritons in a semiconductor microcavity were found to condense into a coherent ground state much like a Bose-Einstein condensate and a superfluid. They have become a unique testbed for generating and manipulating quantum vortices in a driven-dissipative superfluid. Here, we generate an exciton-polariton condensate with a nonresonant Laguerre-Gaussian optical beam and verify the direct transfer of light's orbital angular momentum to an exciton-polariton quantum fluid. Quantized vortices are found in spite of the large energy relaxation involved in nonresonant pumping. We identified phase singularity, density distribution, and energy eigenstates for the vortex states. Our observations confirm that nonresonant optical Laguerre-Gaussian beam can be used to manipulate chirality, topological charge, and stability of the nonequilibrium quantum fluid. These vortices are quite robust, only sensitive to the orbital angular momentum of light and not other parameters such as energy, intensity, size, or shape of the pump beam. Therefore, optical information can be transferred between the photon and exciton-polariton with ease and the technique is potentially useful to form the controllable network of multiple topological charges even in the presence of spectral randomness in a solid state system.

Platform for Electrically Pumped Polariton Simulators and Topological Lasers

Two-dimensional electronic materials such as graphene and transition metal dichalgenides feature unique electrical and optical properties due to the conspirative effect of band structure, orbital coupling, and crystal symmetry. Synthetic matter, as accomplished by artificial lattice arrangements of cold atoms, molecules, electron patterning, and optical cavities, has emerged to provide manifold intriguing frameworks to likewise realize such scenarios. Exciton polaritons have recently been added to the list of promising candidates for the emulation of system Hamiltonians on a semiconductor platform, offering versatile tools to engineer the potential landscape and to access the nonlinear electro-optical regime. In this work, we introduce an electronically driven square and honeycomb lattice of exciton polaritons, paving the way towards real world devices based on polariton lattices for on-chip applications. Our platform exhibits laserlike emission from high-symmetry points under direct current injection, hinting at the prospect of electrically driven polariton lasers with possibly topologically nontrivial properties.

Controlled Ordering of Topological Charges in an Exciton-Polariton Chain

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 signs, is achieved by appropriately shaping an off-resonant pump beam that drives the system to the regime of bosonic condensation. In analogy to spin chains, these vortex sequences realize either a "ferromagnetic" or an "antiferromagnetic" 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 the controlled creation of nontrivial distributions of orbital angular momentum and topological order in a periodic exciton-polariton system.

Exciton-polariton topological insulator

Topological insulators-materials that are insulating in the bulk but allow electrons to flow on their surface-are striking examples of materials in which topological invariants are manifested in robustness against perturbations such as defects and disorder¹. Their most prominent feature is the emergence of edge states at the boundary between areas with different topological properties. The observable physical effect is unidirectional robust transport of these edge states. Topological insulators were originally observed in the integer quantum Hall effect² (in which conductance is quantized in a strong magnetic field) and subsequently suggested^3-5 and observed⁶ to exist without a magnetic field, by virtue of other effects such as strong spin-orbit interaction. These were systems of correlated electrons. During the past decade, the concepts of topological physics have been introduced into other fields, including microwaves^7,8, photonic systems^9,10, cold atoms^11,12, acoustics^13,14 and even mechanics¹⁵. Recently, topological insulators were suggested to be possible in exciton-polariton systems^16-18 organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Exciton-polaritons are part-light, part-matter quasiparticles that emerge from strong coupling of quantum-well excitons and cavity photons¹⁹. Accordingly, the predicted topological effects differ from all those demonstrated thus far. Here we demonstrate experimentally an exciton-polariton topological insulator. Our lattice of coupled semiconductor microcavities is excited non-resonantly by a laser, and an applied magnetic field leads to the unidirectional flow of a polariton wavepacket around the edge of the array. This chiral edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real space and Fourier space to measure photoluminescence and thus visualize the mode as it propagates. We demonstrate that the topological edge mode goes around defects, and that its propagation direction can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for topological phenomena that involve light-matter interaction, amplification and the interaction of exciton-polaritons as a nonlinear many-body system.

Generation of Quantized Polaritons below the Condensation Threshold

Exciton polaritons in high quality semiconductor microcavities can travel long macroscopic distances (>100  μm) due to their ultralight effective mass. The polaritons are repelled from optically pumped exciton reservoirs where they are formed; however, their spatial dynamics is not as expected for pointlike particles. Instead we show polaritons emitted into waveguides travel orthogonally to the repulsive potential gradient and can only be explained if they are emitted as macroscopic delocalized quantum particles, even before they form Bose condensates.

Photon-Number-Resolved Measurement of an Exciton-Polariton Condensate

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.

Quantum metrology beyond Heisenberg limit with entangled matter wave solitons

Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.

