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:1704.08267 · Physical Review A

Vortex precession in trapped superfluids from effective field theory

Angelo Esposito, Rafael Krichevsky, Alberto Nicolis A

Published Sep 11, 2017• 9 citations
arXivHTMLPDF

Abstract

We apply a recently developed effective string theory for vortex lines to the case of two-dimensional trapped superfluids. We do not assume a perturbative microscopic description for the superfluid, but only a gradient expansion for the long-distance hydrodynamical description and for the trapping potential. For any regular trapping potential, we compute the spatial dependence of the superfluid density and the orbital frequency and trajectory of an off-center vortex. Our results are fully relativistic and in the nonrelativistic limit reduce to known results based on the Gross-Pitaevskii model. In our formalism, the leading effect in the nonrelativistic limit arises from two simple Feynman diagrams in which the vortex interacts with the trapping potential through the exchange of hydrodynamical modes.

DOI
10.1103/physreva.96.033615

Related papers

Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

P. G. Kevrekidis, Wenlong Wang, R. Carretero-González +2 more

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\ensuremath{\omega}$ on the chemical potential $\ensuremath{\mu}$, this is no longer true for a general potential $V(r)\ensuremath{\propto}{r}^{p}$. Our calculations suggest that for $p>2$, the precession frequency scales with $\ensuremath{\mu}$ as $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\mu}}^{\ensuremath{-}2/p}$. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov--de Gennes) stability analysis by identifying the relevant precession mode dependence on $\ensuremath{\mu}$ but also through direct numerical computations of the vortex evolution in the large-$\ensuremath{\mu}$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.

arXiv:1706.07137•Physical Review A•Oct 13, 2017•11 citations

Hydrodynamic approach to vortex lifetimes in trapped Bose condensates

Emil Lundh, Ping Ao

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schr\"odinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.

arXiv:cond-mat/9910233•Physical Review A•May 17, 2000•87 citations

Dynamics of a massive superfluid vortex in rk confining potentials

Andrea Richaud, Pietro Massignan, Vittorio Penna +1 more

We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\ensuremath{\propto}{r}^{k}$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential ${V}_{\mathrm{eff}}$. In many cases, ${V}_{\mathrm{eff}}$ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the ${r}^{k}$ trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.

arXiv:2208.03172•Physical Review A•Dec 13, 2022•22 citations

Hydrodynamic theory of motion of quantized vortex rings in trapped superfluid gases

Лев П. Питаевский

I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in quadratures. The results agree with available numerical calculations. Experimental possibilities to check the predictions are discussed.

arXiv:1311.4693•Nov 19, 2013•4 citations

Vortices in spatially inhomogeneous superfluids

Daniel E. Sheehy, Leo Radzihovsky

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density ${\ensuremath{\rho}}_{s}(r)$. The weak radially dependent contribution $[\ensuremath{\propto}{\ensuremath{\nabla}}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\rho}}_{s}(r)]$ to the vortex distribution, that vanishes with the number of vortices ${N}_{v}$ as $1∕{N}_{v}$, arises from the interplay between vortex quantum discreteness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments. One striking consequence of the inhomogeneous vortex distribution is an azimuthally directed, radially shearing superflow.

arXiv:cond-mat/0406205•Physical Review A•Dec 27, 2004•60 citations

Effective Vortex Dynamics in Superfluid Systems

Carlos Wexler, D. J. Thouless

An alternative approach to the derivation of the force on a vortex based in an adiabatic approximation in the action of the superfluid system is developed. Assuming that the vortex motion is relatively slow compared with the characteristic times involved in the microscopic degrees of freedom, the effect of the superfluid and its excitations is reduced to a gauge potential, and the associated transverse force. The vortex velocity part of the transverse force is found in terms of the thermal expectation of the angular momentum of the fluid around the vortex. The excitations countercirculate the vortex reducing the effective density to that of the superfluid part only. Non-adiabatic contributions appear in this formalism as a non-Abelian gauge potential connecting different microscopic states, in particular the renormalization of the vortex mass is given by the lowest order diagonal correction to the adiabatic theory, and the long wavelength contributions found to depend only on the static structure factor for the fluid.

arXiv:cond-mat/9612059•Dec 6, 1996•1 citation
We apply a recently developed effective string theory for vortex lines to the case of two-dimensional trapped superfluids. We do not assume a perturbative microscopic description for the superfluid, but only a gradient expansion for the long-distance hydrodynamical description and for the trapping potential. For any regular trapping potential, we compute the spatial dependence of the superfluid density and the orbital frequency and trajectory of an off-center vortex. Our results are fully relativistic and in the nonrelativistic limit reduce to known results based on the Gross-Pitaevskii model. In our formalism, the leading effect in the nonrelativistic limit arises from two simple Feynman diagrams in which the vortex interacts with the trapping potential through the exchange of hydrodynamical modes.
We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\ensuremath{\omega}$ on the chemical potential $\ensuremath{\mu}$, this is no longer true for a general potential $V(r)\ensuremath{\propto}{r}^{p}$. Our calculations suggest that for p>2p>2p>2, the precession frequency scales with $\ensuremath{\mu}$ as $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\mu}}^{\ensuremath{-}2/p}$. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov--de Gennes) stability analysis by identifying the relevant precession mode dependence on $\ensuremath{\mu}$ but also through direct numerical computations of the vortex evolution in the large-$\ensuremath{\mu}$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.
We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schr\"odinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.
We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\ensuremath{\propto}{r}^{k}$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential Veff{V}_{\mathrm{eff}}Veff​. In many cases, Veff{V}_{\mathrm{eff}}Veff​ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the rk{r}^{k}rk trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.
I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in quadratures. The results agree with available numerical calculations. Experimental possibilities to check the predictions are discussed.
We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density ${\ensuremath{\rho}}_{s}(r)$. The weak radially dependent contribution $[\ensuremath{\propto}{\ensuremath{\nabla}}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\rho}}_{s}(r)]$ to the vortex distribution, that vanishes with the number of vortices Nv{N}_{v}Nv​ as 1∕Nv1∕{N}_{v}1∕Nv​, arises from the interplay between vortex quantum discreteness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments. One striking consequence of the inhomogeneous vortex distribution is an azimuthally directed, radially shearing superflow.
An alternative approach to the derivation of the force on a vortex based in an adiabatic approximation in the action of the superfluid system is developed. Assuming that the vortex motion is relatively slow compared with the characteristic times involved in the microscopic degrees of freedom, the effect of the superfluid and its excitations is reduced to a gauge potential, and the associated transverse force. The vortex velocity part of the transverse force is found in terms of the thermal expectation of the angular momentum of the fluid around the vortex. The excitations countercirculate the vortex reducing the effective density to that of the superfluid part only. Non-adiabatic contributions appear in this formalism as a non-Abelian gauge potential connecting different microscopic states, in particular the renormalization of the vortex mass is given by the lowest order diagonal correction to the adiabatic theory, and the long wavelength contributions found to depend only on the static structure factor for the fluid.