We consider superfluid hydrodynamics of two-dimensional Bose-Einstein condensates. Interpreting the curvature of the macroscopic condensate wavefunction as an effective gravity in such a superfluid universe, we argue for a superfluid equivalence principle---that the gravitational mass of a quantised vortex should be equal to the inertial vortex mass. In this model, gravity and electromagnetism have the same origin and are emergent properties of the superfluid universe, which itself emerges from the underlying collective structure of more elementary particles, such as atoms. The Bose-Einstein condensate is identified as the elusive dark matter of the superfluid universe with vortices and phonons, respectively, corresponding to massive charged particles and massless photons. Implications of this cosmological picture of superfluids to the physics of dense vortex matter are considered.
We use holography to investigate the dynamics of a vortex-anti-vortex dipole in a strongly coupled superfluid in 2+1 dimensions. The system is evaluated in numerical real-time simulations in order to study the evolution of the vortices as they approach and eventually annihilate each other. A tracking algorithm with sub-plaquette resolution is introduced which permits a high-precision determination of the vortex trajectories. With the increased precision of the trajectories it becomes possible to directly compute the vortex velocities and accelerations. We find that in the holographic superflui…
Annihilation process of a pair of vortices in holographic superfluid is numerically simulated. The process is found to consist of two stages which are amazingly separated by vortex size $2r$. The separation distance $δ(t)$ between vortex and anti-vortex as a function of time is well fitted by $α(t_{0}-t)^{n}$, where the scaling exponent $n=1/2$ for $δ(t)>2r$, and $n=2/5$ for $δ(t)<2r$. Then the approaching velocity and acceleration as functions of time and as functions of separation distance are obtained. Thus the attractive force between vortex and anti-vortex is derived as $f(δ)\propto 1/δ^{…
Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by mapping the dynamics of certain quantum theories onto the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov -5/3 scaling law, as it does for turbulent flows in normal fluid…
Holographic duality provides a description of strongly coupled quantum systems in terms of weakly coupled gravitational theories in a higher-dimensional space. It is a challenge, however, to quantitatively determine the physical parameters of the quantum systems corresponding to generic holographic theories. Here, we address this problem for the two-dimensional holographic superfluid, known to exhibit strong dissipation. We numerically simulate the motion of a vortex dipole and perform a high-precision matching of the corresponding dynamics resulting from the dissipative Gross-Pitaevskii equat…
We study two dimensional superfluid turbulence by employing an effective description valid in the limit where the density of superfluid vortices is parametrically small. At sufficiently low temperatures the effective description yields an inverse cascade with Kolmogorov energy spectrum $E(k) \sim k^{-5/3}$. Denoting the number of vortices as a function of time by $N(t)$, we find that the vortex annihilation rate scales like $\dot N \sim N^{5/3}$ in states with an inverse cascade and $\dot N \sim N^2$ for laminar flow.
We report on the experimental observation of vortex cluster shedding from a moving obstacle in an oblate atomic Bose-Einstein condensate. At low obstacle velocities $v$ above a critical value, vortex clusters consisting of two like-sign vortices are generated to form a regular configuration like a von Kármán street, and as $v$ is increased, the shedding pattern becomes irregular with many different kinds of vortex clusters. In particular, we observe that the Stouhal number associated with the shedding frequency exhibits saturation behavior with increasing $v$. The regular-to-turbulent transiti…
We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localised within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.