Two-dimensional semiconductors in the regime of strong light-matter coupling

The optical properties of transition metal dichalcogenide monolayers are widely dominated by excitons, Coulomb-bound electron-hole pairs. These quasi-particles exhibit giant oscillator strength and give rise to narrow-band, well-pronounced optical transitions, which can be brought into resonance with electromagnetic fields in microcavities and plasmonic nanostructures. Due to the atomic thinness and robustness of the monolayers, their integration in van der Waals heterostructures provides unique opportunities for engineering strong light-matter coupling. We review first results in this emerging field and outline future opportunities and challenges.

Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities

The realization of exciton polaritons—hybrid excitations of semiconductor quantum well excitons and cavity photons—has been of great technological and scientific significance. In particular, the short-range collisional interaction between excitons has enabled explorations into a wealth of nonequilibrium and hydrodynamical effects that arise in weakly nonlinear polariton condensates. Yet, the ability to enhance optical nonlinearities would enable quantum photonics applications and open up a new realm of photonic many-body physics in a scalable and engineerable solid-state environment. Here we outline a route to such capabilities in cavity-coupled semiconductors by exploiting the giant interactions between excitons in Rydberg states. We demonstrate that optical nonlinearities in such systems can be vastly enhanced by several orders of magnitude and induce nonlinear processes at the level of single photons.

Strong optical nonlinearities in polariton systems open up experiments on quantum-correlated states of light. Here, Walther et al. study Rydberg excitons inside a cavity and show how enhanced nonlinearities could be achieved in such systems.

First observation of the quantized exciton-polariton field and effect of interactions on a single polariton

Polaritons are quasi-particles that originate from the coupling of light with matter and that demonstrate quantum phenomena at the many-particle mesoscopic level, such as Bose-Einstein condensation and superfluidity. A highly sought and long-time missing feature of polaritons is a genuine quantum manifestation of their dynamics at the single-particle level. Although they are conceptually perceived as entangled states and theoretical proposals abound for an explicit manifestation of their single-particle properties, so far their behavior has remained fully accounted for by classical and mean-field theories. We report the first experimental demonstration of a genuinely quantum state of the microcavity polariton field, by swapping a photon for a polariton in a two-photon entangled state generated by parametric downconversion. When bringing this single-polariton quantum state in contact with a polariton condensate, we observe a disentangling with the external photon. This manifestation of a polariton quantum state involving a single quantum unlocks new possibilities for quantum information processing with interacting bosons.

Evolution of Temporal Coherence in Confined Exciton-Polariton Condensates

We study the influence of spatial confinement on the second-order temporal coherence of the emission from a semiconductor microcavity in the strong coupling regime. The confinement, provided by etched micropillars, has a favorable impact on the temporal coherence of solid state quasicondensates that evolve in our device above threshold. By fitting the experimental data with a microscopic quantum theory based on a quantum jump approach, we scrutinize the influence of pump power and confinement and find that phonon-mediated transitions are enhanced in the case of a confined structure, in which the modes split into a discrete set. By increasing the pump power beyond the condensation threshold, temporal coherence significantly improves in devices with increased spatial confinement, as revealed in the transition from thermal to coherent statistics of the emitted light.

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.

Room temperature strong coupling in a semiconductor microcavity with embedded AlGaAs quantum wells designed for polariton lasing

We report a systematic study of the temperature and excitation density behavior of an AlAs/AlGaAs, vertically emitting microcavity with embedded ternary Al_0.20Ga_0.80As/AlAs quantum wells in the strong coupling regime. Temperature-dependent photoluminescence measurements of the bare quantum wells indicate a crossover from the type-II indirect to the type-I direct transition. The resulting mixing of quantum well and barrier ground states in the conduction band leads to an estimated exciton binding energy systematically exceeding 25 meV. The formation of exciton-polaritons is evidenced in our quantum well microcavity via reflection measurements with Rabi splittings ranging from (13.93 ± 0.15) meV at low temperature (30 K) to (8.58 ± 0.40) meV at room temperature (300 K). Furthermore, the feasibility of polariton laser operation is demonstrated under non-resonant optical excitation conditions at 20 K and emission around 1.835 eV.

Relaxation Oscillations and Ultrafast Emission Pulses in a Disordered Expanding Polariton Condensate

Semiconductor microcavities are often influenced by structural imperfections, which can disturb the flow and dynamics of exciton-polariton condensates. Additionally, in exciton-polariton condensates there is a variety of dynamical scenarios and instabilities, owing to the properties of the incoherent excitonic reservoir. We investigate the dynamics of an exciton-polariton condensate which emerges in semiconductor microcavity subject to disorder, which determines its spatial and temporal behaviour. Our experimental data revealed complex burst-like time evolution under non-resonant optical pulsed excitation. The temporal patterns of the condensate emission result from the intrinsic disorder and are driven by properties of the excitonic reservoir, which decay in time much slower with respect to the polariton condensate lifetime. This feature entails a relaxation oscillation in polariton condensate formation, resulting in ultrafast emission pulses of coherent polariton field. The experimental data can be well reproduced by numerical simulations, where the condensate is coupled to the excitonic reservoir described by a set of rate equations. Theory suggests the existence of slow reservoir temporarily emptied by stimulated scattering to the condensate, generating ultrashort pulses of the condensate emission.

