Spontaneous generation, enhanced propagation and optical imprinting of quantized vortices and dark solitons in a polariton superfluid: towards the control of quantum turbulence
Anne Maitre, Ferdinand Claude, Giovani Lerario, Serguei Koniakhin, Simon Pigeon, Dmitry Solnyshkov, Guillaume Malpuech, Quentin Glorieux, Elisabeth Giacobino, Alberto Bramati
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 principles of the bistability enhanced propagation and of the imprinting technique and we discuss the main achieved results as well as the most promising future research directions.
We investigate theoretically the creation, persistence and detection of quantized vortices in nonequilibrium polariton condensates within a stochastic classical field model. The life time of the quantized vortices is shown to increase with the spatial coherence and to depend on the geometry of the condensate. The relation with superfluidity in conventional superfluids is discussed. Three different ways to measure the vorticity of the polariton condensate are proposed.
We study the dynamics of spontaneously formed vortices in homogeneous microcavity-polariton condensates (MPCs). We find that vortices are stable and appear spontaneously without stirring or rotating MPCs. The dip of the vortex core contains some background of reservoir polaritons and the visibility of a vortex is increasing with respect to the pump strength. The vortex radius is inversely proportional to the square root of the condensate density. Excitation energies of vortices at high and low pump powers are finite and zero, respectively. Vortices at low pump powers exhibit the short lifetime…
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 introduce the phenomenon of spiraling vortices in driven-dissipative (non-equilibrium) exciton-polariton condensates excited by a non-resonant pump beam. At suitable low pump intensities, these vortices are shown to spiral along circular trajectories whose diameter is inversely proportional to the effective mass of the polaritons, while the rotation period is mass independent. Both diameter and rotation period are inversely proportional to the pump intensity. Stable spiraling patterns in the form of complexes of multiple mutually-interacting vortices are also found. At elevated pump intensi…
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…
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…
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.
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…
Solitons and vortices obtain widespread attention in different physical systems as they offer potential use in information storage, processing, and communication. In exciton-polariton condensates in semiconductor microcavities, solitons and vortices can be created optically. However, dark solitons are unstable and vortices cannot be spatially controlled. In the present work we demonstrate the existence of stable dark solitons and vortices under non-resonant incoherent excitation of a polariton condensate with a simple spatially periodic pump. In one dimension, we show that an additional cohere…
We study the spontaneous formation of exciton polariton vortices in an all-optical non-resonantly excited annular trap, which is formed by ring-shaped subpicosecond laser pulses. Since the light emitted by these vortices carries orbital angular momentum (OAM) corresponding to their topological charge, we apply a dedicated OAM spectroscopy technique to detect the OAM of the measurement signal with picosecond time resolution. This allows us to identify the formation of OAM modes and investigate the dynamics of the vortex formation process. We also study the power dependence of this process and h…
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.
The spontaneous formation of lattice structure of quantized vortices is a characteristic feature of superfluidity in closed systems under thermal equilibrium. In exciton-polariton Bose-Einstein condensate, which is a typical example of macroscopic quantum state in open systems, spontaneous vortex lattices have also been proposed by not yet observed. Here, we take into account the finite decay rate of exciton reservoir, and theoretically investigate the vortex structures in circularly pumped polariton Bose-Einstein condensate. Our results show that a decreasing reservoir decay rate can reduce t…
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…
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…
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 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.
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…
We consider two concentric rings formed by bosonic condensates of exciton-polaritons. A circular superfluid flow of polaritons in one of the rings can be manipulated by acting upon the second annular polariton condensate. The complex coupling between the rings with different topological charges triggers nucleation of stable Josephson vortices (JVs) which are revealed as topological defects of the angular dependence of the relative phase between rings. Being dependent on the coupling strength, the structure of the JV governs the difference of the mean angular momenta of the inner and the outer …
Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin-v…
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.
