Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.

Dec 31, 20040 citations

Motion in a Bose condensate: VIII. The electron bubble

Natalia G. Berloff, Paul Harry Roberts

The Bose condensate model is used to elucidate the motion of the electron bubble in superfluids. An asymptotic expansion is developed for steady subcritical flow. Numerical integration of the coupled nonlinear Schrödinger equations, that describe the evolution of the wavefunctions of the Bose condensate and the impurity, is used to study the nucleation and capture of vortex rings. Because an electron bubble is made oblate by its motion relative to the condensate, the critical velocity for the vortex nucleation is reduced by about 20%, in agreement with experiments.The Bose condensate model is used to elucidate the motion of the electron bubble in superfluids. An asymptotic expansion is developed for steady subcritical flow. Numerical integration of the coupled nonlinear Schrödinger equations, that describe the evolution of the wavefunctions of the Bose condensate and the impurity, is used to study the nucleation and capture of vortex rings. Because an electron bubble is made oblate by its motion relative to the condensate, the critical velocity for the vortex nucleation is reduced by about 20%, in agreement with experiments.

Journal of Physics A Mathematical and GeneralDec 19, 200053 citations

Dynamics of bubbles in a two-component Bose-Einstein condensate

Kazuki Sasaki, Naoya Suzuki, Hiroki Saito

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.

arXiv:1011.5578Physical Review AMar 3, 201132 citations

Generating vortex rings in Bose-Einstein condensates in the line-source approximation

M. Guilleumas, Dora M. Jezek, R. Mayol +2 more

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.

arXiv:cond-mat/0202312Physical Review AMay 2, 200216 citations

Solitary waves on vortex lines in Ginzburg--Landau models

Natalia G. Berloff

Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum ( $p$ ) -- substitution energy ( $\hat{\cal E}$ ) plane with $p\to 0.09 ρκ^3/c^2, \hat{\cal E}\to 0.091 ρκ^3/c$ as $U \to c$ , where $ρ$ is the density, $c$ is the speed of sound, $κ$ is the quantum of circulation and $U$ is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particularly, it is shown that during collapse the vortex core becomes significantly compressed and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum ($p$) -- substitution energy ($\hat{\cal E}$) plane with $p\to 0.09 ρκ^3/c^2, \hat{\cal E}\to 0.091 ρκ^3/c$ as $U \to c$, where $ρ$ is the density, $c$ is the speed of sound, $κ$ is the quantum of circulation and $U$ is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particularly, it is shown that during collapse the vortex core becomes significantly compressed and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.

arXiv:cond-mat/0407483Jul 19, 20040 citations

Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

Alberto Villois, Hayder Salman

We study the motion of an electron bubble in the zero-temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schr\"odinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^{4}\mathrm{He}$ at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.We study the motion of an electron bubble in the zero-temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schr\"odinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^{4}\mathrm{He}$ at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.

arXiv:1708.06154Physical review. B./Physical review. BMar 13, 201815 citations

p

) -- substitution energy (

\hat{\cal E}

) plane with

p\to 0.09 ρκ^3/c^2, \hat{\cal E}\to 0.091 ρκ^3/c

U \to c

, where

ρ

is the density,

c

is the speed of sound,

κ

is the quantum of circulation and

U

is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particularly, it is shown that during collapse the vortex core becomes significantly compressed and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.

^{4}\mathrm{He}

at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.