Bose-Einstein Condensation Of Polaritons Research Articles

Spatial Coherence of Exciton–Polariton Bose–Einstein Condensates

Abstract The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir.

Stability of vortices in exciton-polariton condensates with spin–orbital-angular-momentum coupling

The existence and dynamics of stable quantized vortices is an important subject of quantum many-body physics. Spin–orbital-angular-momentum coupling (SOAMC), a special type of spin–orbit coupling, has been experimentally achieved to create vortices in atomic Bose–Einstein condensates (BEC). Here, we generalize the concept of SOAMC to a two-component polariton BEC and analyze the emergence and configuration of vortices under a finite-size circular pumping beam. We find that the regular configuration of vortex lattices induced by a finite-size circular pump is significantly distorted by the spatially dependent Raman coupling of SOAMC, even in the presence of a repulsive polariton interaction which can assist the forming of stable vortex configuration. Meanwhile, a pair of vortices induced by SOAMC located at the center of polariton cloud remains stable. When the Raman coupling is sufficiently strong and interaction is weak, the vortices spiraling in from the edge of polariton cloud will disrupt the polariton BEC.

Critical fluctuations in a confined driven-dissipative quantum condensate.

Phase fluctuations determine the low-energy properties of quantum condensates. However, at the condensation threshold, both density and phase fluctuations are relevant. While strong emphasis has been given to the investigation of phase fluctuations, which dominate the physics of the quantum system away from the critical point, number fluctuations have been much less explored even in thermal equilibrium. In this work, we report experimental observation and theoretical description of fluctuations in a circularly confined nonequilibrium Bose-Einstein condensate of polaritons near the condensation threshold. We observe critical fluctuations, which combine the number fluctuations of a single-mode condensate state and competition between different states. The latter is analogous to mode hopping in photon lasers. Our theoretical analysis indicates that this phenomenon is of a quantum character, while classical noise of the pump is not sufficient to explain the experiments. The manifestation of a critical quantum state competition unlocks possibilities for the study of condensate formation while linking to practical realizations in photonic lasers.

Non-Markovian Stochastic Gross–Pitaevskii Equation for the Exciton–Polariton Bose–Einstein Condensate

Non-Markovian Stochastic Gross–Pitaevskii Equation for the Exciton–Polariton Bose–Einstein Condensate

Dual Control of Enhanced Quasi-Bound States in the Continuum Emission from Resonant c-Si Metasurfaces.

Optical bound states in the continuum (BICs) offer strong interactions with quantum emitters and have been extensively studied for manipulating spontaneous emission, lasing, and polariton Bose-Einstein condensation. However, the out-coupling efficiency of quasi-BIC emission, crucial for practical light-emitting devices, has received less attention. Here, we report an adaptable approach for enhancing quasi-BIC emission from a resonant monocrystalline silicon (c-Si) metasurface through lattice and multipolar engineering. We identify dual-BICs originating from electric quadrupoles (EQ) and out-of-plane magnetic dipoles, with EQ quasi-BICs exhibiting concentrated near-fields near the c-Si nanodisks. The enhanced fractional radiative local density of states of EQ quasi-BICs overlaps spatially with the emitters, promoting efficient out-coupling. Furthermore, coupling the EQ quasi-BICs with Rayleigh anomalies enhances directional emission intensity, and we observe inherent opposite topological charges in the multipolarly controlled dual-BICs. These findings provide valuable insights for developing efficient nanophotonic devices based on quasi-BICs.

Observation of ultra-large Rabi splitting in the plasmon-exciton polaritons at room temperature

Abstract Modifying the light–matter interactions in the plasmonic structures and the two-dimensional (2D) materials not only advances the deeper understanding of the fundamental studies of many-body physics but also provides the opportunities for exploration of novel 2D plasmonic polaritonic devices. Here, we report the plasmon-exciton coupling in the hybrid system with a plasmonic metasurface which can confine the electric field in an extremely compact mode volume. Because of the 2D feature of the designed and fabricated Al plasmonic metasurface, the confined electronic field is distributed in the plane with the same orientation as that of the exciton dipole moment in the transition metal dichalcogenides monolayers. By finely tuning the geometric size of the plasmonic nanostructures, we can significantly modify the dispersion relation of the coupled plasmon and the exciton. Our system shows a strong coupling behavior with an achieved Rabi splitting up to ∼200 meV at room temperature, in ambient conditions. The effective tailoring of the plasmon-exciton coupling with the plasmonic metasurfaces provides the testing platform for studying the quantum electromagnetics at the subwavelength scale as well as exploring plasmonic polariton Bose–Einstein condensation at room temperature.

