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:1108.2097 · Physical Review A

Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction

Deng‐Shan Wang, Shu-Wei Song, Bo Xiong, Wu‐Ming Liu

Published Nov 11, 2011• 93 citations
arXivHTMLPDF

Abstract

We present theoretical analysis and numerical studies of the quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior has been examined by numerical simulation, which shows that a new series of stable vortex states (defined by radial and angular quantum numbers) can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction. We also give an experimental protocol to observe these vortex states in future experiments.

DOI
10.1103/physreva.84.053607

Related papers

Localized nonlinear matter waves in Bose-Einstein condensates with spatially and spatiotemporally modulated nonlinearities

Deng‐Shan Wang, Shu-Wei Song, W M Liu

The novel phenomena arising from Bose-Einstein condensates with spatially and spatiotemporally modulated nonlinearities in external potential is reviewed from a theoretical viewpoint. We first present theoretical analysis and numerical studies of the localized nonlinear matter waves in one-dimensional single and two-component BECs with spatially and spatiotemporally modulated nonlinearities, respectively. It is shown that the spatially or spatiotemporally modulated nonlinearity can support stable novel localized nonlinear matter waves such as the breathing solitons and moving solitons. Then the quasi-two-dimensional BEC with spatially modulated nonlinearity is investigated and we show that all of the BECs, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies. Their properties are determined by the principal quantum number and secondary quantum number. Moreover, we investigate the quantized vortices in a rotating BEC with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior is examined by numerical simulation, which shows that a new series of stable vortex states which are defined by radial and angular quantum numbers, can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction.

Journal of Physics Conference Series•Dec 17, 2012•3 citations

Quantized vortices in spinor Bose–Einstein condensates with time–space modulated interactions and stability analysis*

Yuqin Yao, Ji Li

The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.

Chinese Physics B•Jun 29, 2020•1 citation

Stability and excitations of a dipolar Bose-Einstein condensate with a vortex

Ryan Wilson, Shai Ronen, John L. Bohn

We study the stability of singly and doubly quantized vortex states of harmonically trapped dipolar Bose-Einstein condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to local collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly quantized vortex states are unstable to decay into a different topological state (with two singly quantized vortices) for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive.

arXiv:0811.1233•Physical Review A•Jan 23, 2009•58 citations

Quantized circular motion of a trapped Bose-Einstein condensate: Coherent rotation and vortices

Karl-Peter Marzlin, Weiping Zhang

We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusoidal variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained.

arXiv:cond-mat/9711084•Physical Review A•Jun 1, 1998•49 citations

Stable controllable giant vortex in a trapped Bose–Einstein condensate

S K Adhikari

Abstract In a harmonically-trapped rotating Bose–Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.

arXiv:1906.11108•Laser Physics Letters•Jul 12, 2019•8 citations

Vortices and Persistent Currents in Rotating Bose Gases - a Diagonalization Approach

S. Bargi

In this thesis, I explore the behavior of rotating ultra-cold Bose gases, by diagonalizing the Hamiltonian. This method has the advantage of being exact in the limit of weak interactions, and thus is a useful complement to the more commonly used Gross-Pitaevskii (GP) equation, which relies on a mean-field approximation. It is generally known that an ultra-cold Bose gas shows some remarkable properties under rotation, such as quantized vortices and persistent currents, and these are one main reason why we choose to study rotation. Abstract A repulsively interacting Bose-Einstein condensate (BEC) in a harmonic trapping potential will form singly quantized vortices when rotated. Papers I-V are examples of different kinds of generalizations to this basic system, each showing its particular non-trivial new features. Abstract In Paper I we make the trapping potential weakly anharmonic, and confirm the existence of multiply quantized vortices in both repulsively and attractively interacting condensates, which were previously predicted in Gross-Pitaevskii calculations. Abstract In Papers II and III, we generalize to a two-component system in a harmonic trap. The vortices that form under rotation will in general be coreless, i.e. one component will form a vortex and rotate around the other component. In Paper II we give some analytical expressions for the dispersion relation and occupation numbers at low angular momenta, and in Paper III we show how multiply quantized vortices can be stable in these systems. Abstract Finally we investigate bosons in potentials which can support persistent currents, i.e. rotating states that do not decay in a finite amount of time. These are possible if there is an energy barrier separating the rotating state from the non-rotating ground state. In Paper IV, we have a two-component condensate in a one-dimensional potential and we calculate among other things the minimum interaction strength where persistent currents can occur. In Paper V, we study an experimentally relevant two-dimensional annulus. Again we find that persistent currents are possible above a certain interaction strength, and we find this strength as a function of the width of the annulus, as well as how it depends on the relative population of the two species.

