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

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...

Controlling the way light interacts with material excitations is at the heart of cavity quantum electrodynamics (QED). In the strong-coupling regime, quantum emitters in a microresonator absorb and spontaneously re-emit a photon many times before dissipation becomes effective, giving rise to mixed light-matter eigenmodes. Recent experiments in semiconductor microcavities reached a new limit of ultrastrong coupling, where photon exchange occurs on timescales comparable to the oscillation period of light. In this limit, ultrafast modulation of the coupling strength has been suggested to lead to unconventional QED phenomena. Although sophisticated light-matter coupling has been achieved in all three spatial dimensions, control in the fourth dimension, time, is little developed. Here we use a quantum-well waveguide structure to optically tune light-matter interaction from weak to ultrastrong and turn on maximum coupling within less than one cycle of light. In this regime, a class of extremely non-adiabatic phenomena becomes observable. In particular, we directly monitor how a coherent photon population converts to cavity polaritons during abrupt switching. This system forms a promising laboratory in which to study novel sub-cycle QED effects and represents an efficient room-temperature switching device operating at unprecedented speed.

Artificial cavity photon resonators with ultrastrong light-matter interactions are attracting interest both in semiconductor and superconducting systems, due to the possibility of manipulating the cavity quantum electrodynamic ground state with controllable physical properties. We report here experiments showing ultrastrong light-matter coupling in a terahertz metamaterial where the cyclotron transition of a high mobility two-dimensional electron gas is coupled to the photonic modes of an array of electronic split-ring resonators. We observe a normalized coupling ratio Ω ωc = 0.58 between the vacuum Rabi frequency Ω and the cyclotron frequency ω c . Our system appears to be scalable in frequency and could be brought to the microwave spectral range with the potential of strongly controlling the magnetotransport properties of a highmobility 2DEG.

The regime of ultra-strong light-matter interaction has been investigated theoretically and experimentally, using zero-dimensional electromagnetic resonators coupled with an electronic transition between two confined states of a semiconductor quantum well. We have measured a splitting between the coupled modes that amounts to 48% of the energy transition, the highest ratio ever observed in a light-matter coupled system. Our analysis, based on a microscopic quantum theory, shows that the non-linear polariton splitting, a signature of this regime, is a dynamical effect arising from the self-interaction of the collective electronic polarization with its own emitted field.

In a recent work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. 104, 183601 (2010)] it was numerically shown that in a photonic 'molecule' consisting of two coupled cavities, near-resonant coherent excitation could give rise to strong photon antibunching with a surprisingly weak nonlinearity. Here, we show that a subtle quantum interference effect is responsible for the predicted efficient photon blockade effect. We analytically determine the optimal on-site nonlinearity and frequency detuning between the pump field and the cavity mode. We also highlight the limitations of the proposal and its potential applications in demonstration of strongly correlated photonic systems in arrays of weakly nonlinear cavities. The photon blockade is a quantum optical effect preventing the resonant injection of more than one photon into a nonlinear cavity mode [1], leading to antibunched (sub-Poissonian) single-photon statistics. Signatures of photon blockade have been observed by resonant laser excitation of an optical cavity containing either a single atom [2] or a single quantum dot [3] in the strong coupling regime. Arguably, the most convincing realization was based on a single atom coupled to a micro-toroidal cavity in the Purcell regime [4], suggesting that the strong coupling regime of cavity-QED need not be a requirement. Concurrently, on the theory side there has been a number of proposals investigating strongly correlated photons in coupled cavity arrays [5][6][7] or one-dimensional optical waveguides [8]. The specific proposals based on the photon blockade effect include the fermionization of photons in one-dimensional cavity of arrays [9], the crystallization of polaritons in coupled array of cavities [10], and the quantum-optical Josephson interferometer in a coupled photonic mode system [11].It is commonly believed that photon blockade necessarily requires a strong on-site nonlinearity U for a photonic mode, whose magnitude should well exceed the mode broadening γ. However, in a recent work [12] Liew and Savona numerically showed that a strong antibunching can be obtained with a surprisingly weak nonlinearity (U ≪ γ) in a system consisting of two coupled zerodimensional (0D) photonic cavities (boxes), as shown in Fig. 1(a) [12]. Such a configuration can be obtained, e.g., by considering two modes in two photonic boxes coupled with a finite mode overlap due to leaky mirrors: the corresponding tunnel strength will be designated with J. In Ref.[12] numerical evidence indicated that a nearly perfect antibunching can be achieved for an optimal value of the on-site repulsion energy U and for an optimal value of the detuning between the pump and mode frequency. However, a physical understanding of the mechanism leading to strong photon antibunching is needed to identify the limitations of the scheme in the context of proposed experiments on strongly correlated photons, as well as to determine the dependence of the optimal coupling and detuning on the relevant physical parameters J and γ.In this letter, we show analytical...

In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency Ω 0 . The analogous term 'circuit QED' has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with Ω 0 comparable with the two-level transition frequency, 'superradiant' quantum phase transitions for the cavity vacuum have been predicted, for example, within the Dicke model. In this study, we prove that if the time-independent light-matter Hamiltonian is considered, a superradiant quantum critical point is forbidden for electric dipole atomic transitions because of the oscillator strength sum rule. In circuit QED, the analogous of the electric dipole coupling is the capacitive coupling, and such no-go property can be circumvented by Cooper pair boxes capacitively coupled to a resonator, because of their peculiar Hilbert space topology and a violation of the corresponding sum rule.