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:cond-mat/9912365 · Physical Review A

Dissipation and vortex creation in Bose-Einstein condensed gases

B. Jackson, J F McCann, Charles S. Adams

Published Apr 5, 2000• 95 citations
arXivHTMLPDF

Abstract

We solve the Gross-Pitaevskii equation to study energy transfer from an oscillating ``object'' to a trapped Bose-Einstein condensate. Two regimes are found: for object velocities below a critical value, energy is transferred by excitation of phonons at the motion extrema; while above the critical velocity, energy transfer is via vortex formation. The second regime corresponds to significantly enhanced heating, in agreement with a recent experiment.

DOI
10.1103/physreva.61.051603

Related papers

Vortices in trapped Bose-Einstein condensates

Brian Jackson

In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)

•Jan 1, 2000•1 citation

Motion of an object through a quantum fluid

T. Winiecki, Charles S. Adams

We simulate the motion of a massive object through a dilute Bose-Einstein condensate by numerical solution of the Gross-Pitaevskii equation coupled to an equation of motion for the object. Under a constant applied force, the object accelerates up to a maximum velocity where a vortex ring is formed which slows the object down. If the applied force is less than a critical value, the object becomes trapped within the vortex core. We show that the motion follows the time-independent solutions, and use these solutions to predict the conditions required for vortex detachment.

arXiv:cond-mat/0006125•Europhysics Letters (EPL)•Nov 1, 2000•46 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

Vortex Formation in Dilute Inhomogeneous Bose-Einstein Condensates

Brian K. Jackson, J F McCann, Charles S. Adams

We solve the time-dependent Gross-Pitaevskii in 2D to simulate the flow of an object through a dilute Bose-Einstein condensate trapped in a harmonic well. We demonstrate vortex formation and study the process in terms of the accumulation of phase slip and the evolution of the fluid velocity.

Physical Review Letters•May 4, 1998•167 citations

Vortex shedding and drag in dilute Bose-Einstein condensates

T Winiecki, B Jackson, J F McCann +1 more

Above a critical velocity, the dominant mechanism of energy transfer between a moving object and a dilute Bose-Einstein condensate is vortex formation. In this paper, we discuss the critical velocity for vortex formation and the link between vortex shedding and drag in both homogeneous and inhomogeneous condensates. We find that at supersonic velocities sound radiation also contributes significantly to the drag force.

arXiv:cond-mat/0004430•Journal of Physics B Atomic Molecular and Optical Physics•Sep 15, 2000•83 citations

Properties of vortices in Bose–Einstein condensates

Amandine Aftalion

One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.

Comptes Rendus Physique•Jan 1, 2004•4 citations
We solve the Gross-Pitaevskii equation to study energy transfer from an oscillating ``object'' to a trapped Bose-Einstein condensate. Two regimes are found: for object velocities below a critical value, energy is transferred by excitation of phonons at the motion extrema; while above the critical velocity, energy transfer is via vortex formation. The second regime corresponds to significantly enhanced heating, in agreement with a recent experiment.
In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)
We simulate the motion of a massive object through a dilute Bose-Einstein condensate by numerical solution of the Gross-Pitaevskii equation coupled to an equation of motion for the object. Under a constant applied force, the object accelerates up to a maximum velocity where a vortex ring is formed which slows the object down. If the applied force is less than a critical value, the object becomes trapped within the vortex core. We show that the motion follows the time-independent solutions, and use these solutions to predict the conditions required for vortex detachment.
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.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.