•Jan 1, 2010•1 citation
We present theoretical analysis and numerical studies of the quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior has been examined by numerical simulation, which shows that a new series of stable vortex states (defined by radial and angular quantum numbers) can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction. We also give an experimental protocol to observe these vortex states in future experiments.
The novel phenomena arising from Bose-Einstein condensates with spatially and spatiotemporally modulated nonlinearities in external potential is reviewed from a theoretical viewpoint. We first present theoretical analysis and numerical studies of the localized nonlinear matter waves in one-dimensional single and two-component BECs with spatially and spatiotemporally modulated nonlinearities, respectively. It is shown that the spatially or spatiotemporally modulated nonlinearity can support stable novel localized nonlinear matter waves such as the breathing solitons and moving solitons. Then the quasi-two-dimensional BEC with spatially modulated nonlinearity is investigated and we show that all of the BECs, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies. Their properties are determined by the principal quantum number and secondary quantum number. Moreover, we investigate the quantized vortices in a rotating BEC with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior is examined by numerical simulation, which shows that a new series of stable vortex states which are defined by radial and angular quantum numbers, can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction.
The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.
We study the stability of singly and doubly quantized vortex states of harmonically trapped dipolar Bose-Einstein condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to local collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly quantized vortex states are unstable to decay into a different topological state (with two singly quantized vortices) for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive.
We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusoidal variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained.
Abstract In a harmonically-trapped rotating Bose–Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.
In this thesis, I explore the behavior of rotating ultra-cold Bose gases, by diagonalizing the Hamiltonian. This method has the advantage of being exact in the limit of weak interactions, and thus is a useful complement to the more commonly used Gross-Pitaevskii (GP) equation, which relies on a mean-field approximation. It is generally known that an ultra-cold Bose gas shows some remarkable properties under rotation, such as quantized vortices and persistent currents, and these are one main reason why we choose to study rotation. Abstract A repulsively interacting Bose-Einstein condensate (BEC) in a harmonic trapping potential will form singly quantized vortices when rotated. Papers I-V are examples of different kinds of generalizations to this basic system, each showing its particular non-trivial new features. Abstract In Paper I we make the trapping potential weakly anharmonic, and confirm the existence of multiply quantized vortices in both repulsively and attractively interacting condensates, which were previously predicted in Gross-Pitaevskii calculations. Abstract In Papers II and III, we generalize to a two-component system in a harmonic trap. The vortices that form under rotation will in general be coreless, i.e. one component will form a vortex and rotate around the other component. In Paper II we give some analytical expressions for the dispersion relation and occupation numbers at low angular momenta, and in Paper III we show how multiply quantized vortices can be stable in these systems. Abstract Finally we investigate bosons in potentials which can support persistent currents, i.e. rotating states that do not decay in a finite amount of time. These are possible if there is an energy barrier separating the rotating state from the non-rotating ground state. In Paper IV, we have a two-component condensate in a one-dimensional potential and we calculate among other things the minimum interaction strength where persistent currents can occur. In Paper V, we study an experimentally relevant two-dimensional annulus. Again we find that persistent currents are possible above a certain interaction strength, and we find this strength as a function of the width of the annulus, as well as how it depends on the relative population of the two species.