Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2102.10193 · Physical Review A

Dynamics of elliptical vortices in a trapped quantum fluid

Chuanzhou Zhu, Mark E. Siemens, Mark T. Lusk

Published Oct 13, 2021• 6 citations
arXivHTMLPDF

Abstract

The nonequilibrium dynamics of vortices in two-dimensional quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.

DOI
10.1103/physreva.104.043306

Related papers

The Dynamics of a Tilted Vortex in a Trapped Quantum Fluid

Chuanzhou Zhu, Mark E. Siemens, Mark T. Lusk

The nonequilibrium dynamics of vortices in 2D quantum fluids are shown to obey a kinetic equation in which vortex tilt (ellipticity) is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a trapped, tilted vortex is analytically found to move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself, allowing experimental measurement of vortex tilt via path observation. A combination of analysis and simulation is then used to show that nonlinear interactions cause the vortex tilt to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex tilt and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate local vortex structure is expected to prove useful in designing few-vortex systems in which tilt is a ubiquitous, as-yet-unharnessed feature.

•Feb 19, 2021•0 citations

Motion of quantum vortices on inhomogeneous backgrounds

Peter Mason, Natalia G. Berloff

The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and an approximation for the density background is useful to understand vortex motion. We analyze the vortex motion on a variety of background configurations motivated by experiments on trapped Bose-Einstein condensates including linear and quadratic traps. We show that close to the center of the condensate cloud in the Thomas-Fermi regime the vortex is moving predominantly due to the image vortex that is effectively shifted because of the large density depletion of the condensate at the boundary. Close to the boundary the vortex moves mostly due to a large background density gradient across the vortex core. The vortex velocity is a nonlinear combination of these effects and of the global shape of the background density. We find the complete families of the traveling coherent structures in an infinitely long two-dimensional channel and derive an approximation of the velocity of a single vortex moving close to the center of the channel in the Thomas-Fermi regime.

Physical Review A•Mar 20, 2008•28 citations

Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: The case of an elliptical boundary

Matteo Caldara, Andrea Richaud, Pietro Massignan +1 more

Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex configurations may be computed on a complicated (curved or bounded) surface, provided that one knows a conformal map that links the latter to a simpler domain (like the full plane, or a circular boundary). We also prove that Hamilton’s equations based on the vortex energy agree with the complex dynamical equations for the vortex dynamics, demonstrating that the vortex trajectories are constant-energy curves. We use these ideas to study the dynamics of vortices in a two-dimensional incompressible superfluid with an elliptical boundary, and we derive an analytical expression for the complex potential describing the hydrodynamic flow throughout the fluid. For a vortex inside an elliptical boundary, the orbits are nearly self-similar ellipses.

arXiv:2311.13545•SciPost Physics•Aug 8, 2024•0 citations

Jetlike tunneling from a trapped vortex

Eliahu Cohen, Stefan Muenzel, O. V. Farberovich +3 more

We analyze tunneling from vortex states in elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (nonlinear Schr\"odinger) equation, we derive analytically and demonstrate numerically an interesting type of quantum fluid flow: a jetlike singularity formed by the interaction between the vortex and the asymmetric trap. For strongly elongated traps and high enough vorticity, the ellipticity overwhelms the circular rotation, resulting in the ejection of jets in narrow, well-defined directions. These jets are formed due to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. Under proper conditions they will appear in any coherent wave system with angular momentum and noncircular symmetry, such as superfluids, Bose-Einstein condensates, and light.

arXiv:1107.0627•Physical Review A•Oct 17, 2013•6 citations

Exact Vortex Clusters of Two-Dimensional Quantum Fluid with Harmonic Confinement

Guishu Chong, Lingling Zhang, Wenhua Hai

A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schrödinger equation is presented, which describes different kinds of vortex structures. The dynamics of different vortex clusters, such as the single vortex, vortex pair, vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact solutions. The time evolutions of the wave of such vortices are demonstrated, and the orbits of motion of singular points in the vortices are also explored. The interactions of vortices in many-vortex clusters are discussed. A repulsive interaction between vortices with the same topological charge, and inter-annihilation and inter-creation of vortices with opposite topological charge, are shown.

Chinese Physics Letters•Apr 1, 2013•0 citations

Trapped vortex dynamics implemented in composite Bessel beams

Andrew A. Voitiv, Mark E. Siemens, Mark T. Lusk

The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement—theoretically and experimentally—initial conditions of vortex configurations first predicted in harmonically trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard-wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard-wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.

arXiv:2401.10132•Physics of Fluids•Jan 1, 2024•2 citations
The nonequilibrium dynamics of vortices in two-dimensional quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.
The nonequilibrium dynamics of vortices in 2D quantum fluids are shown to obey a kinetic equation in which vortex tilt (ellipticity) is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a trapped, tilted vortex is analytically found to move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself, allowing experimental measurement of vortex tilt via path observation. A combination of analysis and simulation is then used to show that nonlinear interactions cause the vortex tilt to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex tilt and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate local vortex structure is expected to prove useful in designing few-vortex systems in which tilt is a ubiquitous, as-yet-unharnessed feature.
The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and an approximation for the density background is useful to understand vortex motion. We analyze the vortex motion on a variety of background configurations motivated by experiments on trapped Bose-Einstein condensates including linear and quadratic traps. We show that close to the center of the condensate cloud in the Thomas-Fermi regime the vortex is moving predominantly due to the image vortex that is effectively shifted because of the large density depletion of the condensate at the boundary. Close to the boundary the vortex moves mostly due to a large background density gradient across the vortex core. The vortex velocity is a nonlinear combination of these effects and of the global shape of the background density. We find the complete families of the traveling coherent structures in an infinitely long two-dimensional channel and derive an approximation of the velocity of a single vortex moving close to the center of the channel in the Thomas-Fermi regime.
Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex configurations may be computed on a complicated (curved or bounded) surface, provided that one knows a conformal map that links the latter to a simpler domain (like the full plane, or a circular boundary). We also prove that Hamilton’s equations based on the vortex energy agree with the complex dynamical equations for the vortex dynamics, demonstrating that the vortex trajectories are constant-energy curves. We use these ideas to study the dynamics of vortices in a two-dimensional incompressible superfluid with an elliptical boundary, and we derive an analytical expression for the complex potential describing the hydrodynamic flow throughout the fluid. For a vortex inside an elliptical boundary, the orbits are nearly self-similar ellipses.
We analyze tunneling from vortex states in elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (nonlinear Schr\"odinger) equation, we derive analytically and demonstrate numerically an interesting type of quantum fluid flow: a jetlike singularity formed by the interaction between the vortex and the asymmetric trap. For strongly elongated traps and high enough vorticity, the ellipticity overwhelms the circular rotation, resulting in the ejection of jets in narrow, well-defined directions. These jets are formed due to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. Under proper conditions they will appear in any coherent wave system with angular momentum and noncircular symmetry, such as superfluids, Bose-Einstein condensates, and light.
A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schrödinger equation is presented, which describes different kinds of vortex structures. The dynamics of different vortex clusters, such as the single vortex, vortex pair, vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact solutions. The time evolutions of the wave of such vortices are demonstrated, and the orbits of motion of singular points in the vortices are also explored. The interactions of vortices in many-vortex clusters are discussed. A repulsive interaction between vortices with the same topological charge, and inter-annihilation and inter-creation of vortices with opposite topological charge, are shown.
The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement—theoretically and experimentally—initial conditions of vortex configurations first predicted in harmonically trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard-wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard-wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.