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/0309487 · Physical Review A

Structure of excited vortices with higher angular momentum in Bose-Einstein condensates

Jian‐Ming Tang

Published Oct 25, 2004• 1 citation
arXivHTMLPDF

Abstract

The structure of vortices in Bose-Einstein condensed atomic gases is studied taking into account many-body correlation effects. It is shown that for excited vortices the particle density in the vortex core increases as the angular momentum of the system increases. The core density can increase by several times with only a few percent change in the angular momentum. This result provides an explanation for the observations in which the measured angular momentum is higher than the estimation based on counting the number of vortices and the visibility of the vortex cores is simultaneously reduced. The calculated density profiles for the excited vortices are in good agreement with experimental measurements of a single vortex.

DOI
10.1103/physreva.70.043626

Related papers

Quantized vortices in dipolar supersolid Bose-Einstein-condensed gases

Albert Gallemí, S. M. Roccuzzo, S. Stringari +1 more

We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.

arXiv:2005.05718•Physical Review A•Aug 21, 2020•73 citations

Phantom vortices: hidden angular momentum in ultracold dilute Bose-Einstein condensates

Storm Weiner, Marios C. Tsatsos, L. S. Cederbaum +1 more

Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.

Scientific Reports•Jan 16, 2017•50 citations

Single vortex states in a confined Bose-Einstein condensate

Stavros Komineas, Nigel R. Cooper, N. Papanicolaou

It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

arXiv:cond-mat/0508562•Physical Review A•Nov 21, 2005•25 citations

Quantized vortices in atomic Bose-Einstein condensates

Kenichi Kasamatsu, Makoto Tsubota

In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.

arXiv:0709.1042•Sep 7, 2007•15 citations

Bose-Einstein Condensates with Large Number of Vortices

Tin-Lun Ho

We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.

arXiv:cond-mat/0104522•Physical Review Letters•Jul 23, 2001•268 citations

Explanation of critical angular velocities of the vortex formation in a stirred Bose-Einstein condensate

A. A. Kozhevnikov

The problem of explaining the critical angular velocity Ω c when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible is considered in the framework of the variational approach. The origin of smallness of the calculated Ω c in comparison with the measured values, which takes place for a pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured Ω c is achieved upon admitting a small admixture of the zero angular-momentum state in the wave function of the one-vortex quantum state prepared after stirring. A portion of this admixture amounts to 1–13% of the total condensed atoms. A possible test of this hypothesis is proposed.

arXiv:cond-mat/0011104•Journal of Experimental and Theoretical Physics Letters•Dec 1, 2000•0 citations
The structure of vortices in Bose-Einstein condensed atomic gases is studied taking into account many-body correlation effects. It is shown that for excited vortices the particle density in the vortex core increases as the angular momentum of the system increases. The core density can increase by several times with only a few percent change in the angular momentum. This result provides an explanation for the observations in which the measured angular momentum is higher than the estimation based on counting the number of vortices and the visibility of the vortex cores is simultaneously reduced. The calculated density profiles for the excited vortices are in good agreement with experimental measurements of a single vortex.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.
It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.
The problem of explaining the critical angular velocity Ω c when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible is considered in the framework of the variational approach. The origin of smallness of the calculated Ω c in comparison with the measured values, which takes place for a pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured Ω c is achieved upon admitting a small admixture of the zero angular-momentum state in the wave function of the one-vortex quantum state prepared after stirring. A portion of this admixture amounts to 1–13% of the total condensed atoms. A possible test of this hypothesis is proposed.