We experimentally and theoretically explore the creation and time evolution of vortex lines in the polar magnetic phase of a trapped spin-1 $^{87}$Rb Bose-Einstein condensate. A process of phase-imprinting a nonsingular vortex, its decay into a pair of singular spinor vortices, and a rapid exchange of magnetic phases creates a pair of three-dimensional, singular singly-quantized vortex lines with core regions that are filled with atoms in the ferromagnetic phase. Atomic interactions guide the subsequent vortex dynamics, leading to core structures that suggest the decay of the singly-quantized …
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…
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrastedto the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of {\em stable} nonlinear single or multi-vortex excitations. The potential i…
Dynamically Stable Vortices in Exciton-Polariton Condensates Engineered by Repulsive Interactions
Bharathidasan University（巴塔迪达桑大学）；Centre for Nonlinear Science (CeNSc), Government College for Women (Autonomous)（非线性科学中心（自治）女子政府学院）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）
We generalize the spin Meissner effect for exciton-polariton condensate confined in annular geometries to the case of non-trivial topology of the condensate wavefunction. In contrast to the conventional spin Meissner state, topological spin Meissner states can in principle be observed at arbitrary high magnetic field not limited by the critical magnetic field value for the condensate in a simply-connected geometry. One special example of the topological Meissner states are half-vortices. We show that in the absence of magnetic field half-vortices in a ring exist in a form of superposition of e…
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…
If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantised vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a non-equilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond time scales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortice…
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…
Nonequilibrium condensate systems such as exciton-polariton condensates are capable of supporting a spontaneous vortex nucleation. The spatial inhomogeneity of pumping field or/and disordered potential creates velocity flow fields that may become unstable to vortex formation. This letter considers ways in which turbulent states of interacting vortices can be created. It is shown that by combining just two pumping intensities it is possible to create a superfluid turbulence state of well-separated vortices, a strong turbulence state of de-structured vortices, or a weak turbulence state in which…
We study the formation of topological defects (quantum vortices) during the formation of a 2D polariton condensate at the $Γ$ point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as $0.95\pm0.05$. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We mo…
Quantum vortices are the quantized version of classical vortices. Their center is a phase singularity or vortex core around which the flow of particles as a whole circulates and is typical in superfluids, condensates and optical fields. However, the exploration of the motion of the phase singularities in coherently-coupled systems is still underway. We theoretically analyze the propagation of an interference dislocation in the regime of strong coupling between light and matter, with strong mass imbalance, corresponding to the case of microcavity exciton-polaritons. To this end, we utilize comb…
Exciton-polariton condensates display a variety of intriguing pattern-forming behaviors, particularly when confined in potential traps. It has previously been predicted that triangular lattices of vortices of the same sign will form spontaneously as the result of surface instabilities in a harmonic trap. However, natural disorder, deviation of the external potential from circular symmetry, or higher-order terms modifying the dynamical equations may all have detrimental effects and destabilize the circular trajectories of vortices. Here we address these issues, by characterizing the robustness …
Exciton-polaritons have been shown to be an optimal system in order to investigate the properties of bosonic quantum fluids. We report here on the observation of dark solitons in the wake of engineered circular obstacles and their decay into streets of quantized vortices. Our experiments provide a time-resolved access to the polariton phase and density, which allows for a quantitative study of instabilities of freely evolving polaritons. The decay of solitons is quantified and identified as an effect of disorder-induced transverse perturbations in the dissipative polariton gas.
In this work we perform a numerical study of a rotating, harmonically trapped, Bose-Einstein condensate of microcavity polaritons. An efficient numerical method (toolbox) to solve the complex Gross-Pitaevskii equation is developed. Using this method, we investigate how the behavior of the number of vortices formed inside the condensate changes as the various system parameters are varied. In contrast to the atomic condensates, we show, there exists an (experimentally realizable) range of parameter values in which all the vortices can be made to vanish even when there is a high rotation. We furt…
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 present a survey of macroscopic excitations of harmonically confined Bose-Einstein condensates (BEC), described by Gross-Pitaevskii (GP) equation, in search of routes to develop quantum turbulence. These excitations can all be created by phase imprinting techniques on an otherwise equilibrium Bose-Einstein condensate. We analyze two crossed vortices, two parallel anti-vortices, a vortex ring, a vortex with topological charge Q = 2, and a tangle of 4 vortices. Since GP equation is time-reversal invariant, we are careful to distinguish time intervals in which this symmetry is preserved and th…
Vortices are topological objects representing the circular motion of a fluid. With their additional degree of freedom, the 'vorticity', they have been widely investigated in many physical systems and different materials for fundamental interest and for applications in data storage and information processing. Vortices have also been observed in non-equilibrium exciton-polariton condensates in planar semiconductor microcavities. There they appear spontaneously or can be created and pinned in space using ring-shaped optical excitation profiles. However, using the vortex state for information proc…
Spinorial or multi-component Bose-Einstein condensates may sustain fractional quanta of circulation, vorticant topological excitations with half integer windings of phase and polarization. Matter-light quantum fluids, such as microcavity polaritons, represent a unique test bed for realising strongly interacting and out-of-equilibrium condensates. The direct access to the phase of their wavefunction enables us to pursue the quest of whether half vortices ---rather than full integer vortices--- are the fundamental topological excitations of a spinor polariton fluid. Here, we are able to directly…
Polariton condensates have proved to be model systems to investigate topological defects, as they allow for direct and non-destructive imaging of the condensate complex order parameter. The fundamental topological excitations of such systems are quantized vortices. In specific configurations, further ordering can bring the formation of vortex lattices. In this work we demonstrate the spontaneous formation of ordered vortical states, consisting in geometrically self-arranged vortex-antivortex pairs. A mean-field generalized Gross-Pitaevskii model reproduces and supports the physics of the obser…
The coexistence of the energy and enstrophy cascades in 2D quantum turbulence is one of the important open questions in the studies of quantum fluids. Here, we show that polariton condensates are particularly suitable for the possible observation of scaling on sufficiently large scales. The shape of raw energy spectra depends on the procedure of condensate excitation (stirring), but the energy spectra of clustered vortices always exhibit the -5/3 power law. In the optimal case, the cascade can be observed over almost 2 decades.
Persistent currents in annular geometries have played an important role in disclosing the quantum phase coherence of superconductors and mesoscopic electronic systems. Ultracold atomic gases in multiply connected traps also exhibit long-lived supercurrents, and have attracted much interest both for fundamental studies of superfluid dynamics and as prototypes for atomtronic circuits. Here, we report on the realization of supercurrents in homogeneous, tunable fermionic rings. We gain exquisite, rapid control over quantized persistent currents in all regimes of the BCS-BEC crossover through a uni…
Strongly-coupled quantum fields, such as multi-component atomic condensates, optical fields and polaritons, are remarkable systems where the simple dynamics of coupled oscillators can meet the intricate phenomenology of quantum fluids. When the coupling between the components is coherent, not only the particles number, but also their phase texture that maps the linear and angular momentum, can be exchanged. Here, on a system of exciton-polaritons, we have realized a so-called full-Bloch beam: a configuration in which all superpositions of the upper and the lower polariton -- all quantum states…
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic pha…
The unitary Fermi gas (UFG) offers an unique opportunity to study quantum turbulence both experimentally and theoretically in a strongly interacting fermionic superfluid. It yields to accurate and controlled experiments, and admits the only dynamical microscopic description via time-dependent density functional theory (DFT) - apart from dilute bosonic gases - of the crossing and reconnection of superfluid vortex lines conjectured by Feynman in 1955 to be at the origin of quantum turbulence in superfluids at zero temperature. We demonstrate how various vortex configurations can be generated by …
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…
Topological defects such as quantized vortices are one of the most striking manifestations of the superfluid nature of Bose-Einstein condensates and typical examples of quantum mechanical phenomena on a macroscopic scale. Here we demonstrate the formation of a lattice of vortex-antivortex pairs and study, for the first time, its properties in the non-linear regime at high polarion-density where polariton-polariton interactions dominate the behaviour of the system. In this work first we demonstrate that the array of vortex-antivortex pairs can be generated in a controllable way in terms of size…
Exciton-polaritons in a microcavity are composite two-dimensional bosonic quasiparticles, arising from the strong coupling between confined light modes in a resonant planar optical cavity and excitonic transitions, typically using excitons in semiconductor quantum wells (QWs) placed at the antinodes of the same cavity. Quantum phenomena such as Bose-Einstein condensation (BEC), quantized vortices, and macroscopic quantum states have been reported at temperatures from tens of Kelvin up to room temperatures, and polaritonic devices such as spin switches \cite{Amo2010} and optical transistors hav…
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 …
Although only a handful of organic materials have shown polariton condensation, their study is rapidly becoming more accessible. The spontaneous appearance of long-range spatial coherence is often recognized as a defining feature of such condensates. In this work, we study the emergence of spatial coherence in an organic microcavity and demonstrate a number of unique features stemming from the peculiarities of this material set. Despite its disordered nature, we find that correlations extend over the entire spot size and we measure $g^{(1)}(r,r')$ values of nearly unity at short distances and …
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 study the vortex dynamics of a quantum degenerate Bose gas through the intensity fluctuations of the interference from particles extracted at two different positions. It is shown numerically with classical field simulations that an interacting Bose gas with proliferating vortices exhibits long correlation times for these intensity fluctuations. This behavior is contrasted with the case of a noninteracting gas, that we describe analytically, and with the case of a well condensed Bose gas without vortices. We discuss the observability of our predictions in quantum fluids of exciton-polaritons…
