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:1505.04113

Non-coaxial vortices in two-component Bose-Einstein condensates: Persistent precession and nutation

Rodislav Driben, V. V. Konotop, T. Meier

Published May 15, 2015• 0 citations
arXivHTMLPDF

Abstract

It is demonstrated that a two-component Bose-Einstein condensate (BEC) with all-repulsive inter-atomic interactions loaded into a radially symmetric harmonic trap supports robust non-coaxial vortices with approximately orthogonal vortex lines in each of the components. These cross vortices are excited from the linear modes by a sudden switch-on of the nonlinearity (via Feshbach resonance) and are characterized by persistent dynamical regimes of precession with nutation, resembling the motion of a rigid body. The obtained dynamics can be understood qualitatively on the basis of a simple mechanical model.

DOI
10.48550/arxiv.1505.04113

Related papers

Nonlinear Dynamics of Multi-Component Bose-Einstein Condensates

Katsuhiro Nakamura

Bose-Einstein condensate(BEC) provides a nice stage when the nonlinear Schrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance rij on short scale and logarithmic in rij on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore “the chaos in the three-body problem” in the context of vortices with inertia.

Progress of Theoretical Physics Supplement•Jan 1, 2007•3 citations

Dynamics of inertial vortices in multicomponent Bose-Einstein condensates

Katsuhiro Nakamura, Doniyor Babajanov, Davron U. Matrasulov +1 more

With use of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multicomponent Bose-Einstein condensates (BECs) with a harmonic trap in two dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The interparticle (vortex-vortex) interaction is singularly repulsive and short ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. ``Chaos in the three-body problem'' in the three-vortice system can be seen, which is not expected in the corresponding point vortices without inertia in two dimensions.

arXiv:1212.0198•Physical Review A•Nov 14, 2012•9 citations

NONLINEAR DYNAMICS OF WAVE PACKETS AND VORTICES IN BOSE-EINSTEIN CONDENSATES Chaos and Billiard Motion

Kaoru Nakamura

We study the dynamics of single and multi-component Bose-Einstein condensates (BECs) in two dimensions with and without a harmonic trap by using various variants of non- linear Schrodinger (or Gross-Pitaevskii) equation. Firstly, we examine the three-component repulsive BEC with cubic nonlinearity in a harmonic trap, and see the conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which are equivalent to three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r ij on short length scale and logarithmic in r ij on large length scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore chaos in the three-body problem in the context of vortices with inertia. Secondly, by choosing the nonlinear Schrodinger equation with saturable nonlinearity, we investigate the single and multi-component WP dynamics within the hard-walled square and stadium billiards with neither a harmonic trap nor driving field. We analyze the stability of WPs by using the variational (collective-coordinate) method. By emitting the radiation the Gaussian WP becomes deformed to a bell-shaped one and then stabilized. As the velocity increases, WPs tend to be stable against many collisions with billiard walls.

•Jan 1, 2009•0 citations

Precession and nutation dynamics of nonlinearly coupled non-coaxial three-dimensional matter wave vortices

Rodislav Driben, V. V. Konotop, T. Meier

Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.

Scientific Reports•Mar 11, 2016•9 citations

Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

Simone Serafini, Matteo Barbiero, M. Debortoli +5 more

We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

arXiv:1507.01511•Physical Review Letters•Oct 21, 2015•69 citations

Vortex stability in interacting Bose-Einstein condensates

Ajay Srinivasan, Aaron Wirthwein, Stephan Haas

We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.

arXiv:2501.06119•Physical review. B./Physical review. B•Sep 10, 2025•0 citations
It is demonstrated that a two-component Bose-Einstein condensate (BEC) with all-repulsive inter-atomic interactions loaded into a radially symmetric harmonic trap supports robust non-coaxial vortices with approximately orthogonal vortex lines in each of the components. These cross vortices are excited from the linear modes by a sudden switch-on of the nonlinearity (via Feshbach resonance) and are characterized by persistent dynamical regimes of precession with nutation, resembling the motion of a rigid body. The obtained dynamics can be understood qualitatively on the basis of a simple mechanical model.
Bose-Einstein condensate(BEC) provides a nice stage when the nonlinear Schrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance rij on short scale and logarithmic in rij on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore “the chaos in the three-body problem” in the context of vortices with inertia.
With use of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multicomponent Bose-Einstein condensates (BECs) with a harmonic trap in two dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The interparticle (vortex-vortex) interaction is singularly repulsive and short ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. ``Chaos in the three-body problem'' in the three-vortice system can be seen, which is not expected in the corresponding point vortices without inertia in two dimensions.
We study the dynamics of single and multi-component Bose-Einstein condensates (BECs) in two dimensions with and without a harmonic trap by using various variants of non- linear Schrodinger (or Gross-Pitaevskii) equation. Firstly, we examine the three-component repulsive BEC with cubic nonlinearity in a harmonic trap, and see the conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which are equivalent to three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r ij on short length scale and logarithmic in r ij on large length scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore chaos in the three-body problem in the context of vortices with inertia. Secondly, by choosing the nonlinear Schrodinger equation with saturable nonlinearity, we investigate the single and multi-component WP dynamics within the hard-walled square and stadium billiards with neither a harmonic trap nor driving field. We analyze the stability of WPs by using the variational (collective-coordinate) method. By emitting the radiation the Gaussian WP becomes deformed to a bell-shaped one and then stabilized. As the velocity increases, WPs tend to be stable against many collisions with billiard walls.
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.
We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.