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 the 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 nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, 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 the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (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 the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

In the past decade, a two-dimensional matter-light system called the microcavity exciton-polariton has emerged as a new promising candidate of Bose-Einstein condensation BEC in solids. Many pieces of important evidence of polariton BEC have been established recently in GaAs and CdTe microcavities at the liquid helium temperature, opening a door to rich many-body physics inaccessible in experiments before. Technological progress also made polariton BEC at room temperatures promising. In parallel with experimental progresses, theoretical frameworks and numerical simulations are developed, and our understanding of the system has greatly advanced. In this article, recent experiments and corresponding theoretical pictures based on the Gross-Pitaevskii equations and the Boltzmann kinetic simulations for a finite-size BEC of polaritons are reviewed.

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Exciton-polariton Bose-Einstein condensation

Similar to atoms in cold gases, exciton–polaritons in semiconductor microcavities can undergo Bose–Einstein condensation. A striking consequence of the appearance of macroscopic coherence in these systems is superfluidity. Now, clear evidence for such behaviour has been found in an exciton–polariton condensate. 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 condensation3,4,5. In solid-state systems, it has been anticipated that exciton–polaritons in semiconductor microcavities should behave as an unusual quantum fluid6,7,8, with unique properties stemming from its intrinsically non-equilibrium nature. This has stimulated the quest for an experimental demonstration of superfluidity effects in polariton systems9,10,11,12,13. 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, a Cerenkov-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 theory12,13, and establish microcavity polaritons as a system for exploring the rich physics of non-equilibrium quantum fluids.

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Superfluidity of polaritons in semiconductor microcavities

Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. Martin Weitz and colleagues have now realized such conditions experimentally, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources. Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. These authors experimentally realise such conditions, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources. Bose–Einstein condensation (BEC)—the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density—has been observed in several physical systems1,2,3,4,5,6,7,8,9, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied10; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons11 or photon–photon scattering in a nonlinear resonator configuration12,13. Number-conserving thermalization was experimentally observed14 for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a ‘white-wall’ box. Here we report the observation of a Bose–Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose–Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases9 and new coherent ultraviolet sources15.

Bose–Einstein condensation of photons in an optical microcavity

Recently a new type of system exhibiting spontaneous coherence has emerged—the exciton–polariton condensate. Exciton–polaritons (or polaritons for short) are bosonic quasiparticles that exist inside semiconductor microcavities, consisting of a superposition of an exciton and a cavity photon. Above a threshold density the polaritons macroscopically occupy the same quantum state, forming a condensate. The polaritons have a lifetime that is typically comparable to or shorter than thermalization times, giving them an inherently non-equilibrium nature. Nevertheless, they exhibit many of the features that would be expected of equilibrium Bose–Einstein condensates (BECs). The non-equilibrium nature of the system raises fundamental questions as to what it means for a system to be a BEC, and introduces new physics beyond that seen in other macroscopically coherent systems. In this review we focus on several physical phenomena exhibited by exciton–polariton condensates. In particular, we examine topics such as the difference between a polariton BEC, a polariton laser and a photon laser, as well as physical phenomena such as superfluidity, vortex formation, and Berezinskii–Kosterlitz–Thouless and Bardeen–Cooper–Schrieffer physics. We also discuss the physics and applications of engineered polariton structures. Exciton–polaritons, resulting from the light–matter coupling between an exciton and a photon in a cavity, form Bose–Einstein-like condensates above a critical density. Various aspects of the physics of exciton–polariton condensates are now reviewed.

Exciton–polariton condensates

We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.

https://science.sciencemag.org/content/sci/316/5827/1007.full.pdf

Bose-Einstein Condensation of Microcavity Polaritons in a Trap

Recent experiments have shown that polaritons in microcavities behave like a Bose-Einstein condensate above a critical density threshold and at low temperature. The polaritons are not in full equilibrium, however, due to particle decay and streaming in of generated particles from high-energy states. In this paper we present a full simulation of the thermalization of polariton and exciton populations, including polariton-polariton and exciton-exciton scattering, phonon emission and absorption, and polariton scattering with free electrons. We find that we can obtain good fits over a wide range of polariton densities. The fits imply that the enhancement of the polariton-polariton scattering due to Bose-Einstein statistics does indeed play the major role in the particles piling up in low-energy states, which is the precursor to Bose condensation. Our fits also indicate that at low density, scattering of the polaritons with free electrons plays a more important role than polaritonphonon scattering.

Numerical simulations of the polariton kinetic energy distribution in GaAs quantum-well microcavity structures

We report the fabrication of waveguides in lithium tantalate using a 250kHz high-repetition rate ultrafast laser at 771nm and the characterization of the resulting laser induced structure with second harmonic microscopy. Waveguides operating at the 1.5μm telecommunication wavelength were formed above and below the focal volume using pulse energies ranging from 100to1.6J and translation speeds from 100μm∕sto5mm∕s. The second harmonic microscopy reveals no degradation of the electro-optic coefficient in the guiding region above the focal volume.

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Waveguiding and nonlinear optical properties of three-dimensional waveguides in LiTaO3 written by high-repetition rate ultrafast laser

In this paper we discuss the issues of the equilibration dynamics of spatially indirect two-dimensional excitons in a coupled quantum well structure, in particular those trapped by an in-plane harmonic potential trap. We discuss the relative timescales for several processes. In the experiments with an in-plane trap, we can use the size of the exciton cloud as a measure of the temperature of particles. At low lattice temperatures the exciton temperature is higher than that of the lattice, even long after equilibrium has obviously been reached. We discuss the effects that can be responsible for this.

Considerations on equilibration of two-dimensional excitons in coupled quantum well structures.

The polariton-polariton interaction strength is an important parameter for all kinds of applications using the nonlinear properties of polaritons, such as optical switching and single-photon blockade devices. Over the past few years, as experiments with polariton condensates in microcavities have become more sophisticated, there have been several different types of experiments aimed at establishing the absolute value of this parameter. In this paper, we review and compare the results of many of these experiments, and present new theoretical analysis of some of them. The results of measurements sensitive to the polariton scattering rate, though frequently neglected, are especially significant for the low-density estimates. We find that even when adjustments are made to correct for new understanding of past experiments, the values range over two orders of magnitude, with the low values mostly coming from experiments with high polariton density, and the high values coming from experiments at low density. We show that calculation of many-body effects on the effective interaction can give a significant reduction of the effective interaction strength at high density.

V. Hartwell

Papers

Bose-Einstein Condensation of Microcavity Polaritons in a Trap

Numerical simulations of the polariton kinetic energy distribution in GaAs quantum-well microcavity structures

Waveguiding and nonlinear optical properties of three-dimensional waveguides in LiTaO3 written by high-repetition rate ultrafast laser

Considerations on equilibration of two-dimensional excitons in coupled quantum well structures.

Experimental determinations of polariton-polariton interactions in microcavities