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 magnets3-6 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 coherence8-17. 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 laws18,19, 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'.

Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices.

We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n = 0 and n = ±1 Landau levels, experimentally demonstrating a novel way of engineering propagating edge states in photonic lattices. In light of recent advances in the enhancement of polariton-polariton nonlinearities, the Landau levels reported here are promising for the study of the interplay between pseudomagnetism and interactions in a photonic system.

Excitation Ladder of Cavity Polaritons.

Multidimensional coherent spectroscopy directly unravels multiply excited states that overlap in a linear spectrum. We report multidimensional coherent optical photocurrent spectroscopy in a semiconductor polariton diode and explore the excitation ladder of cavity polaritons. We measure doubly and triply avoided crossings for pairs and triplets of exciton polaritons, demonstrating the strong coupling between light and dressed doublet and triplet semiconductor excitations. These results demonstrate that multiply excited excitonic states strongly coupled to a microcavity can be described as two coupled quantum-anharmonic ladders.

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.

Treatment of feline injection-site sarcoma with surgery and iridium-192 brachytherapy: retrospective evaluation of 22 cats.

OBJECTIVES: The aim of this retrospective descriptive study was to determine the effectiveness of using iridium implants in addition to surgery in cats with feline injection-site sarcomas (FISSs) in terms of time to progression and disease-specific survival and to identify prognostic factors for patient outcome. METHODS: Medical records of cats presented at our institution with FISS were reviewed. Inclusion criteria included histologic diagnosis of a tumor type associated with post-injection neoplastic development, tumor located at a site associated with vaccination, no other therapies prior to the administration of brachytherapy with the exception of surgery and adequate follow-up data. RESULTS: Twenty-two cats with FISS were treated with surgery and brachytherapy delivered by postoperative iridium-192 interstitial implants. Radiation doses ranged from 4000 to 6000 cGy (median dose 5079.55 cGy), with most doses delivered over 7 days. The median number of surgeries prior to brachytherapy was one (range 1-4). The complications associated with postoperative brachytherapy were typically mild, although four cats developed more severe complications. The median time to progression for all cats was 619 days and disease-specific survival time for all cats was 1242 days. The 1 and 2 year tumor-free rates in these cats were 63.6% and 40.9%, respectively. The local failure rate was 54.5% and the distant failure rate was 13.6% due to lung metastasis. There was a significant difference in time to progression of cats that had a single surgery performed prior to brachytherapy and those that had multiple surgeries (undefined vs 310 days; P = 0.01). There were no other statistically significant identified prognostic factors. CONCLUSIONS AND RELEVANCE: These data suggest that the addition of brachytherapy postoperatively in cats with FISS was well tolerated and is comparable to other forms of adjuvant therapy.

Dispersion relation of the collective excitations in a resonantly driven polariton fluid.

Exciton-polaritons in semiconductor microcavities constitute the archetypal realization of a quantum fluid of light. Under coherent optical drive, remarkable effects such as superfluidity, dark solitons or the nucleation of vortices have been observed, and can be all understood as specific manifestations of the condensate collective excitations. In this work, we perform a Brillouin scattering experiment to measure their dispersion relation [Formula: see text] directly. The results, such as a speed of sound which is apparently twice too low, cannot be explained upon considering the polariton condensate alone. In a combined theoretical and experimental analysis, we demonstrate that the presence of an excitonic reservoir alongside the polariton condensate has a dramatic influence on the characteristics of the quantum fluid, and explains our measurement quantitatively. This work clarifies the role of such a reservoir in polariton quantum hydrodynamics. It also provides an unambiguous tool to determine the condensate-to-reservoir fraction in the quantum fluid, and sets an accurate framework to approach ideas for polariton-based quantum-optical applications.

Emergence of quantum correlations from interacting fibre-cavity polaritons.

Over the past decade, exciton-polaritons in semiconductor microcavities have revealed themselves as one of the richest realizations of a light-based quantum fluid1, subject to fascinating new physics and potential applications2-6. For instance, in the regime of large two-body interactions, polaritons can be used to manipulate the quantum properties of a light field7-9. In this work, we report on the emergence of quantum correlations in laser light transmitted through a fibre-cavity polariton system. We observe a dispersive shape of the autocorrelation function around the polariton resonance that indicates the onset of this regime. The weak amplitude of these correlations indicates a state that still remains far from a low-photon-number state. Nonetheless, given the underlying physical mechanism7, our work opens up the prospect of eventually using polaritons to turn laser light into single photons.

Two-photon injection of polaritons in semiconductor microstructures.

We experimentally demonstrate that two-photon pumping of "dark" excitons in quantum wells embedded in semiconductor microcavities can result in exciton-polariton injection and photon lasing. In the case of a semiconductor micropillar pumped at half of the exciton frequency, we observe a clear threshold behavior, characteristic of the vertical cavity surface emitting laser transition. These results are interpreted in terms of stimulated emission of terahertz photons, which allows for conversion of "dark" excitons into exciton-polaritons.

Formation and control of Turing patterns in a coherent quantum fluid.

Nonequilibrium patterns in open systems are ubiquitous in nature, with examples as diverse as desert sand dunes, animal coat patterns such as zebra stripes, or geographic patterns in parasitic insect populations. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light. The unique features of polaritons in semiconductor microcavities allow us to go one step further and to study Turing patterns in an interacting coherent quantum fluid. We demonstrate formation and control of these patterns. We also demonstrate the promise of these quantum Turing patterns for applications, such as low-intensity ultra-fast all-optical switches.

