Synchronized and desynchronized phases of exciton-polariton condensates in the presence of disorder

Asynchronous locking in metamaterials of fluids of light and sound

Lattices of exciton-polariton condensates represent an attractive platform for the study and implementation of non-Hermitian bosonic quantum systems with strong non-linear interactions. The possibility to actuate on them with a time dependent drive could provide for example the means to induce resonant inter-level transitions, or to perform Floquet engineering or Landau-Zener-Stückelberg state preparation. Here, we introduce polaromechanical metamaterials, two-dimensional arrays of μm-sized traps confining zero-dimensional light-matter polariton fluids and GHz phonons. A strong exciton-mediated polariton-phonon interaction induces a time-dependent inter-site polariton coupling J(t) with remarkable consequences for the dynamics. When locally perturbed by continuous wave optical excitation, a mechanical self-oscillation sets-in and polaritons respond by locking the energy detuning between neighbor sites at integer multiples of the phonon energy, evidencing asynchronous locking involving the polariton and phonon fields. These results open the path for the coherent control of dissipative quantum light fluids with hypersound in a scalable platform.

Emulating the local Kuramoto model with an injection-locked photonic crystal laser array

The Kuramoto model is a mathematical model for describing the collective synchronization phenomena of coupled oscillators. We theoretically demonstrate that an array of coupled photonic crystal lasers emulates the Kuramoto model with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our novel strategy employs indirect coupling between lasers via additional cold cavities. By installing cold cavities between laser cavities, we avoid the strong coupling of lasers and realize ideal mutual injection-locking with effective non-delayed dissipative coupling. First, after discussing the limit cycle interpretation of laser oscillation, we demonstrate the synchronization of two indirectly coupled lasers by numerically simulating coupled-mode equations. Second, by performing a phase reduction analysis, we show that laser dynamics in the proposed device can be mapped to the local Kuramoto model. Finally, we briefly demonstrate that a chain of indirectly coupled photonic crystal lasers actually emulates the one-dimensional local Kuramoto chain. We also argue that our proposed structure, which consists of periodically aligned cold cavities and laser cavities, will best be realized by using state-of-the-art buried multiple quantum well photonic crystals.

Designs toward synchronization of optical limit cycles with coupled silicon photonic crystal microcavities

A driven high-Q Si microcavity is known to exhibit limit cycle oscillation originating from carrier-induced and thermo-optic nonlinearities. We propose a novel nanophotonic device to realize synchronized optical limit cycle oscillations with coupled silicon (Si) photonic crystal (PhC) microcavities. Here, coupled limit cycle oscillators are realized by using coherently coupled Si PhC microcavities. By simulating coupled-mode equations, we theoretically demonstrate mutual synchronization (entrainment) of two limit cycles induced by coherent coupling. Furthermore, we interpret the numerically simulated synchronization in the framework of phase description. Since our proposed design is perfectly compatible with current silicon photonics fabrication processes, the synchronization of optical limit cycle oscillations will be implemented in future silicon photonic circuits.

Thermal Decoherence of a Nonequilibrium Polariton Fluid

Exciton polaritons constitute a unique realization of a quantum fluid interacting with its environment. Using selenide-based microcavities, we exploit this feature to warm up a polariton condensate in a controlled way and monitor its spatial coherence. We determine directly the amount of heat picked up by the condensate by measuring the phonon-polariton scattering rate and comparing it with the loss rate. We find that, upon increasing the heating rate, the spatial coherence length decreases markedly, while localized phase structures vanish, in good agreement with a stochastic mean-field theory. From the thermodynamical point of view, this regime is unique, as it involves a nonequilibrium quantum fluid with no well-defined temperature but which is nevertheless able to pick up heat with dramatic effects on the order parameter.

Macroscopic Two-Dimensional Polariton Condensates

We report a record-size, two-dimensional polariton condensate of a fraction of a millimeter radius free from the presence of an exciton reservoir. This macroscopically occupied state is formed by the ballistically expanding polariton flow that relaxes and condenses over a large area outside of the excitation spot. The density of this trap-free condensate is <1  polariton/μm^{2}, reducing the phase noise induced by the interaction energy. Moreover, the backflow effect, recently predicted for the nonparabolic polariton dispersion, is observed here for the first time in the fast-expanding wave packet.

