We study the necessary condition under which a resonantly driven exciton polariton superfluid flowing against an obstacle can generate turbulence. The value of the critical velocity is well estimated by the transition from elliptic to hyperbolic of an operator following ideas developed by Frisch, Pomeau, Rica for a superfluid flow around an obstacle, though the nature of equations governing the polariton superfluid is quite different. We find analytical estimates depending on the pump amplitude and on the pump energy detuning, quite consistent with our numerical computations.
We theoretically demonstrate how the resonant coupling between a pair of cavity-polaritons and a biexciton state can lead to a large single-photon Kerr nonlinearity in a semiconductor solid-state system. A fully analytical model of the scattering process between a pair of cavity-polaritons is developed, which explicitly includes the biexcitonic intermediate state. A dramatic enhancement of the polariton-polariton interactions is predicted in the vicinity of the biexciton Feshbach resonance. Application to the generation of non-classical light from polariton dots is discussed.
We theoretically investigate how the presence of a reservoir of incoherent excitations affects the superfluidity properties of resonantly driven polariton fluids. While in the absence of reservoir the two cases of a defect moving in a fluid at rest and of a fluid flowing against a static defect are linked by a formal Galilean transformation, here the reservoir defines a privileged reference frame attached to the semiconductor structure and causes markedly different features between the two settings. The consequences on the critical velocity for superfluidity are highlighted and compared to exp…
We consider the possible phases of microcavity polaritons tuned near a bipolariton Feshbach resonance. We show that, as well as the regular polariton superfluid phase, a "molecular" superfluid exists, with (quasi-)long-range order only for pairs of polaritons. We describe the experimental signatures of this state. Using variational approaches we find the phase diagram (critical temperature, density and exciton-photon detuning). Unlike ultracold atoms, the molecular superfluid is not inherently unstable, and our phase diagram suggests it is attainable in current experiments.
Motivated by recent experiments, we theoretically analyze the flow past an obstacle of a one-dimensional "quantum fluid of light" which is resonantly driven, and exhibits bistability. The flow is found to abruptly change several times when the fluid velocity or the obstacle potential strength are increased. In contrast to the cases of usual fluids and superfluids, the transitions take place between stationary states. They involve the fluid bistability in an essential way. Remarkably, at the transitions points, the fluid in the obstacle wake lies in the unstable intermediate density state.
In the linear response approximation, coherently driven microcavity polaritons in the pump-only configuration are expected to satisfy the Landau criterion for superfluidity at either strong enough pump powers or small flow velocities. Here, we solve non-perturbatively the time dependent Gross-Pitaevskii equation describing the resonantly-driven polariton system. We show that, even in the limit of asymptotically large densities, where in linear response approximation the system satisfies the Landau criterion, the fluid always experiences a residual drag force when flowing through the defect. We…
We study the spectrum of a one-dimensional Kitaev chain placed in a microwave cavity. In the off-resonant regime, the frequency shift of the cavity can be used to identify the topological phase transition of the coupled system. In the resonant regime, the topology of the system can be controlled via the microwave cavity occupation and, moreover, for a large number of photons (classical limit), the physics becomes similar to that of periodically-driven systems (Floquet insulators). We also analyze numerically a finite chain and show the existence of a degenerate subspace in the presence of the …
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 hydrodynamic vortices have been observed. These phenomena can be all understood as a specific manifestation of collective excitations forming on top of the polariton condensate. In this work, we performed a Brillouin scattering experiment to measure their dispersion relation $ω(\mathbf{k})$ directly. The result, such as a speed of sound which is apparently twice too low, ca…