High-Q planar organic-inorganic Perovskite-based microcavity.

We report on the fabrication of a perovskite-based ((C6H5C2H4 - NH3)2 PbI4) planar microcavity with a technique of a top dielectric mirror's migration in liquid, avoiding the degradation of the perovskite material. This approach allows for increasing the cavity Q-factor, without degrading the fragile molecular material. Strong coupling of the perovskite exciton to both the cavity mode and the first Bragg mode is evidenced from angle-resolved reflectivity and microphotoluminescence measurements at room temperature; an efficient relaxation toward the minimum of the main polariton branch is observed. The measured quality factor is significantly increased compared to previous reports where a top metallic mirror was used, showing the decisive advantage of the present fabrication technique toward the achievement of stimulated effects and polariton lasing with perovskite materials.

Polariton condensation in photonic molecules.

We report on polariton condensation in photonic molecules formed by two coupled micropillars. We show that the condensation process is strongly affected by the interaction with the cloud of uncondensed excitons and thus strongly depends on the exact localization of these excitons within the molecule. Under symmetric excitation conditions, condensation is triggered on both binding and antibinding polariton states of the molecule. On the opposite, when the excitonic cloud is injected in one of the two pillars, condensation on a metastable state is observed and a total transfer of the condensate into one of the micropillars can be achieved. Our results highlight the crucial role played by relaxation kinetics in the condensation process.

Interactions in confined polariton condensates.

We investigate the effect of interactions in zero-dimensional polariton condensates. The shape of the condensate wave function is shown to be modified by repulsive interactions with the reservoir of uncondensed excitons. In large micropillar cavities, when uncondensed excitons are located at the center, the condensate is ejected toward the pillar edges. The same effect results in the generation of optical traps in wire cavities. Once polariton condensates are spatially separated from the excitonic reservoir, spectral signatures of polariton-polariton interactions within the condensate are evidenced.

Ultrabright source of entangled photon pairs.

A source of triggered entangled photon pairs is a key component in quantum information science; it is needed to implement functions such as linear quantum computation, entanglement swapping and quantum teleportation. Generation of polarization entangled photon pairs can be obtained through parametric conversion in nonlinear optical media or by making use of the radiative decay of two electron-hole pairs trapped in a semiconductor quantum dot. Today, these sources operate at a very low rate, below 0.01 photon pairs per excitation pulse, which strongly limits their applications. For systems based on parametric conversion, this low rate is intrinsically due to the Poissonian statistics of the source. Conversely, a quantum dot can emit a single pair of entangled photons with a probability near unity but suffers from a naturally very low extraction efficiency. Here we show that this drawback can be overcome by coupling an optical cavity in the form of a 'photonic molecule' to a single quantum dot. Two coupled identical pillars-the photonic molecule-were etched in a semiconductor planar microcavity, using an optical lithography method that ensures a deterministic coupling to the biexciton and exciton energy states of a pre-selected quantum dot. The Purcell effect ensures that most entangled photon pairs are emitted into two cavity modes, while improving the indistinguishability of the two optical recombination paths. A polarization entangled photon pair rate of 0.12 per excitation pulse (with a concurrence of 0.34) is collected in the first lens. Our results open the way towards the fabrication of solid state triggered sources of entangled photon pairs, with an overall (creation and collection) efficiency of 80%.

Optical bistability in a GaAs-based polariton diode.

We report on a new type of optical nonlinearity in a polariton p-i-n microcavity. Abrupt switching between the strong and weak coupling regime is induced by controlling the electric field within the cavity. As a consequence, bistable cycles are observed for low optical powers (2-3 orders of magnitude less than for Kerr induced bistability). Signatures of switching fronts propagating through the whole 300 x 300 microm2 mesa surface are evidenced.

Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities.

Polariton lasing is demonstrated on the zero-dimensional states of single GaAs/GaAlAs micropillar cavities. Under nonresonant excitation, the measured polariton ground-state occupancy is found as large as 10(4). Changing the spatial excitation conditions, competition between several polariton lasing modes is observed, ruling out Bose-Einstein condensation. When the polariton state occupancy increases, the emission blueshift is the signature of self-interaction within the half-light half-matter polariton lasing mode.

Polariton lasing vs. photon lasing in a semiconductor microcavity.

Nearly one decade after the first observation of Bose-Einstein condensation in atom vapors and realization of matter-wave (atom) lasers, similar concepts have been demonstrated recently for polaritons: half-matter, half-light quasiparticles in semiconductor microcavities. The half-light nature of polaritons makes polariton lasers promising as a new source of coherent and nonclassical light with extremely low threshold energy. The half-matter nature makes polariton lasers a unique test bed for many-body theories and cavity quantum electrodynamics. In this article, we present a series of experimental studies of a polariton laser, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure. The polaritons have an effective mass that is twice the cavity photon effective mass, yet seven orders of magnitude less than the hydrogen atom mass; hence, they can potentially condense at temperatures seven orders of magnitude higher than those required for atom Bose-Einstein condensations. Accompanying the phase transition, a polariton laser emits coherent light but at a threshold carrier density two orders of magnitude lower than that needed for a normal photon laser in a same structure. It also is shown that, beyond threshold, the polariton population splits to a thermal equilibrium Bose-Einstein distribution at in-plane wave number k parallel > 0 and a nonequilibrium condensate at k parallel approximately 0, with a chemical potential approaching to zero. The spatial distributions and polarization characteristics of polaritons also are discussed as unique signatures of a polariton laser.

Condensation of semiconductor microcavity exciton polaritons.

A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.