Self-Induced Valley Bosonic Stimulation of Exciton Polaritons in a Monolayer Semiconductor

The newly discovered valley degree of freedom in atomically thin two-dimensional transition metal dichalcogenides offers a promising platform to explore rich nonlinear physics, such as spinor Bose-Einstein condensate and novel valleytronics applications. However, the critical nonlinear effect, such as valley polariton bosonic stimulation, has long remained an unresolved challenge due to the generation of limited polariton ground state densities necessary to induce the stimulated scattering of polaritons in specific valleys. Here, we report the self-induced valley bosonic stimulation of exciton polaritons via spin-valley locking in a WS_{2} monolayer microcavity. This is achieved by the resonant injection of valley polaritons at specific energy and wave vector, which allows spin-polarized polaritons to efficiently populate their ground state and induce a valley-dependent bosonic stimulation. As a result, we observe the nonlinear self-amplification of polariton emission from the valley-dependent ground state. Our finding paves the way for the investigation of spin ordering and phase transitions in transition metal dichalcogenides polariton Bose-Einstein condensate, offering a promising route for the realization of polariton spin lattices in moiré polariton systems and spin lasers.

Interaction between an Impurity and Nonlinear Excitations in a Polariton Condensate.

Exploring the dynamics of a mobile impurity immersed in field excitations is challenging, as it requires to account for the entanglement between the impurity and the surrounding excitations. To this end, the impurity's effective mass has to be considered as finite, rather than infinite. Here, we theoretically investigate the interaction between a finite-mass impurity and a dissipative soliton representing nonlinear excitations in the polariton Bose-Einstein condensate (BEC). Using the Lagrange variational method and the open-dissipative Gross-Pitaevskii equation, we analytically derive the interaction phase diagram between the impurity and a dissipative bright soliton in the polariton BEC. Depending on the impurity mass, we find the dissipative soliton colliding with the impurity can transmit through, get trapped, or be reflected. This work opens a new perspective in understanding the impurity dynamics when immersed in field excitations, as well as potential applications in information processing with polariton solitons.

Control over Amplification in Exciton Polariton Condensate

Exciton polariton condensates are the most well-studied case of Bose-Einstein condensation (BEC) of quasiparticles. Together with their prominent fundamental importance, the exciton-polariton condensates have a wide spectrum of engineering applications covering interferometry and metrology, different types of SQUIDs and accelerometers, and forming a universal gate set for quantum computing via the control with external laser pulses. The efficient experimental manipulation with the polariton BEC can be realized via the bosonic final-state stimulation, matter-wave amplification, or by lasing of polaritons, but a satisfactory theoretical model for such control has not been developed yet. Here we study the polariton matter-wave amplifier based on the stimulated scattering of massive particles. The amplification of the injected quasiparticles is achieved through an elastic scattering of so-called lower polaritons (LPs). Such an amplifier has many advantages compared with a standard lasing or using a photon amplifier: it can provide a sufficient gain coefficient. To develop an efficient control algorithm for the polariton amplifier we use here the dynamical model for the LP population proposed by Ciuti, Savona, et al. in 1998. The phenomenological model for the gain coefficient is based on the experiments with cold collisions of polaritons performed by Deng, Haug, and Yamamoto in 2010 and later. We use different feedback algorithms (speed gradient vs target attractor) to track efficiently the polariton population in the amplifier. We compare the pros and cons of our alternative approaches and discuss their possible engineering applications.