Ultra-low threshold polariton lasing at room temperature in a GaN membrane microcavity with a zero-dimensional trap

Polariton lasers are coherent light sources based on the condensation of exciton-polaritons in semiconductor microcavities, which occurs either in the kinetic or thermodynamic (Bose-Einstein) regime. Besides their fundamental interest, polariton lasers have the potential of extremely low operating thresholds. Here, we demonstrate ultra-low threshold polariton lasing at room temperature, using an all-dielectric, GaN membrane-based microcavity, with a spontaneously-formed zero-dimensional trap. The microcavity is fabricated using an innovative method, which involves photo-electrochemical etching of an InGaN sacrificial layer and allows for the incorporation of optimally-grown GaN active quantum wells inside a cavity with atomically-smooth surfaces. The resulting structure presents near-theoretical Q-factors and pronounced strong-coupling effects, with a record-high Rabi splitting of 64 meV at room-temperature. Polariton lasing is observed at threshold carrier densities 2.5 orders of magnitude lower than the exciton saturation density. Above threshold, angle-resolved emission spectra reveal an ordered pattern in k-space, attributed to polariton condensation at discrete levels of a single confinement site. This confinement mechanism along with the high material and optical quality of the microcavity, accounts for the enhanced performance of our polariton laser, and pave the way for further developments in the area of robust room temperature polaritonic devices.

Prototype of a bistable polariton field-effect transistor switch

Microcavity exciton polaritons are promising candidates to build a new generation of highly nonlinear and integrated optoelectronic devices. Such devices range from novel coherent light emitters to reconfigurable potential landscapes for electro-optical polariton-lattice based quantum simulators as well as building blocks of optical logic architectures. Especially for the latter, the strongly interacting nature of the light-matter hybrid particles has been used to facilitate fast and efficient switching of light by light, something which is very hard to achieve with weakly interacting photons. We demonstrate here that polariton transistor switches can be fully integrated in electro-optical schemes by implementing a one-dimensional polariton channel which is operated by an electrical gate rather than by a control laser beam. The operation of the device, which is the polariton equivalent to a field-effect transistor, relies on combining electro-optical potential landscape engineering with local exciton ionization to control the scattering dynamics underneath the gate. We furthermore demonstrate that our device has a region of negative differential resistance and features a completely new way to create bistable behavior.

Tunable Bragg polaritons and nonlinear emission from a hybrid metal-unfolded ZnSe-based microcavity

Strong light-matter interaction in Bragg structures possesses several advantages over conventional microcavity system. These structures provide an opportunity to incorporate a large number of quantum wells without increasing the mode volume. Further, it is expected that the strong coupling could occur over the entire thickness of the Bragg structure, and the system offers an improved overlap between exciton wave function and light mode. However, advanced experiments in Bragg structures require a precise control and manipulation of quantum states of Bragg polaritons. Here, we propose and experimentally demonstrate novel methods for the modulation of Bragg polariton eigenstates. The modulation will be shown to even exceed 10 meV if the thickness of the top layer of the ZnSe-based Bragg structure is changed or if a thin silver layer is deposited on top of the structure. The Q value of the Bragg mode will be enhanced by a factor of 2.3 for a 30 nm silver layer. In addition, we report on the observation of nonlinear emission of the lower Bragg polariton mode in the hybrid structure being achieved when excitation dependent measurements are performed. Our results open the door to create a confined Bragg polariton system similar to conventional microcavities.

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.

Visualising Berry phase and diabolical points in a quantum exciton-polariton billiard

Diabolical points (spectral 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 beam, 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 visualization of the Berry phase associated with the diabolical point. The Berry phase is observed and measured by direct imaging of the macroscopic exciton-polariton probability densities.

Observation of a hybrid state of Tamm plasmons and microcavity exciton polaritons

We present evidence for the existence of a hybrid state of Tamm plasmons and microcavity exciton polaritons in a II-VI material based microcavity sample covered with an Ag metal layer. The bare cavity mode shows a characteristic anticrossing with the Tamm-plasmon mode, when microreflectivity measurements are performed for different detunings between the Tamm plasmon and the cavity mode. When the Tamm-plasmon mode is in resonance with the cavity polariton four hybrid eigenstates are observed due to the coupling of the cavity-photon mode, the Tamm-plasmon mode, and the heavy- and light-hole excitons. If the bare Tamm-plasmon mode is tuned, these resonances will exhibit three anticrossings. Experimental results are in good agreement with calculations based on the transfer matrix method as well as on the coupled-oscillators model. The lowest hybrid eigenstate is observed to be red shifted by about 13 meV with respect to the lower cavity polariton state when the Tamm plasmon is resonantly coupled with the cavity polariton. This spectral shift which is caused by the metal layer can be used to create a trapping potential channel for the polaritons. Such channels can guide the polariton propagation similar to one-dimensional polariton wires.