A new mechanism of parity breakdown in a spinor Bose gas is predicted; it causes a single-mode state of polaritons to be spontaneously divided into different polarization domains which annihilate each other at the interface areas. In a polariton wire, such interface is a dark soliton that can run in space without dissipation. In a planar cavity, quantized vortices arise in which phase difference of orthogonally polarized components makes one complete turn around the core. Coupled vortex-antivortex pairs and straight filaments can form in analogy to Bose-Einstein condensates and superconductors…
Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and n…
In this paper we discuss, within the Gross--Pitaevskii framework, superfluidity, soliton nucleation, and instabilities in a non-equilibrium polariton fluid injected by a spatially localized and continuous-wave coherent pump and flowing against a defect located outside the pump spot. In contrast to equilibrium condensates, the steady-state solutions of the driven-dissipative equations in this specific geometry hardly show a clean superfluid flow around the defect and rather feature a crossover from shallow to deep soliton-like perturbation. This is explained in terms of the properties of one-di…
We report the formation of a ring-shaped array of vortices after injection of angular momentum in a polariton superfluid. The angular momentum is injected by a $\ell= 8$ Laguerre-Gauss beam, whereas the global rotation of the fluid is hindered by a narrow Gaussian beam placed at its center. In the linear regime a spiral interference pattern containing phase defects is visible. In the nonlinear (superfluid) regime, the interference disappears and the vortices nucleate as a consequence of the angular momentum quantization. The radial position of the vortices evolves freely in the region between …
We study the linear response of a coherently driven polariton fluid in the pump-only configuration scattering against a point-like defect and evaluate analytically the drag force exerted by the fluid on the defect. When the system is excited near the bottom of the lower polariton dispersion, the sign of the interaction-renormalised pump detuning classifies the collective excitation spectra in three different categories [C. Ciuti and I. Carusotto, physica status solidi (b) 242, 2224 (2005)]: linear for zero, diffusive-like for positive, and gapped for negative detuning. We show that both cases …
Recently, exciton-polaritons in a semiconductor microcavity were found to condense into a coherent ground state much like a Bose-Einstein condensate and a superfluid. They have become a unique testbed for generating and manipulating quantum vortices in a driven-dissipative superfluid. Here, we generate exciton-polariton condensate with non-resonant Laguerre-Gaussian (LG) optical beam and verify the direct transfer of light's orbital angular momentum to exciton-polariton quantum fluid. Quantized vortices are found in spite of large energy relaxation involved in non-resonant pumping. We identifi…
We report the experimental investigation and theoretical modeling of a rotating polariton superfluid relying on an innovative method for the injection of angular momentum. This novel, multi-pump injection method uses four coherent lasers arranged in a square, resonantly creating four polariton populations propagating inwards. The control available over the direction of propagation of the superflows allows injecting a controllable non-quantized amount of optical angular momentum. When the density at the center is low enough to neglect polariton-polariton interactions, optical singularities, ass…
We present a simple method to compensate for losses in a polariton superfluid. Based on a weak support field, it allows for an extended propagation of a resonantly driven polariton superfluid at a minimal energetic cost. Moreover, this setup based on optical bistability, leads to a significant release of the phase constraint imposed by the resonant driving. This release, together with the macroscopic polariton propagation, offers a unique opportunity to study the hydrodynamics of topological excitations of polariton superfluids such as quantized vortices and dark solitons. We numerically study…
The dynamics of an exciton-polariton superfluid resonantly pumped in a semiconductor microcavity are investigated by mean-field theory. Modulational instability develops into crystalline order and then ordered and disordered states alternately form. A supersolid-like state is also found, in which superflow coexists with crystalline order at rest.
Steady states reached in a coherently pumped exciton-polariton superfluid are investigated. As the pump parameter is changed, the translational symmetry of the uniform system is spontaneously broken, and various steady patterns of quantized vortices are formed. This is peculiar to nonequilibrium dissipative systems with continuous pumping.
Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral \textit{p}-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically non-trivial Bardeen-Cooper-Schrieffer (BCS) superfluid. Near the topological phase transition at zero chemical potential, $μ=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of …
We theoretically study Hawking radiation processes from an analog acoustic black hole in a flowing superfluid of exciton-polaritons in a one-dimensional semiconductor microcavity. Polaritons are coherently injected into the microcavity by a laser pump with a suitably tailored spot profile. An event horizon with a large analog surface gravity is created by inserting a defect in the polariton flow along the cavity plane. Experimentally observable signatures of the analog Hawking radiation are identified in the scattering of phonon wavepackets off the horizon, as well as in the spatial correlatio…
We study the Berezinskii-Kosterlitz-Thouless mechanism for vortex-antivortex pair formation in two-dimensional superfluids for nonequilibrium condensates. Our numerical study is based on a classical field model for driven-dissipative quantum fluids that is applicable to polariton condensates. We investigate the critical noise needed to create vortex-antivortex pairs in the systems, starting from a state with uniform phase. The dependence of the critical noise on the nonequilibrium and energy relaxation parameters is analyzed in detail.
We develop a theory for the interaction of light with superfluid optical media, describing the motion of quantum impurities that are created and dragged through the liquid by propagating photons. It is well known that a mobile impurity suffers dissipation due to phonon emission as soon as it moves faster than the speed of sound in the superfluid - Landau's critical velocity. Surprisingly we find that in the present hybrid light-matter setting, polaritonic impurities can be protected against environmental decoherence and be allowed to propagate well above the Landau velocity without jeopardizin…
We report the formation of a macroscopic coherent state emerging from colliding polariton fluids. Four lasers with random relative phases, arranged in a square, pump resonantly a planar microcavity, creating four coherent polariton fluids propagating toward each other. When the density (interactions) increases, the four fluids synchronise and the topological excitations (vortex or soliton) disappear to form a single superfluid.
The dynamics of an exciton--polariton superfluid resonantly injected into a semiconductor microcavity are investigated numerically. The results reveal that a Bénard--von Kármán vortex street is generated in the wake behind an obstacle potential, in addition to the generation of quantized vortex dipoles and dark solitons. The vortex street is shown to be robust against a disorder potential in a sample and it can be observed even in time-integrated measurements.
We study the spin vortices and skyrmions coherently imprinted into an exciton-polariton condensate on a planar semiconductor microcavity. We demonstrate that the presence of a polarization anisotropy can induce a complex dynamics of these structured topologies, leading to the twist of their circuitation on the Poincaré sphere of polarizations. The theoretical description of the results carries the concept of generalized quantum vortices in two-component superfluids, which are conformal with polarization loops around an arbitrary axis in the pseudospin space.
Due to their driven-dissipative nature, photonic quantum fluids present new challenges in understanding superfluidity. Some associated effects have been observed, and notably the report of nearly dissipationless flow for coherently driven microcavity-polaritons was taken as a smoking gun for superflow. Here we show that the superfluid response --- the difference between responses to longitudinal and transverse forces --- is zero for coherently driven polaritons. This is a consequence of the gapped excitation spectrum caused by external phase locking. Furthermore, while a normal component exist…
We study non-equilibrium polariton superfluids in the optical parametric oscillator (OPO) regime using a two-component Gross-Pitaevskii equation with pumping and decay. We identify a regime above OPO threshold, where the system undergoes spontaneous symmetry breaking and is unstable towards vortex formation without any driving rotation. Stable vortex solutions differ from metastable ones; the latter can persist in OPO superfluids but can only be triggered externally. Both spontaneous and triggered vortices are characterised by a generalised healing length, specified by the OPO parameters only.
We investigate a two-component mixture of resonantly interacting Fermi gases as a function of the ratio κof the heavy to the light mass of the two species. The diffusion Monte Carlo method is used to calculate the ground-state energy and the pair correlation function starting from two different guiding wave functions, which describe respectively the superfluid and the normal state of the gas. Results show that the mixture is stable and superfluid for mass ratios smaller than the critical value κ_c = 13 +/- 1. For larger values of κsimulations utilizing the wave function of the normal state are…
We study the properties of propagating polariton wave-packets and their connection to the stability of doubly charged vortices. Wave-packet propagation and related photoluminescence spectra exhibit a rich behaviour dependent on the excitation regime. We show that, because of the non-quadratic polariton dispersion, doubly charged vortices are stable only when initiated in wave-packets propagating at small velocities. Vortices propagating at larger velocities, or those imprinted directly into the polariton optical parametric oscillator (OPO) signal and idler are always unstable to splitting.
