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

Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity ? to entropy density s in units of /kB is bounded by a constant. Here, is Planck's constant and kB is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that ?/s ? /(4?kB). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of ?/s that are smaller than /kB. These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.

Nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas

The ongoing experimental and theoretical effort aimed at understanding nonclassical rotational inertia in solid helium has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this Colloquium is to provide a general theoretical framework for the phenomenon of supersolidity, review some of the experimental evidence for solid $^{4}\mathrm{He}$, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). Quantitative support to our theoretical scenarios by means of first-principle numerical simulations is provided. Alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms, are also discussed.

Colloquium: Supersolids: What and where are they?

Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity eta to entropy density s in units of hbar/k_B is bounded by a constant. Here, hbar is Planck's constant and k_B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that eta/s is greater or equal to hbar/(4 pi k_B). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of eta/s that are smaller than hbar/k_B. These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases, and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory, and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.

Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible—thanks to tremendous progress in cooling, trapping and manipulating ultracold samples—to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.

https://iopscience.iop.org/article/10.1088/0034-4885/75/4/046401/pdf

Few-body physics with ultracold atomic and molecular systems in traps

We present benchmark, high precision measurements of the dynamic structure factor $J(Q,y)$ of liquid ${}^{4}\mathrm{He}$ at several temperatures over a wide wave vector transfer range $15l~Ql~29 {\mathrm{\AA{}}}^{\ensuremath{-}1}.$ $J(Q,y)$ is very different in the superfluid phase below ${T}_{\ensuremath{\lambda}}$ and in the normal phase above ${T}_{\ensuremath{\lambda}}$ where ${T}_{\ensuremath{\lambda}}=2.17 \mathrm{K}.$ Below ${T}_{\ensuremath{\lambda}},$ $J(Q,y)$ contains a pronounced additional contribution near $y=0$ that is asymmetric about $y=0,$ reflecting a condensate contribution modified by asymmetric final-state (FS) effects. The asymmetry in $J(Q,y)$ is direct qualitative evidence of a condensate. We analyze the data at all T using the same model of $J(Q,y)$ consisting of a condensate fraction ${n}_{0},$ a momentum distribution ${n}^{*}(\mathbf{k})$ for states $kg0$ above the condensate, and a FS broadening function $R(Q,y).$ We find a condensate fraction given by ${n}_{0}{(T)=n}_{0}(0)[1\ensuremath{-}{(T/T}_{\ensuremath{\lambda}}{)}^{\ensuremath{\gamma}}]$ with ${n}_{0}(0)=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ and $\ensuremath{\gamma}=5.5\ifmmode\pm\else\textpm\fi{}1.0$ for $Tl{T}_{\ensuremath{\lambda}},$ which is 30% below existing observed values, and ${n}_{0}=(0\ifmmode\pm\else\textpm\fi{}0.3)%$ for $Tg{T}_{\ensuremath{\lambda}}.$ We determine $n(k)$ in both phases. The ${n}^{*}(\mathbf{k})$ is significantly narrower than a Gaussian in both superfluid and normal ${}^{4}\mathrm{He}$ and narrowest in the normal phase. The final-state function is determined from the data and is the same within precision above and below ${T}_{\ensuremath{\lambda}}.$ The precise form of $R(Q,y)$ is important in determining the value of ${n}_{0}(T)$ below ${T}_{\ensuremath{\lambda}}.$ When independent, theoretical $R(Q,y)$ are used in the analysis, the ${n}_{0}(T)$ is found to be the same as or smaller than the above value.

W. G. Stirling

Papers

Condensate, momentum distribution, and final-state effects in liquid 4 He