We study numerically the formation of a vortex lattice inside a rotating bucket containing superfluid helium, paying attention to an important feature which is practically unavoidable in all experiments: the microscopic roughness of the bucket's surface. We model this using the Gross-Pitaevskii for a weakly-interacting Bose gas, a model which is idealised when applied to superfluid helium but captures the key physics of the vortex dynamics which we are interested in. We find that the vortex lattice arises from the interaction and reconnections of nucleated U-shaped vortex lines, which merge an…
We apply a recently developed effective string theory for vortex lines to the case of two-dimensional trapped superfluids. We do not assume a perturbative microscopic description for the superfluid, but only a gradient expansion for the long-distance hydrodynamical description and for the trapping potential. For any regular trapping potential, we compute the spatial dependence of the superfluid density and the orbital frequency and trajectory of an off-center vortex. Our results are fully relativistic, and in the non-relativistic limit reduce to known results based on the Gross-Pitaevskii mode…
We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response pro…
We present a systematic derivation of the effective action for interacting vortices in a non-relativistic two-dimensional superfluid described by the Gross-Pitaevskii equation by integrating out longitudinal fluctuations of the order parameter. There are no logarithmically divergent coefficients in the equations of motion. Our analysis is valid in a dilute limit of vortices where the intervortex spacing is large compared to the core size, and where number fluctuations of atoms in vortex cores are suppressed. We analyze sound-induced corrections to the dynamics of a vortex-antivortex pair and s…
We theoretically investigate the generation of the vortex dipoles in superfluid Fermi gas in the BCS limit. The vortex dipoles are generated in superfluid either by moving an obstacle above a critical speed or due to the decay of the shock waves obtained on the sudden mixing of two superfluid fragments. We observe that in pancake-shaped traps, the shock waves can lead to the formation of density ripples, which decay into vortex dipoles due to the onset of snake instability.
We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled, using truncated Wigner approximation. On short time scales the relative phase shows "light cone" like thermalization and creates a metastable superfluid state, which can be supercritical. On longer time scales this state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a {\it reverse-Kibble-Zurek effect}. We observe dynamics of creation of vortex anti-vortex pairs and their…
In this letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to different vortex core structure of the Fermi superfluid in the BCS regime and in the BEC regime. In the former the vortex core is nearly filled, while the density at the vortex core gradually decreases until it empties out at the BEC regime. Therefore, with the density-density interaction between the Bose and the Fermi superfluids, the two sets of vortex lattices int…
Mutual friction and vortex Hall angle in a strongly interacting Fermi superfluid
University of Florence（佛罗伦萨大学）；European Laboratory for Nonlinear Spectroscopy (LENS), University of Florence（佛罗伦萨大学非线性光谱学欧洲实验室）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家研究委员会光学研究所）；INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France（巴黎高等师范学院-巴黎文理研究大学-法国国家科学研究中心-索邦大学-法兰西公学院卡斯勒布罗塞尔实验室）；Department of Physics and Astronomy, University of Bologna（博洛尼亚大学物理与天文学系）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）
We use optical images of a superfluid consisting of a weakly interacting Bose-Einstein condensate of sodium atoms to investigate the structure of quantized three-dimensional vortex filaments. We find that the measured optical contrast and the width of the vortex core quantitatively agree with the predictions of the Gross-Pitaevskii equation.
The superfluid flow velocity is proportional to the gradient of the phase of the superfluid order parameter, leading to the quantization of circulation around a vortex core. In this work, we study the dynamics of a superfluid film on the surface of a torus. Such a compact surface allows only configurations of vortices with zero net vorticity. We derive analytic expressions for the flow field, the total energy, and the time-dependent dynamics of the vortex cores. The local curvature of the torus and the presence of non-contractable loops on this multiply connected surface alter both the superfl…
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…
We consider geometric phases of mobile quantum vortices in superfluid Bose-Einstein condensates. Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, $γ_{\mathcal C}=2πN_{\mathcal C}$, of such a vortex is determined by the number of condensate atoms $N_{\mathcal C}$ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase;…
Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles a…
We follow the time evolution of a superfluid Fermi gas of resonantly interacting $^6$Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a vortex ring, which in turn breaks to finally leave behind a single solitonic vortex. In intermediate stages we find evidence for an exotic structure resembling the $Φ$-soliton, a combination of a vortex ring and a vortex line. Direct imaging of the nodal surface reveals its undulation dynamics and its decay via the puncture of the initial soliton plane. The ob…
We characterize the mechanisms of vortex pinning in a superfluid thin film described by the two-dimensional Gross-Pitaevskii equation. We consider a vortex "scattering experiment" whereby a single vortex in a superfluid flow interacts with a circular, uniform pinning potential. By an analogy with linear dielectrics, we develop an analytical hydrodynamic approximation that predicts vortex trajectories, the vortex fixed point and the unpinning velocity. We then solve the Gross-Pitaevskii equation to validate this model, and build a phase portrait of vortex pinning. We identify two different dyna…
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 dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal transformation from the surface to the complex plane allows us to use familiar formalism to describe the motion of the quantized vortices and to find the total energy. The simplest case is a vortex dipole with unit vortex charges on an axisymmetric ellipsoid. We study two special symmetric vortex-dipole configurations along with a general asymmetric one.
Within the simplest holographic superfluid model and without any ingredients put by hand, it is shown that vortices can be generated when the angular velocity of rotating superfluids exceeds certain critical values, which can be precisely determined by linear perturbation analyses (quasi-normal modes of the bulk AdS black brane). These vortices appear at the edge of the superfluid system first, and then automatically move into the bulk of the system, where they are eventually stabilized into certain vortex lattices. For the case of 18 vortices generated, we find (at least) five different patte…
We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana ferm…
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 study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimental…
A statistical model is advanced for describing quantum turbulence in a superfluid system with Bose-Einstein condensate. Such a turbulent superfluid can be realized for trapped Bose atoms subject to either an alternating trapping potential or to an alternating magnetic field modulating the atomic scattering length by means of Feshbach resonance. The turbulent system is represented as a continuous mixture of states each of which is characterized by its own vorticity corresponding to a particular vortex.
We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: $m_1\ne m_2$. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case $m_2/m_1 = 2$ and list a number of geometries that are found for higher integer mass ratios.
We study the motion of a vortex under the influence of a harmonic force in an approximately two dimensional trapped Bose-condensed gas. The Hall-Vinen-Iordanskii equations, modified to include a fluctuational force and an inertial mass term, are solved for the vortex motion. The mass of the vortex has a strong influence on the time it takes the vortex to escape the trap. Since the vortex mass also depends on the trap size we have an additional dependence on the trap size in the escape time which we compare to the massless case.
Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved exactly in a model "slab" geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterizing the vortex cores, to the slab width. The key dynamical properties of the vortex, the inerti…
We derive an effective action for the vortex position degree-of-freedom in a superfluid by integrating out condensate phase and density fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius $R$, or the typical distance between vortices, is very much larger than the coherence length $ξ$. We go beyond the adiabatic approximation numerically, accounting for the …
Motivated by ongoing experimental efforts to make closed Bose-Einstein condensate (BEC) shells in microgravity environments, this work studies the energy and dynamics of singly quantized vortices on a thin spherical superfluid shell, where the overall vortex charge must vanish (as on any compact surface). For each vortex, stereographic projection yields the corresponding complex potential on the tangent plane. The resulting stream function then provides both the total energy and the dynamics of a system of overall neutral vortices on a spherical film. Although a single vortex dipole follows a …
We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform single-component superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov--de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.
We study quantum vortex states consisting of a ring of vortices with alternating sign, in a homogeneous superfluid confined to a circular domain. We find an exact stationary solution of the point vortex model for the neutral vortex necklace. We investigate the stability of the necklace state within both the point-vortex model and the Gross-Pitaevskii equation describing a trapped atomic Bose-Einstein condensate at low temperature. The point-vortex stationary states are found to also be stationary states of the Gross-Pitaevskii equation provided the finite thickness of the outer fluid boundary …
We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the straight sides. The sector can then be mapped conformally to the whole plane, leading to the relevant stream function. In this way, we show that a superfluid vortex on the cone precesses uniformly at fixed distance from the apex. The stream function also yields directly the interaction energy of two vortices on the cone. We then study the vortex dynamics on unbo…
We propose a robust imaging technique that makes it possible to distinguish vortices from antivortices in quasi-two-dimensional Bose--Einstein condensates from a single image of the density of the atoms. Tilting the planar condensate prior to standard absorption imaging excites a generalized gyroscopic mode of the condensate revealing the sign and location of each vortex. This technique is anticipated to enable experimental measurement of the incompressible kinetic energy spectrum of the condensate and the observation of a negative temperature phase transition of the vortex gas, driven by two-…
We study the dynamics of a vortex in a quasi two-dimensional Bose gas consisting of light matter coupled atoms forming two-component pseudo spins. The gas is subject to a density dependent gauge potential, hence governed by an interacting gauge theory, which stems from a collisionally induced detuning between the incident laser frequency and the atomic energy levels. This provides a back-action between the synthetic gauge potential and the matter field. A Lagrangian approach is used to derive an expression for the force acting on a vortex in such a gas. We discuss the similarities between this…
I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in …
The stability conditions for the singular vortex which accompanies Majorana zero modes at the core are investigated for p-wave resonant superfluids of atomic Fermi gases. Within the Ginzburg-Landau framework we determine the stable conditions in the parameter space for the external rotation frequency and the harmonic trap frequency. There exists the narrow stable region in this parameter space for quasi-two-dimensional condensates. We also describe the detailed characterizations of the spatial structure of the order parameter in the chiral p-wave superfluids under rotation.
We study spontaneous-symmetry-broken phase-separated vortex lattice in a weakly interacting uniform rapidly rotating binary Bose superfluid contained in a quasi-two-dimensional circular or square bucket. For the inter-species repulsion above a critical value, the two superfluid components separate and form a demixed phase with practically no overlap in the vortex lattices of the two components, which will permit an efficient experimental observation of such vortices and study their properties. In case of a circular bucket with equal intra-species energies of the two components, the two compone…
The superfluid mixture of interacting Bose and Fermi species is a remarkable many-body quantum system. Dilute degenerate atomic gases, especially for two species of distinct masses, are excellent candidates for exploring fundamental features of superfluid mixture. However, producing a mass-imbalance Bose-Fermi superfluid mixture, providing an unambiguous visual proof of two-species superfluidity and probing inter-species interaction effects remain challenging. Here, we report the realization of a two-species superfluid of lithium-6 and potassium-41. By rotating the dilute gases, we observe the…
Two-dimensional flow past an infinitely long cylinder of nanoscopic radius in superfluid He-4 at zero temperature is studied by time-dependent density functional theory. The calculations reveal two distinct critical phenomena for the onset of dissipation: 1) vortex-antivortex pair shedding from the periphery of the moving cylinder and 2) appearance of cavitation in the wake, which possesses similar geometry as observed experimentally for fast moving micrometer-scale particles in superfluid He-4. Vortex pairs with the same circulation are occasionally emitted in the form of dimers, which consti…
The bound states that can occur in a superfluid vortex have recently called for attention owing to the capability of detecting them experimentally. However, a detailed theoretical account for the presence of these vortex bound states is still lacking, for all temperatures in the superfluid phase and couplings along the BCS-BEC crossover. Here, we fill this gap and present a systematic theoretical study based on the Bogoliubov-de~Gennes equations for the bound states that occur over the two characteristic (inner and outer) spatial ranges in which the extension of a superfluid vortex can be part…
Two-dimensional superfluidity and quantum turbulence are directly connected to the microscopic dynamics of quantized vortices. However, surface effects have prevented direct observations of coherent vortex dynamics in strongly-interacting two-dimensional systems. Here, we overcome this challenge by confining a two-dimensional droplet of superfluid helium at microscale on the atomically-smooth surface of a silicon chip. An on-chip optical microcavity allows laser-initiation of vortex clusters and nondestructive observation of their decay in a single shot. Coherent dynamics dominate, with therma…