Stability window of trapless polariton Bose-Einstein condensates

We theoretically explore the possibility of stabilizing the trapless polariton Bose-Einstein condensates (pBECs). Exploiting the variational method, we solve the associated nonlinear, complex Gross-Pitaevskii (cGP) equation and derive the equation of motion for the amplitude and width of the condensate. These variational results described by ordinary differential equations are rewritten to perform a linear stability analysis to generate a stability window in the repulsive domain. A set of coupled nonlinear ordinary differential equations obtained through variational approach are then solved by numerical simulations through the fourth order Runge-Kutta method, which are further supported by split-step Crank-Nicholson method, thereby setting the platform for stable pBECs. In particular, we generate a window containing system parameters in the $g_1-\gamma_{eff}$ space within which the system can admit stable condensates. The highlight of the results is that one observes beating effects in the real time evolution of the condensates with attractive interactions much similar to multicomponent BECs, and their periodicity can be varied by manipulating linear and nonlinear loss/gain terms. For repulsive condensates, one notices the stretching of the density.

Bose enhancement of excitation-energy transfer with molecular-exciton-polariton condensates.

Room-temperature Bose-Einstein condensates (BECs) of exciton polaritons have been realized in organic molecular systems owing to strong light-matter interaction, strong exciton binding energy, and low effective mass of a polaritonic particle. These molecular-exciton-polariton BECs have demonstrated their potential in nonlinear optics and optoelectronic applications. In this study, we first demonstrate that molecular-polariton BECs can be utilized for Bose enhancement of excitation-energy transfer (EET) in a molecular system with an exciton donor coupled to a group of exciton acceptors that are further strongly coupled to a single mode of an optical cavity. Similar to the stimulated emission of light in which photons are bosonic particles, a greater rate of EET is observed if the group of acceptors is prepared in the exciton-polariton BEC state than if the acceptors are initially either in their electronic ground states or in a normal excited state with an equal average number of molecular excitations. The Bose enhancement also manifests itself as the growth of the EET rate with an increasing number of exciton polaritons in the BEC. Finally, a generalization to the EET in many-donor-many-acceptor molecular systems is considered, and a permutation-symmetry-based approach to suppress the EET to the huge manifold of dark states in the acceptor group is proposed to facilitate the Bose-enhanced EET to the polariton BEC.

Polariton Bose-Einstein condensate from a bound state in the continuum.

Bound states in the continuum (BICs)1-3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose-Einstein condensation of polaritons-hybrid light-matter excitations-occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reachednot in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits.

Exact Analytical Solution for the Density Matrix of a Nonequilibrium Polariton Bose-Einstein Condensate.

In this Letter, we give an analytical quantum description of a nonequilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a nonequilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the nonequilibrium nature of polariton systems, we show the average population of polariton states exhibits the Bose-Einstein distribution with an almost zero effective chemical potential above the condensation threshold similar to an equilibrium BEC. We demonstrate that above threshold the effective temperature of polaritons drops below the reservoir temperature.

Dynamics of Two Dark Solitons in a Polariton Condensate

We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping, based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation. The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach. In particular, the analytical expression of the effective potential between two dark solitons is given. The resulting equation of motion captures how the open-dissipative character of a polariton Bose–Einstein condensate affects properties of dynamics of two-dark soliton, i.e., two-dark soliton relax by blending with the background at a finite time. We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity, in excellent agreement with the analytical results. The prediction of this work is sufficient for the experimental observations within current facilities.

Stimulated Axion-Like Bipolariton Generation in the Globular Photonic Crystal

Axion is the dark particle introduced to the quantum chromodynamics to solve the strong CP-problem. Because of its dark nature, there are many indirect evidences, but axion itself have not been registered till now. In the paper, we report the observation of dark axion-like particles formed by the polariton coupling in the resonant microcavity of a globular photonic crystal. To overcome the very small cross-section, we use the Bose-Einstein condensation of polaritons into the nearest-to-the-surface microcavity of an opal-like globular photonic crystal. This way, the synchronicity conditions are met and all polaritons have the same wavefunction to be coupled. Moreover, the giant density of states of a Bose-condensate makes polariton coupling not only allowed but stimulated. At the experiment, we observe “Light Shining through a Wall” Primakoff effect which proves dark particles. The additional spectral peak at the unitary polariton line of a maximal transparency of a crystal allows to differ bipolaritons from other particles. The results can be used not only to generate dark particles at a lab, but also to get a laboratory source of an optical-frequency gravitational waves.