We study the properties of a binary microcavity polariton superfluid coherently injected by two lasers. The crossover from the supersonic to subsonic regime, where motion is frictionless, is described by evaluating the Bogoliubov spectra. We show that according to the Landau criteria, the coupling between the two components precludes the existence of superfluidity just for one component but not for the other. By analysing the drag force exerted on a defect, we give a recipe to experimentally address the crossover from the supersonic to the subsonic regime.
The experimental investigation of spontaneously created vortices is of utmost importance for the understanding of quantum phase transitions towards a superfluid phase, especially for two dimensional systems that are expected to be governed by the Berezinski-Kosterlitz-Thouless physics. By means of time resolved near-field interferometry we track the path of such vortices, created at random locations in an exciton-polariton condensate under pulsed non-resonant excitation, to their final pinning positions imposed by the stationary disorder. We formulate a theoretical model that successfully repr…
Rotation of a container holding a viscous fluid forms a vortex which grows with increasing angular velocity. A superfluid, however, is intrinsically different from these normal fluids because its rotation is quantized. Even if a container of superfluid is rotating, the fluid itself remains still until a critical velocity is reached. Beyond the critical velocity, all the particles conspire to suddenly pick up an angular momentum of $\hbar$ each and forms a quantized vortex. As a result, a superfluid is known to increase its rotation by a total angular momentum of $N\hbar$. In this letter, we sh…
In this work, we implement a new experimental configuration which exploits the specific properties of the optical bistability exhibited by the polariton system and we demonstrate the generation of a superfluid turbulent flow in the wake of a potential barrier. The propagation and direction of the turbulent flow are sustained by a support beam on distances an order of magnitude longer than previously reported. This novel technique is a powerful tool for the controlled generation and propagation of quantum turbulences and paves the way to the study of the hydrodynamic of quantum turbulence in dr…
The general theory of dark solitons relies on repulsive interactions and therefore predicts the impossibility to form dark-soliton bound states. One important exception to this prediction is the observation of bound solitons in non-local nonlinear media. Here, we report that exciton-polariton superfluids can also sustain dark-soliton molecules although the interactions are fully local. With a novel all optical technique, we create two dark solitons and bind them to each other to form an unconventional dark-soliton molecule. We demonstrate that the stability of this structure and the separation…
In resonantly pumped polariton superfluids we recently explored a new regime based on the bistability of the polariton system to enhance the propagation of polariton fluids up to macroscopic distances. This technique together with an all-optical imprinting method allowed the generation and control of various topological excitations such as quantized vortices and dark solitons. The flexibility and scalability of the new experimental scheme opens the way to the systematic study of quantum turbulence in driven dissipative quantum fluids of light. In this article we review the basic working princi…
Exciton-polariton condensate in semiconductor microcavities constitute a novel kind of non-equilibrium superfluid. In a recent experiment [P. Stepanov, {\it et. al.,} Nat. Commun. {\bf 10}, 1038 (2019)], the dispersion relation of collective excitations in a polariton condensate under the resonant pumping has been investigated with the emphasis on the role of reservoir of long-lived excitons in determining the superfluidity. Inspired by such an experimental advance, we study the superfluidity of a exciton-polaritonn condensate under non-resonant pumping by calculating the drag force exerted on…
A quantum fluid passing an obstacle behaves differently from a classical one. When the flow is slow enough, the quantum gas enters a superfluid regime and neither whirlpools nor waves form around the obstacle. For higher flow velocities, it has been predicted that the perturbation induced by the defect gives rise to the turbulent emission of quantised vortices and to the nucleation of solitons. Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, we report the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets …
Exciton-polaritons are quasi-particles arising from the strong coupling regime between excitons and photons. In planar microcavitites, phenomena such as superfluidity or Bose-Einstein condensation can be observed. Those systems have demonstrated to be very efficient in the hydrodynamic generation of topological excitations, such as vortex-antivortex pairs or dark solitons. However, the lifetime and motion of those excitations were limited by the driven dissipative nature of the system. In this thesis, we present a rich variety of results about the generation and control of such topological exc…
The appearance of quantised vortices in the classical ``rotating bucket'' experiments of liquid helium and ultracold dilute gases provides the means for fundamental and comparative studies of different superfluids. Here, we realize the ``rotating bucket'' experiment for optically trapped quantum fluid of light based on exciton-polariton Bose-Einstein condensate in semiconductor microcavity. We utilise the beating note of two frequency-stabilized single-mode lasers to generate an asymmetric time-periodic rotating, non-resonant excitation profile that both injects and stirs the condensate throug…
Quantum fluids of light are an emerging platform for energy efficient signal processing, ultra-sensitive interferometry and quantum simulators at elevated temperatures. Here we demonstrate the optical control of the topological excitations induced in a large polariton condensate, realising the bosonic analog of a long Josephson junction and reporting the first observation of bosonic Josephson vortices. When a phase difference is imposed at the boundaries of the condensate, two extended regions become separated by a sharp $π$-slippage of the phase and a solitonic depletion of the density, formi…
The dark solitons observed in a large variety of nonlinear media are unstable against the modulational (snake) instabilities and can break in vortex streets. This behavior has been investigated in nonlinear optical crystals and ultracold atomic gases. However, a deep characterization of this phenomenon is still missing. In a resonantly pumped 2D polariton superfluid, we use an all-optical imprinting technique together with the bistability of the polariton system to create dark solitons in confined channels. Due to the snake instabilities, the solitons are unstable and break in arrays of vortex…
Inspired by the renewed experimental activities on $p$-wave resonantly interacting atomic Fermi gases, we theoretically investigate some experimental observables of such systems at zero temperature in two dimensions, using both mean-field theory and Gaussian pair fluctuation theory. These observables include the two $p$-wave contact parameters and the breathing mode frequency, which can be readily measured in current cold-atom setups with $^{40}$K and $^{6}$Li atoms. We find that the many-body component of the two contact parameters exhibits a pronounced peak slightly above the resonance and c…
We present a driven dissipative protocol for creating an optical analog of the Laughlin state in a system of Rydberg polaritons in a twisted optical cavity. We envision resonantly driving the system into a 4-polariton state by injecting photons in carefully selected modes. The dissipative nature of the polariton-polariton interactions leads to a decay into a two-polariton analog of the Laughlin state. Generalizations of this technique could be used to explore fractional statistics and anyon based quantum information processing. We also model recent experiments that attempt to coherently drive …
Superfluidity, the ability of a liquid or gas to flow with zero viscosity, is one of the most remarkable implications of collective quantum coherence. In equilibrium systems like liquid 4He and ultracold atomic gases, superfluid behaviour conjugates diverse yet related phenomena, such as persistency of metastable flow in multiply connected geometries and the existence of a critical velocity for frictionless flow when hitting a static defect. The link between these different aspects of superfluid behaviour is far less clear in driven-dissipative systems displaying collective coherence, such as …
Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, 2D dark solitons are unstable and collapse into vortices due to snake instabilities. Making use of the optical bistability in exciton-polariton microcavities, we demonstrate that a pair of dark solitons can be formed in the wake of an obstacle in a polariton flow resonantly supported by a homogeneous laser beam. Unlike the purely dissipative case where the solitons are grey and spatially separate, here the two solitons are fully dark, rapidly align…
We resonantly excite exciton-polariton states confined in cylindrical traps. Using a homodyne detection setup, we are able to image the phase and amplitude of the confined polariton states. We evidence the excitation of vortex states, carrying an integer angular orbital momentum m, analogous to the transverse TEM01* "donut" mode of cylindrically symmetric optical resonators. Tuning the excitation conditions allows us to select the charge of the vortex. In this way, the injection of singly charged (m = 1 & m = -1) and doubly charged (m = 2) polariton vortices is shown. This work demonstrates th…
