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:0909.1683 · Physical Review A

Nonequilibrium dynamics of vortex arrest in a finite-temperature Bose-Einstein condensate

Tod M. Wright, Ashton S. Bradley, R. J. Ballagh

Published Jan 15, 2010• 10 citations
arXivHTMLPDF

Abstract

We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.

DOI
10.1103/physreva.81.013610

Related papers

Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking

Tod M. Wright, Ashton S. Bradley, R. J. Ballagh

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.

arXiv:0908.2551•Physical Review A•Nov 24, 2009•20 citations

Vortex Lattice in a Rotating Bose-Einstein Condensate

Enikő J. M. Madarassy

Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.

arXiv:0807.3633•Jul 23, 2008•0 citations

Finite-temperature dynamics of vortices in Bose-Einstein condensates

Sandeep Gautam, Arko Roy, Subroto Mukerjee

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

arXiv:1309.6205•Physical Review A•Jan 14, 2014•22 citations

Dynamics of quantum vortices at finite temperature

Tod M. Wright

In this thesis, we perform investigations into the behaviour of finite-temperature degenerate Bose gases using a classical-field formalism, focussing in particular on the dynamics of quantum vortices in these systems. We demonstrate that the coherence of the classical field can be characterised by its temporal correlations, and discuss how the phase-symmetry-broken averages familiar from mean-field theories emerge from the field trajectories. We show that a finite-temperature condensate containing a precessing vortex in a cylindrically symmetric trap can be realised as an ergodic equilibrium of the classical-field theory, and demonstrate the identification of the rotationally symmetry-broken condensate orbital and core-filling thermal component from the field correlations. We then consider the nonequilibrium dynamics that result when such a precessing-vortex configuration is subjected to a static trap anisotropy which arrests its rotation, and observe novel coupled relaxation dynamics of the condensed and noncondensed components of the field. Finally, we consider the nucleation of vortices in an initially zero-temperature quasi-two-dimensional condensate stirred by a rotating trap anisotropy. We quantify the emergence of a rotating thermal component of the field, which drives the nucleation of vortices from condensate-surface oscillations, and study the relaxation and rotational equilibration of the initially turbulent collection of vortices. We find that thermal fluctuations of the field prevent the vortices from settling into a rigid crystalline lattice in this reduced dimensionality, and that true condensation in the field is completely destroyed by the disordered motion of vortices. We show, however, that the temporal correlations of the field distinguish the quasi-coherent vortex-liquid phase in the trap centre from the truly thermal material in its periphery.

arXiv:1011.5710•Nov 26, 2010•1 citation

Dynamical thermalization and vortex formation in stirred two-dimensional Bose-Einstein condensates

Tod M. Wright, R. J. Ballagh, Ashton S. Bradley +2 more

We present a quantum-mechanical treatment of the mechanical stirring of Bose-Einstein condensates using classical field techniques. In our approach the condensate and excited modes are described using a Hamiltonian classical field method in which the atom number and (rotating frame) energy are strictly conserved. We simulate a $T=0$ quasi-two-dimensional condensate perturbed by a rotating anisotropic trapping potential. Vacuum fluctuations in the initial state provide an irreducible mechanism for breaking the initial symmetries of the condensate and seeding the subsequent dynamical instability. Highly turbulent motion develops and we quantify the emergence of a rotating thermal component that provides the dissipation necessary for the nucleation and motional damping of vortices in the condensate. Vortex lattice formation is not observed, rather the vortices assemble into a spatially disordered vortex liquid state. We discuss methods we have developed to identify the condensate in the presence of an irregular distribution of vortices, determine the thermodynamic parameters of the thermal component, and extract damping rates from the classical field trajectories.

arXiv:0808.3552•Physical Review A•Dec 2, 2008•29 citations

Diffusive instability of a vortex in a rotating Bose gas

Ashton S. Bradley, Crispin W. Gardiner

The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.

arXiv:cond-mat/0509592•Sep 23, 2005•1 citation
We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.
We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.
In this thesis, we perform investigations into the behaviour of finite-temperature degenerate Bose gases using a classical-field formalism, focussing in particular on the dynamics of quantum vortices in these systems. We demonstrate that the coherence of the classical field can be characterised by its temporal correlations, and discuss how the phase-symmetry-broken averages familiar from mean-field theories emerge from the field trajectories. We show that a finite-temperature condensate containing a precessing vortex in a cylindrically symmetric trap can be realised as an ergodic equilibrium of the classical-field theory, and demonstrate the identification of the rotationally symmetry-broken condensate orbital and core-filling thermal component from the field correlations. We then consider the nonequilibrium dynamics that result when such a precessing-vortex configuration is subjected to a static trap anisotropy which arrests its rotation, and observe novel coupled relaxation dynamics of the condensed and noncondensed components of the field. Finally, we consider the nucleation of vortices in an initially zero-temperature quasi-two-dimensional condensate stirred by a rotating trap anisotropy. We quantify the emergence of a rotating thermal component of the field, which drives the nucleation of vortices from condensate-surface oscillations, and study the relaxation and rotational equilibration of the initially turbulent collection of vortices. We find that thermal fluctuations of the field prevent the vortices from settling into a rigid crystalline lattice in this reduced dimensionality, and that true condensation in the field is completely destroyed by the disordered motion of vortices. We show, however, that the temporal correlations of the field distinguish the quasi-coherent vortex-liquid phase in the trap centre from the truly thermal material in its periphery.
We present a quantum-mechanical treatment of the mechanical stirring of Bose-Einstein condensates using classical field techniques. In our approach the condensate and excited modes are described using a Hamiltonian classical field method in which the atom number and (rotating frame) energy are strictly conserved. We simulate a T=0T=0T=0 quasi-two-dimensional condensate perturbed by a rotating anisotropic trapping potential. Vacuum fluctuations in the initial state provide an irreducible mechanism for breaking the initial symmetries of the condensate and seeding the subsequent dynamical instability. Highly turbulent motion develops and we quantify the emergence of a rotating thermal component that provides the dissipation necessary for the nucleation and motional damping of vortices in the condensate. Vortex lattice formation is not observed, rather the vortices assemble into a spatially disordered vortex liquid state. We discuss methods we have developed to identify the condensate in the presence of an irregular distribution of vortices, determine the thermodynamic parameters of the thermal component, and extract damping rates from the classical field trajectories.
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.