Dynamical evolution study of exciton–polariton Bose–Einstein condensate with vortex manipulation

For the exciton–polariton BEC system modulated by vortex light, we study its evolution based on the driven-dissipative Gross–Pitaevskii equation model. Via modified variational method, we first derive the two-dimensional system’s evolution pattern from the initially coherent state prepared by vortex light modulation for non-rotating states and rotating states with various angular velocities. We identify close qualitatively matched patterns by comparing our theoretically derived evolution patterns with that from pure numerical simulation, demonstrating the applicability of our theoretical treatment presented. The derived exciton–polariton evolution pattern formulation can then be used to guide experimental observations of vortex manipulation effects for the exciton–polariton BEC system, with the possible identification of quantum gyroscopic effects.

Enhanced Light–Matter Interaction and Polariton Relaxation by the Control of Molecular Orientation

AbstractExciton‐polaritons, in which the electronic state of an excited organic molecule and a photonic state are strongly coupled, can form a Bose–Einstein condensate (BEC) at room temperature. However, so far, the reported thresholds of organic polariton BECs under optical excitation are as high asPth = 11–500 μJ cm–2. One route toward lowering the condensation threshold is to increase the Rabi energy by aligning the molecular transition dipole moments. In this report, it is demonstrated that control of the orientation of a perylene‐based discotic dye, which is able to self‐organize in mesogenic columnar structures, can significantly enhance exciton–photon interaction and polariton relaxation rate in optical cavities. These results show the importance of the molecular orientation for strong light–matter interactions and provide a promising strategy toward the realization of an organic low threshold polariton BEC system and electrically driven organic polariton BEC.

Spontaneous Formations of Dynamical Steady States in Polariton Condensates

We present a numerical analysis on dynamical steady states of polariton Bose–Einstein condensates (BECs) in an incoherent exciton reservoir driven by a ring-shaped optical pump. The balance between the loss and gain of polariton BEC induces a variety of steady states with different configurations, including approximate Gaussian distribution and topological defects, such as vortex–antivortex pairs, vortices with a winding number, and solitons. Besides, the system becomes unstable under fast decay rates and small pumping ring, where BECs can no longer exist in the long-time limit. We also confirm the soliton is dynamically stable in this system, with a steady polariton current induced by the repulsive polariton–polariton and polariton–exciton interactions.

Room temperature exciton\u2013polariton Bose\u2013Einstein condensation in organic single-crystal microribbon cavities

Exciton–polariton Bose–Einstein condensation (EP BEC) is of crucial importance for the development of coherent light sources and optical logic elements, as it creates a new state of matter with coherent nature and nonlinear behaviors. The demand for room temperature EP BEC has driven the development of organic polaritons because of the large binding energies of Frenkel excitons in organic materials. However, the reliance on external high-finesse microcavities for organic EP BEC results in poor compactness and integrability of devices, which restricts their practical applications in on-chip integration. Here, we demonstrate room temperature EP BEC in organic single-crystal microribbon natural cavities. The regularly shaped microribbons serve as waveguide Fabry–Pérot microcavities, in which efficient strong coupling between Frenkel excitons and photons leads to the generation of EPs at room temperature. The large exciton–photon coupling strength due to high exciton densities facilitates the achievement of EP BEC. Taking advantages of interactions in EP condensates and dimension confinement effects, we demonstrate the realization of controllable output of coherent light from the microribbons. We hope that the results will provide a useful enlightenment for using organic single crystals to construct miniaturized polaritonic devices.

A weakly-interacting many-body system of Rydberg polaritons based on electromagnetically induced transparency

The combination of Rydberg atoms and electromagnetically induced transparency (EIT) has been extensively studied in the strong-interaction regime. Here we proposed utilizing an EIT medium with a high optical depth (OD) and a Rydberg state of low principal quantum number to create a many-body system of Rydberg polaritons in the weak-interaction regime. The phase shift and attenuation induced by the dipole–dipole interaction (DDI) were still significant, and can be viewed as the consequences of elastic and inelastic collisions among Rydberg polaritons. We further observed that the width of the transverse momentum distribution of Rydberg polaritons at the exit of the system became notably smaller as compared with that at the entrance. The observation demonstrates the cooling effect in this system. The μs-long interaction time due to the high-OD EIT medium plus the μm2-size collision cross section due to the DDI suggests a feasible platform of polariton Bose–Einstein condensation.