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:2411.18355

Vortices in D-dimensional anisotropic Bose-Einstein condensates: dimensional perturbation theory with hypercylindrical symmetry

Maria Isabelle Fite, Brett Allen McKinney

Published Nov 27, 2024• 0 citations
arXivHTMLPDF

Abstract

We investigate D-dimensional atomic Bose-Einstein condensates in a hypercylindrical trap with a vortex core along the z-axis and quantized circulation $\hbar m$. We analytically approximate the hypercylindrical Gross-Pitaevskii equation using dimensional perturbation theory with perturbation parameter $δ=1/(D+2|m|-d)$, \textcolor{black}{where $d$ controls the contribution of kinetic energy at zeroth order}. We derive the zeroth-order ($δ\to 0$) semiclassical approximations for the condensate energy, density, chemical potential, and critical vortex rotation speed in arbitrary dimensions. We investigate the effect of trap anisotropy on lower effective dimensionality and compute properties of vortices in higher dimensions motivated by the study of synthetic dimensions and holographic duality, where a higher-dimensional gravitational model corresponds to a lower-dimensional quantum model. In the zeroth-order approximation, we observe crossings between energy levels for different dimensions as a function of interaction strength and anisotropy parameters.

DOI
10.48550/arxiv.2411.18355

Related papers

Free expansion of Bose-Einstein condensates with quantized vortices

F. Dalfovo, Michele Modugno

The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.

arXiv:cond-mat/9907102•Physical Review A•Jan 14, 2000•62 citations

Vortex lattice of a Bose-Einstein condensate in a rotating anisotropic trap

Mehmet Özgür Oktel

We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.

arXiv:cond-mat/0309613•Physical Review A•Feb 26, 2004•52 citations

Vortex Stability of Interacting Bose-Einstein Condensates Confined in Anisotropic Harmonic Traps

David L. Feder, Charles W. Clark, Barry I. Schneider

Vortex states of weakly interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.

arXiv:cond-mat/9904269•Physical Review Letters•Jun 21, 1999•133 citations

Rotating anisotropic Bose gas with large number of vortices

Ahmet Keleş

Rapidly rotating atomic gases provide a platform for studying phenomena akin to type-II superconductors and quantum Hall systems. Recently, these systems have attracted renewed interest due to technological advances in the trap anisotropy control, in-situ observation capabilities, and cooling and rotating complex atomic species such as dipolar gases. Understanding the vortex lattice formation and quantum melting is crucial for exploring quantum Hall physics in these systems. In this paper, we theoretically investigate the vortex lattices in anisotropic quantum gases. We formulate the rotating gas Hamiltonian in the Landau gauge, and consider the effects of additional perturbations such as the trap potential in the lowest Landau level (LLL). Focusing on the gases with short-range interactions, we obtain the many-body Hamiltonian projected to lowest Landau level. We consider the limit of full Bose-Einstein condensation and obtain the governing Gross-Pitaevskii equation to identify the possible vortex phases. We numerically solve the Gross-Pitaevskii equation using the imaginary time evolution, and demonstrate the possible vortex lattices as a function of anisotropy, rotation speed and interaction strength. We show that the number of states with a support in the LLL, which determines the number of vortices, follows a Thomas-Fermi type scaling albeit with slightly different coefficients from the usual condensates.

arXiv:2503.21982•TURKISH JOURNAL OF PHYSICS•Apr 15, 2025•1 citation

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

David L. Feder, Charles W. Clark, Barry I. Schneider

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

arXiv:cond-mat/9910288•Physical Review A•Dec 8, 1999•95 citations

Bose-Einstein condensation in variable dimensionality

Brett Allen McKinney, D. K. Watson

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali-metal gases. The perturbation parameter is $\ensuremath{\delta}=1/\ensuremath{\kappa},$ where $\ensuremath{\kappa}$ depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ Thomas-Fermi ground-state approximation of the Gross-Pitaevskii equation. The approximation presented here is well suited for calculating properties of states in three dimensions and in low-effective dimensionality, such as vortex states in a highly anisotropic trap.

arXiv:cond-mat/0102362•Physical Review A•Feb 6, 2002•11 citations
We investigate D-dimensional atomic Bose-Einstein condensates in a hypercylindrical trap with a vortex core along the z-axis and quantized circulation ℏm\hbar mℏm. We analytically approximate the hypercylindrical Gross-Pitaevskii equation using dimensional perturbation theory with perturbation parameter δ=1/(D+2∣m∣−d)δ=1/(D+2|m|-d)δ=1/(D+2∣m∣−d), \textcolor{black}{where ddd controls the contribution of kinetic energy at zeroth order}. We derive the zeroth-order (δ→0δ\to 0δ→0) semiclassical approximations for the condensate energy, density, chemical potential, and critical vortex rotation speed in arbitrary dimensions. We investigate the effect of trap anisotropy on lower effective dimensionality and compute properties of vortices in higher dimensions motivated by the study of synthetic dimensions and holographic duality, where a higher-dimensional gravitational model corresponds to a lower-dimensional quantum model. In the zeroth-order approximation, we observe crossings between energy levels for different dimensions as a function of interaction strength and anisotropy parameters.
The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.
We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.
Vortex states of weakly interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.
Rapidly rotating atomic gases provide a platform for studying phenomena akin to type-II superconductors and quantum Hall systems. Recently, these systems have attracted renewed interest due to technological advances in the trap anisotropy control, in-situ observation capabilities, and cooling and rotating complex atomic species such as dipolar gases. Understanding the vortex lattice formation and quantum melting is crucial for exploring quantum Hall physics in these systems. In this paper, we theoretically investigate the vortex lattices in anisotropic quantum gases. We formulate the rotating gas Hamiltonian in the Landau gauge, and consider the effects of additional perturbations such as the trap potential in the lowest Landau level (LLL). Focusing on the gases with short-range interactions, we obtain the many-body Hamiltonian projected to lowest Landau level. We consider the limit of full Bose-Einstein condensation and obtain the governing Gross-Pitaevskii equation to identify the possible vortex phases. We numerically solve the Gross-Pitaevskii equation using the imaginary time evolution, and demonstrate the possible vortex lattices as a function of anisotropy, rotation speed and interaction strength. We show that the number of states with a support in the LLL, which determines the number of vortices, follows a Thomas-Fermi type scaling albeit with slightly different coefficients from the usual condensates.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali-metal gases. The perturbation parameter is $\ensuremath{\delta}=1/\ensuremath{\kappa},$ where $\ensuremath{\kappa}$ depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ Thomas-Fermi ground-state approximation of the Gross-Pitaevskii equation. The approximation presented here is well suited for calculating properties of states in three dimensions and in low-effective dimensionality, such as vortex states in a highly anisotropic trap.