This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically non-equilibrium nature. We present a rich variety of photon hydrodynamical effects that have been recently observed, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While our review is mostly focused on a class of semiconductor systems that have been extensively studied in recent years (namely planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of our article is devoted to a review of the exciting perspectives to achieve strongly correlated photon gases. In particular, we present different mechanisms to obtain efficient photon blockade, we discuss the novel quantum phases that are expected to appear in arrays of strongly nonlinear cavities, and we point out the rich phenomenology offered by the implementation of artificial gauge fields for photons.Comment: Accepted for publication on Rev. Mod. Phys. (in press, 2012

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Superfluidity, the ability of a quantum fluid to flow without friction, is one of the most spectacular phenomena occurring in degenerate gases of interacting bosons. Since its first discovery in liquid helium-4 (refs 1, 2), superfluidity has been observed in quite different systems, and recent experiments with ultracold trapped atoms have explored the subtle links between superfluidity and Bose-Einstein condensation 3-5 . In solid-state systems, it has been anticipated that excitonpolaritons in semiconductor microcavities should behave as an unusual quantum fluid 6-8 , with unique properties stemming from its intrinsically non-equilibrium nature. This has stimulated the quest for an experimental demonstration of superfluidity effects in polariton systems 9-13 . Here, we report clear evidence for superfluid motion of polaritons. Superfluidity is investigated in terms of the Landau criterion and manifests itself as the suppression of scattering from defects when the flow velocity is slower than the speed of sound in the fluid. Moreover, aČerenkov-like wake pattern is observed when the flow velocity exceeds the speed of sound. The experimental findings are in quantitative agreement with predictions based on a generalized Gross-Pitaevskii theory 12,13 , and establish microcavity polaritons as a system for exploring the rich physics of non-equilibrium quantum fluids.Bound electron-hole particles, known as excitons, are fascinating objects in semiconductor nanostructures. In a quantum well with a thickness of the order of a few nanometres, the external motion of the exciton is quantized in the direction perpendicular to the well, whereas it is free within the plane of the well. When the quantum well is placed in a high-finesse microcavity, the strong-coupling regime between excitons and light is easily reached 14 , giving rise to exciton-photon mixed quasiparticles called polaritons, which are an interesting kind of two-dimensional composite boson. Thanks to their sharp dispersion, polaritons have a small effective mass (of the order of 10 −5 times the free-electron mass) that allows the building of many-body coherent effects, such as Bose-Einstein condensation 15,16 , at a lattice temperature of a few kelvins. Furthermore, their partially excitonic character results in strong interactions between polaritons, which are expected to lead to the appearance of superfluid phenomena. Indirect evidence of superfluid motion in polariton systems has recently been reported through the observation of pinned quantized vortices 9 , Bogoliubov-like dispersions 10 and pioneering experiments on polariton parametric oscillators 11 . Despite these remarkable works, a direct demonstration of exciton-polariton superfluidity is however still missing. In this Letter, we report the observation of superfluid motion of a quantum fluid of polaritons created by a laser in a semiconductor microcavity.In our experiments, to probe superfluidity we study the perturbation that is produced in an optically created moving polariton fluid when a static ...

We present a quantum description of a planar microcavity photon mode strongly coupled to a semiconductor intersubband transition in presence of a two-dimensional electron gas. We show that, in this kind of system, the vacuum Rabi frequency ΩR can be a significant fraction of the intersubband transition frequency ω12. This regime of ultra-strong light-matter coupling is enhanced for long wavelength transitions, because for a given doping density, effective mass and number of quantum wells, the ratio ΩR/ω12 increases as the square root of the intersubband emission wavelength. We characterize the quantum properties of the ground state (a two-mode squeezed vacuum), which can be tuned in-situ by changing the value of ΩR, e.g., through an electrostatic gate. We finally point out how the tunability of the polariton quantum vacuum can be exploited to generate correlated photon pairs out of the vacuum via quantum electrodynamics phenomena reminiscent of the dynamical Casimir effect.In the last decade, the study of intersubband electronic transitions 1 in semiconductor quantum wells has enjoyed a considerable success, leading to remarkable opto-electronic devices such as the quantum cascade lasers 2,3,4 . In contrast to the more conventional interband transitions between conduction and valence bands, the frequency of intersubband transitions is not determined by the energy gap of the semiconductor material system used, but rather can be chosen via the thickness of the quantum wells in the active region, providing tunable sources emitting in the mid and far infrared.One of the most fascinating aspects of light-matter interaction is the so-called strong light-matter coupling regime, which is achieved when a cavity mode is resonant with an electronic transition of frequency ω 12 , and the so-called vacuum Rabi frequency Ω R exceeds the cavity mode and electronic transition linewidths. The strong coupling regime has been first observed in the late '80s using atoms in metallic cavities 5,6 , and a few years later in solid-state systems using excitonic transitions in quantum wells embedded in semiconductor microcavities 7 . In this regime, the normal modes of the system consist of linear superpositions of electronic and photonic excitations, which, in the case of semiconductor materials, are the so-called polaritons. In both these systems, the vacuum Rabi frequency Ω R does not exceed a very small fraction of the transition frequency ω 12 .Recently, Dini et al. 8 have reported the first demonstration of strong coupling regime between a cavity photon mode and a mid-infrared intersubband transition, in agreement with earlier semiclassical theoretical predictions by Liu 9 . The dielectric Fabry-Perot structure realized by Dini et al. 8 consists of a modulation doped multiple quantum well structure embedded in a microcavity, whose mirrors work thanks to the principle of total internal reflection. The strong coupling regime has been also observed in quantum well infra-red detectors 10 . As we will show in detail, an important advant...