Ghost Branch Photoluminescence From a Polariton Fluid Under Nonresonant Excitation

An expanding polariton condensate is investigated under pulsed nonresonant excitation with a small laser pump spot. Far above the condensation threshold we observe a pronounced increase in the dispersion curvature, with a subsequent linearization of the spectrum and strong luminescence from a ghost branch orthogonally polarized with respect to the linearly polarized condensate emission. Polarization of both branches is understood in terms of spin-dependent polariton-polariton scattering. The presence of the ghost branch has been confirmed in time-resolved measurements. The effects of disorder and dissipation in the photoluminescence of polariton condensates and their excitations are discussed.

Spatial Coherence and Stability in a Disordered Organic Polariton Condensate

Although only a handful of organic materials have shown polariton condensation, their study is rapidly becoming more accessible. The spontaneous appearance of long-range spatial coherence is often recognized as a defining feature of such condensates. In this Letter, we study the emergence of spatial coherence in an organic microcavity and demonstrate a number of unique features stemming from the peculiarities of this material set. Despite its disordered nature, we find that correlations extend over the entire spot size, and we measure g(1)(r,r') values of nearly unity at short distances and of 50% for points separated by nearly 10  μm . We show that for large spots, strong shot-to-shot fluctuations emerge as varying phase gradients and defects, including the spontaneous formation of vortices. These are consistent with the presence of modulation instabilities. Furthermore, we find that measurements with flat-top spots are significantly influenced by disorder and can, in some cases, lead to the formation of mutually incoherent localized condensates.

Frequency combs with weakly lasing exciton-polariton condensates

We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton interaction generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak distributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot noise arising from the influx of polaritons. That results in a complex inhomogeneous line broadening.

Synchronization in a semiclassical Kuramoto model

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.

Room-temperature Bose-Einstein condensation of cavity exciton-polaritons in a polymer

A Bose-Einstein condensate (BEC) is a state of matter in which extensive collective coherence leads to intriguing macroscopic quantum phenomena. In crystalline semiconductor microcavities, bosonic quasiparticles, known as exciton-polaritons, can be created through strong coupling between bound electron-hole pairs and the photon field. Recently, a non-equilibrium BEC (ref. ) and superfluidity have been demonstrated in such structures. With organic crystals grown inside dielectric microcavities, signatures of polariton lasing have been observed. However, owing to the deleterious effects of disorder and material imperfection on the condensed phase, only crystalline materials of the highest quality have been used until now. Here we demonstrate non-equilibrium BEC of exciton-polaritons in a polymer-filled microcavity at room temperature. We observe thermalization of polaritons and, above a critical excitation density, clear evidence of condensation at zero in-plane momentum, namely nonlinear behaviour, blueshifted emission and long-range coherence. The key signatures distinguishing the behaviour from conventional photon lasing are presented. As no crystal growth is involved, our approach radically reduces the complexity of experiments to investigate BEC physics and paves the way for a new generation of opto-electronic devices, taking advantage of the processability and flexibility of polymers.

Spontaneous pattern formation in a polariton condensate

Exciton-polariton condensation can be regarded as a self-organization phenomenon, where phase ordering is established among particles in the system. In such condensed systems, further ordering can occur in the particle density distribution, under particular experimental conditions. In this work we report on spontaneous pattern formation in a polariton condensate under nonresonant optical pumping. The slightly elliptical ring-shaped excitation laser that we employ forces condensation to occur into a single-energy state with periodic boundary conditions, giving rise to a multilobe standing-wave patterned state.

Polariton condensation in a one-dimensional disordered potential

We study the coherence and density modulation of a nonequilibrium exciton-polariton condensate in a one-dimensional valley with disorder. By means of interferometric measurements we evidence a modulation of the first-order coherence function and we relate it to a disorder-induced modulation of the condensate density, that increases as the pump power is increased. The nonmonotonic spatial coherence function is found to be the result of the strong nonequilibrium character of the one-dimensional system, in the presence of disorder.

Superfluidity and critical velocities in nonequilibrium Bose-Einstein condensates

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.

Dynamics of long-range ordering in an exciton-polariton condensate

We report on time-resolved measurements of the first order spatial coherence in an exciton-polariton Bose-Einstein condensate. Long-range spatial coherence is found to set in right at the onset of stimulated scattering, on a picosecond time scale. The coherence reaches its maximum value after the population and decays slowly, staying up to a few hundred picoseconds. This behavior can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential.