Dynamics Of Quantized Vortices Research Articles

Quantized vortex dynamics of the nonlinear wave equation on the torus

Quantized vortex dynamics of the nonlinear wave equation on the torus

Influence of Quantized Vortex Dynamics on Superconducting Detectors

Influence of Quantized Vortex Dynamics on Superconducting Detectors

Vortex detection in atomic Bose–Einstein condensates using neural networks trained on synthetic images

Quantum vortices in atomic Bose–Einstein condensates (BECs) are topological defects characterized by quantized circulation of particles around them. In experimental studies, vortices are commonly detected by time-of-flight imaging, where their density-depleted cores are enlarged. In this work, we describe a machine learning-based method for detecting vortices in experimental BEC images, particularly focusing on turbulent condensates containing irregularly distributed vortices. Our approach employs a convolutional neural network (CNN) trained solely on synthetic simulated images, eliminating the need for manual labeling of the vortex positions as ground truth. We find that the CNN achieves accurate vortex detection in real experimental images, thereby facilitating analysis of large experimental datasets without being constrained by specific experimental conditions. This novel approach represents a significant advancement in studying quantum vortex dynamics and streamlines the analysis process in the investigation of turbulent BECs.

Relative dynamics of quantum vortices and massive cores in binary BECs

We study the motion of superfluid vortices with filled massive cores. Previous point-vortex models already pointed out the impact of the core mass on the vortex dynamical properties, but relied on an assumption that is questionable in many physical systems where the immiscibility condition is barely satisfied: the fact that the massive core always lays at the very bottom of the effective confining potential constituted by the hosting vortex. Here, we relax this assumption and present a new point-vortex model where quantum vortices are harmonically coupled to their massive cores. We thoroughly explore the new dynamical regimes offered by this improved model; we then show that the functional dependence of the system normal modes on the microscopic parameters can be correctly interpreted only within this new generalized framework. Our predictions are benchmarked against the numerical simulations of coupled Gross–Pitaevskii equations for a realistic mixture of atomic Bose–Einstein condensates.

Quantized vortex dynamics of the nonlinear Schrödinger equation on torus with non-vanishing momentum

We derive rigorously the reduced dynamical law for quantized vortex dynamics of the nonlinear Schrödinger equation on the torus with non-vanishing momentum when the vortex core size ɛ→0. The reduced dynamical law is governed by a Hamiltonian flow driven by a renormalized energy. A key ingredient is to construct a new canonical harmonic map to include the effect from the non-vanishing momentum into the dynamics. Finally, some properties of the reduced dynamical law are discussed.

Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero temperature limit. In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt (C. Coste, 1998 [22]) to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II. We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii model based on a slip velocity respecting the dynamics of vortex lines in the normal fluid. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations. Finally, we numerically test and validate the new numerical system against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings). The new coupling model has the advantage to keep the full Gross-Pitaevskii model for the superfluid, and thus describe quantized vortex dynamics without any phenomenological approximation. This opens new possibilities to revisit and enrich existing numerical results for complex quantum fluids, such as quantum turbulent flows.

Dissipative Dynamics of Quantum Vortices in Fermionic Superfluid.

In a recent article, Kwon etal. [Nature (London) 600, 64 (2021)NATUAS0028-083610.1038/s41586-021-04047-4] revealed nonuniversal dissipative dynamics of quantum vortices in a fermionic superfluid. The enhancement of the dissipative process is pronounced for the Bardeen-Cooper-Schrieffer interaction regime, and it was suggested that the effect is due to the presence of quasiparticles localized inside the vortex core. We test this hypothesis through numerical simulations with time-dependent density-functional theory: a fully microscopic framework with fermionic degrees of freedom. The results of fully microscopic calculations expose the impact of the vortex-bound states on dissipative dynamics in a fermionic superfluid. Their contribution is too weak to explain the experimental measurements, and we identify that thermal effects, giving rise to mutual friction between superfluid and the normal component, dominate the observed dynamics.

Dipole dynamics in the point vortex model

At the very heart of turbulent fluid flows are many interacting vortices that produce a chaotic and seemingly unpredictable velocity field. Gaining new insight into the complex motion of vortices and how they can lead to topological changes of flows is of fundamental importance in our strive to understand turbulence. Our aim is form an understanding of vortex interactions by investigating the dynamics of point vortex dipoles interacting with a hierarchy of vortex structures using the idealized point vortex model. Motivated by its close analogy to the dynamics of quantum vortices in Bose–Einstein condensates, we present new results on dipole size evolution, stability properties of vortex clusters, and the role of dipole–cluster interactions in turbulent mixing in 2D quantum turbulence. In particular, we discover a mechanism of rapid cluster disintegration analogous to a time-reversed self-similar vortex collapse solution.

How trapped particles interact with and sample superfluid vortex excitations

Particles have been used for more than a decade to visualize and study the dynamics of quantum vortices in superfluid helium. In this work we study how the dynamics of a collection of particles set inside a vortex reflects the motion of the vortex. We use a self-consistent model based on the Gross-Pitaevskii equation coupled with classical particle dynamics. We find that each particle oscillates with a natural frequency proportional to the number of vortices attached to it. We then study the dynamics of an array of particles trapped in a quantum vortex and use particle trajectories to measure the frequency spectrum of the vortex excitations. Surprisingly, due to the discreetness of the array, the vortex excitations measured by the particles exhibits bands, gaps and Brillouin zones, analogous to the ones of electrons moving in crystals. We then establish a mathematical analogy where vortex excitations play the role of electrons and particles that of the potential barriers constituting the crystal. We find that the height of the effective potential barriers is proportional to the particle mass and the frequency of the incoming waves. We conclude that large-scale vortex excitations could be in principle directly measured by particles and novel physics could emerge from particle-vortex interaction.

Kähler quantization of vortex moduli

We discuss the K\"ahler quantization of moduli spaces of vortices in line bundles over compact surfaces $\Sigma$. This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schr\"odinger-Chern-Simons model. We follow Deligne's approach to Quillen's metric in determinants of cohomology to construct all the quantum Hilbert spaces in this context. An alternative description of the quantum wavesections, in terms of multiparticle states of spinors on $\Sigma$ itself (valued in a prequantization of a multiple of its area form), is also obtained. This viewpoint sheds light on the nature of the quantum solitonic particles that emerge from the gauge theory. We find that in some cases (where the area of $\Sigma$ is small enough in relation to its genus) the dimensions of the quantum Hilbert spaces may be sensitive to the input data required by the quantization scheme, and also address the issue of relating different choices of such data geometrically.

Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates

We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose–Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta.

Braiding and Fusion of Non-Abelian Vortex Anyons.

We have studied topology and dynamics of quantum vortices in spin-2 Bose-Einstein condensates. By computationally modeling controllable braiding and fusion of these vortices, we have demonstrated that certain vortices in such spinor condensates behave as non-Abelian anyons. We identify these anyons as fluxon, chargeon, and dyon quasiparticles. The pertinent anyon models are defined by the quantum double of the underlying discrete non-Abelian symmetry group of the condensate ground state order parameter.

Нелінійна динаміка квантових вихорів у довгих Джозефсонових переходах

Нелінійна динаміка квантових вихорів у довгих Джозефсонових переходах

Chaotic vortex filaments in a Bose – Einstein condensate and in superfluid helium

A statement of the quantum turbulence problem in both a Bose – Einstein condensate (BEC) and superfluid helium is formulated. In superfluid helium use is made of a so-called vortex filament method, in which quantum vortices are represented by string-like objects, i.e. vortex lines. The dynamics of the vortex lines is determined by deterministic equations of motion, supplemented by random reconnections. Unlike He II, the laws of the dynamics of quantum vortices in BEC are based on the nonlinear Schrödinger equation. This makes it possible to obtain a microscopic description of the collision of vortices, the structure of a vortex filament, etc. A comparative analysis of these complementary approaches is carried out. It is shown that there are some features that do not automatically transfer the results obtained for BEC to vortices in He II and vice versa.

Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law

We study analytically and numerically stability and interaction patterns of quantized vortex lattices governed by the reduced dynamical law -- a system of ordinary differential equations (ODEs) -- in superconductivity. By deriving several non-autonomous first integrals of the ODEs, we obtain qualitatively dynamical properties of a cluster of quantized vortices, including global existence, finite time collision, equilibrium solution and invariant solution manifolds. For a vortex lattice with 3 vortices, we establish orbital stability when they have the same winding number and find different collision patterns when they have different winding numbers. In addition, under several special initial setups, we can obtain analytical solutions for the nonlinear ODEs.

Visualization of grid-generated turbulence in He II using PTV

Due to its low viscosity, cryogenic He II has potential use for simulating large-scale, high Reynolds number turbulent flow in a compact and efficient apparatus. To realize this potential, the behavior of the fluid in the simplest cases, such as turbulence generated by flow past a mesh grid, must be well understood. We have designed, constructed, and commissioned an apparatus to visualize the evolution of turbulence in the wake of a mesh grid towed through He II. Visualization is accomplished using the particle tracking velocimetry (PTV) technique, where μm-sized tracer particles are introduced to the flow, illuminated with a planar laser sheet, and recorded by a scientific imaging camera; the particles move with the fluid, and tracking their motion with a computer algorithm results in a complete map of the turbulent velocity field in the imaging region. In our experiment, this region is inside a carefully designed He II filled cast acrylic channel measuring approximately 16 × 16 × 330 mm. One of three different grids, which have mesh numbers M = 3, 3.75, or 5 mm, can be attached to the pulling system which moves it through the channel with constant velocity up to 600 mm/s. The consequent motion of the solidified deuterium tracer particles is used to investigate the energy statistics, effective kinematic viscosity, and quantized vortex dynamics in turbulent He II.

Dynamics of quantum vortices in a quasi-two-dimensional Bose–Einstein condensate with two “holes”

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

Hydrodynamics of vortices in Bose-Einstein condensates: A defect-gauge field approach

This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the $U(1)$ phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal $t^{1/2}$ behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid $^{4}$He, dipolar condensates, and mixtures of different superfluid systems.

Dynamics of Quantized Vortices Before Reconnection

The main goal of this paper is to investigate numerically the dynamics of quantized vortex loops, just before the reconnection at finite temperature, when mutual friction essentially changes evolution of lines. Modeling is performed on the base of vortex filament method with using the full Biot-Savart equation. It was discovered that initial position of vortices and the temperature strongly affect the dependence on time of the minimum distance $\delta (t)$ between tips of two vortex loops. In particular, in some cases the shrinking and collapse of vortex loops due to mutual friction occur earlier than reconnection, thereby cancelling the latter. However, this relationship takes a universal square-root form $\delta\left(t\right)=\sqrt{\left(\kappa/2\pi\right)\left(t_{*}-t\right)}$ at distances smaller than the one, satisfying the Schwarz criterion, when nonlocal contribution to the Biot-Savart equation becomes about equal to local contribution. In the "universal" the nearest parts of vortices form a pyramid-like structure with angles which are also don't depend both on the initial configuration of filaments and on the temperature.

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.