We have developed a mean-field model to describe the dynamics of a non-equilibrium BoseEinstein condensate of exciton-polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied in different geometries. A diffusive behaviour of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry. [4,5]. The system under investigation consists of a semiconductor microcavity containing a few quantum wells with an excitonic transition strongly coupled to the cavity photon mode. In this strong coupling regime, the basic excitations of the system are excitonpolaritons, i.e. linear superpositions of a quantum well exciton and a cavity photon. As compared to other examples of BEC, namely in liquid 4 He and ultracold atomic gases, the main novelty of the present polariton system is its intrinsic non-equilibrium nature due to the finite lifetime of polaritons. The condensate has in fact to be continuously replenished from the relaxation of optically injected high energy excitations (e.g. free carriers or hot polaritons), and its steady state results from a dynamical equilibrium between pumping and losses. This makes the present system a unique candidate for the study of the BEC phase transition in a non-equilibrium context. Recent theoretical work [6] has suggested that the non-equilibrium condition is responsible for dramatic changes in the dispersion of low-lying excitations of incoherently pumped polariton condensates: the sound mode of equilibrium condensates is replaced by a diffusive mode with flat dispersion, as it typically happens in coherently driven pattern forming systems, such as Benard cells in heat convection [7] or optical parametric oscillators [8].The present Letter is devoted to the development of a simple and generic model of a non-equilibrium condensate which does not involve the microscopic physics of the polariton, and can be used to describe the dynamics independently of the details of the specific pumping scheme. Our model is inspired by classical treatments of laser operation [9], and closely resembles the generic model of atom lasers developed in [10]. In this way, we are able not only to confirm the conclusions of Ref.[6] but also to analytically relate the elementary excitation spectrum to experimentally accessible quantities. The same model is then applied to the Josephson effect [11,12,13] in a system of two weakly coupled polaritonic condensates: predictions are given for the frequency and the intrinsic damping rate of Josephson oscillations, and overdamped behavior is anticipated in the case of strong damping.The experimental scheme used to create the polariton condensate is sketched in Fig.1a: under a continuouswave high energy illumination, hot free carriers are generated in the semiconductor material forming the microcavity. Their cooling down by phonon emission leads the formation of a incoherent gas of bound excitons in the quantum wells, ...

One of the most striking quantum effects in an interacting Bose gas at low temperature is superfluidity. First observed in liquid 4 He, this phenomenon has been intensively studied in a variety of systems for its remarkable features such as the persistence of superflows and the proliferation of quantized vortices 1 . The achievement of Bose-Einstein condensation in dilute atomic gases 2 provided the opportunity to observe and study superfluidity in an extremely clean and well-controlled environment. In the solid state, Bose-Einstein condensation of exciton polaritons has been reported recently 3-6 . Polaritons are strongly interacting light-matter quasiparticles that occur naturally in semiconductor microcavities in the strong-coupling regime and constitute an interesting example of composite bosons. Here, we report the observation of spontaneous formation of pinned quantized vortices in the Bose-condensed phase of a polariton fluid. Theoretical insight into the possible origin of such vortices is presented in terms of a generalized Gross-Pitaevskii equation. Whereas the observation of quantized vortices is, in itself, not sufficient for establishing the superfluid nature of the non-equilibrium polariton condensate, it suggests parallels between our system and conventional superfluids.Vortices in superfluids carry quantized phase winding and circulation of the superfluid particles around their core. By definition, vortices are characterized by (1) a rotation of the phase around the vortex by an integer multiple of 2π, commonly known as the topological charge of the vortex and (2) the vanishing of the superfluid population at their core. Owing to their major importance for the understanding of superfluidity, they have been intensively studied theoretically 7 and experimentally 8-10 in disorder-free, stirred three-dimensional Bose-Einstein condensates (BECs) of dilute atomic gases and in quasi-two-dimensional BECs where they spontaneously emerge from thermal fluctuations 11,12 and are strictly related to the Berezinskii-Kosterlitz-Thouless phase transition [13][14][15] . Here, we observed the spontaneous appearance of pinned singly quantized vortices as an intrinsic feature of non-equilibrium polariton BECs in the presence of disorder. The same planar CdTe microcavity sample was used as in our previous studies 3, 16,17 . The polariton condensate was created by means of non-resonant continuous-wave optical excitation, the intensity of which is used to drive the polaritons throughout the phase transition, as demonstrated by the condensate emission energy being located close to the bottom of the polariton dispersion. The condensate steady state is determined by a dynamical balance between the incoming and the outgoing flow of polaritons: in contrast to atomic BECs, the polariton condensate is in an intrinsically non-equilibrium condition. From this point of view, it is therefore closer to a laser, but fundamental differences are still to be noted with respect to a standard photon laser: the bosonic particles under in...

Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.

We report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic horizon in a flowing one-dimensional atomic Bose-Einstein condensate. The presence of Hawking radiation is revealed from peculiar long-range patterns in the density-density correlation function of the gas. Quantitative agreement between our fully microscopic calculations and the prediction of analog models is obtained in the hydrodynamic limit. New features are predicted and the robustness of the Hawking signal against a finite temperature discussed.