The study of superfluid and Berezinskii-Kosterlitz-Thouless phases in exciton-polaritons requires an understanding of vortex dynamics in a dissipative unconfined condensate. In this article we study the motion of dynamic vortex-antivortex pairs and show that vortex pair stability defined as ordered motion as opposed to rapid separation or recombination is the result of balance between dissipative velocities in the condensate and interaction with thermal polaritons. The addition of a trapping potential is further shown to considerably enhance the lifetime of a single vortex pair in this system.…
We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of…
Quantum effects of fields on curved spacetimes may be studied in the laboratory thanks to quantum fluids. Here we use a polariton fluid to study the Hawking effect, the correlated emission from the quantum vacuum at the acoustic horizon. We show how out-of-equilibrium physics affects the dispersion relation, and hence the emission and propagation of correlated waves: the fluid properties on either side of the horizon are critical to observing the Hawking effect. We find that emission may be optimised by supporting the phase and density of the fluid upstream of the horizon in a regime of optica…
Singly quantized vortices have been already observed in many systems including the superfluid helium, Bose Einstein condensates of dilute atomic gases, and condensates of exciton polaritons in the solid state. Two dimensional superfluids carrying spin are expected to demonstrate a different type of elementary excitations referred to as half quantum vortices characterized by a pi rotation of the phase and a pi rotation of the polarization vector when circumventing the vortex core. We detect half quantum vortices in an exciton-polariton condensate by means of polarization resolved interferometry…
We report an experimental study of superfluid hydrodynamic effects in a one-dimensional polariton fluid flowing along a laterally patterned semiconductor microcavity and hitting a micron-sized engineered defect. At high excitation power, superfluid propagation effects are observed in the polariton dynamics, in particular, a sharp acoustic horizon is formed at the defect position, separating regions of sub- and super-sonic flow. Our experimental findings are quantitatively reproduced by theoretical calculations based on a generalized Gross-Pitaevskii equation. Promising perspectives to observe …
Motivated by recent experiments on generation of wave patterns by a polariton condensate incident on a localized obstacle, we study the characteristics of such flows under the condition that irreversible processes play a crucial role in the system. The dynamics of a non-resonantly pumped polariton condensate in a quasi-one-dimensional quantum wire is modeled by a Gross-Pitaevskii equation with additional phenomenological terms accounting for the dissipation and pumping processes. The response of the condensate flow to an external potential describing a localized obstacle is considered in the w…
The phenomenon of stable persistent currents is central to the studies of superfluidity in a range of physical systems. While all of the previous theoretical studies of superfluid flows in annular geometries concentrated on conservative systems, here we extend the stability analysis of persistent currents to open-dissipative exciton-polariton superfluids. By considering an exciton-polariton condensate in an optically-induced annular trap, we determine stability conditions for an initially imposed flow with a non-zero orbital angular momentum. We show, theoretically and numerically, that the sy…
We consider a polariton microcavity resonantly driven by two external lasers which simultaneously pump both lower and upper polariton branches at normal incidence. In this setup, we study the occurrence of instabilities of the pump-only solutions towards the spontaneous formation of patterns. Their appearance is a consequence of the spontaneous symmetry breaking of translational and rotational invariance due to interaction induced parametric scattering. We observe the evolution between diverse patterns which can be classified as single-pump, where parametric scattering occurs at the same energ…
Besides being superfluids, microcavity exciton-polariton condensates are capable of spontaneous pattern formation due to their forced-dissipative dynamics. Their macroscopic and easily detectable response to small perturbations can be exploited to create sensitive devices. We show how controlled pumping in the presence of a peak-dip shaped potential can be used to detect small externally applied velocities which lead to the formation of traveling holes in one dimension and vortex pairs in two dimensions. Combining an annulus geometry with a weak link, the set up that we describe can be used to…
