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

CRC Press eBooks

Group-theoretical and algebraic aspects of Bose-Einstein condensation of interacting particles in traps

Oleg Vorov, Mahir Saleh Hussein, P. Vanisacker

Published Nov 30, 2003• 0 citations
Publisher

Abstract

Trapped bosonic atoms with manipulated interaction strength near the sign flip of the scattering length are considered. Analytic solutions for the rotating ground states are obtained within algebraic approach, using permutation symmetry and group-theoretical properties of Bose operators. It is shown that the form of the ground states at any angular momentum is universal, and it does not depend on the details of the interaction. The ground states are either “collective rotations” or “condensed vortex states”, depending on the sign of the “modified Born scattering length”.

DOI
10.1201/9781482269079-120

Related papers

Rotating Ground States of Trapped Atoms in a Bose-Einstein Condensate with Arbitrary Two-Body Interactions

Oleg Vorov, Mahir Saleh Hussein, P. Van Isacker

In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.

arXiv:cond-mat/0207339•Physical Review Letters•May 21, 2003•8 citations

Rotating ground states of trapped Bose atoms with arbitrary two-body interactions

Oleg Vorov, Mahir Saleh Hussein, P. Van Isacker

In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.

•Jul 22, 2002•0 citations

Ground state of a weakly interacting Bose gas of atoms in a tight trap

Maciej Lewenstein, Li You

We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•23 citations

Ground state properties of rotating spin-orbital-angular-momentum coupled Bose-Einstein condensates

Lei Zhao, Xu Qiu, Yi LIANG +2 more

By numerically solving the single-particle stationary Schrödinger equation and the Gross-Pitaevskii equation with mean-field interactions at zero temperature, the ground state properties of the rotating spin-orbital-angular-momentum coupled Bose-Einstein condensates in a harmonic trapping potential are investigated in this work. The results show that the rotation lifts the double degeneracy of the single-particle energy spectrum in the angular momentum space, and leads to the vortex state. The angular momentum of the vortex depends on the rotating frequency, the intensity of the laser beam, and the spin-orbital-angular-momentum coupling. In particular, if the rotating frequency is below a critical value, the angular momentum of the ground state vortex remains unaffected by the rotating frequency. When the rotating frequency exceeds the critical value, the angular momentum of the ground state vortex will increase with the rotating frequency increasing. By assuming that the system is confined in a ring trap, the expression of the single-particle energy spectrum in the angular momentum space can be obtained, which clarifies how the rotation frequency affects the angular momentum of the ground state. In the presence of atomic interactions, similar phenomena can also be observed in the mean-field ground state at zero temperature.

Acta Physica Sinica•Jan 1, 2025•0 citations

Multi-vortex phase transitions in rotating Bose-Einstein condensates

Oleg Vorov

We study the lowest energy states of a weakly interacting trapped atomic Bose-Einstein condensate in both quantum and classical cases. An analytic expression for the ground-state wavefunction of a rotating Gross-Pitaevskii condensate of trapped atoms describes the onset of vorticity in an accelerated trap, starting from the vortex entry followed by formation of growing symmetric Wigner molecules. Within a unified picture, it explains the staircase of the angular momentum jumps and the behavior of the bosonic occupancies observed in numerical and variational studies. The similarity of this behavior and mesoscopic superconductors is discussed.

AIP conference proceedings•Jan 1, 2005•2 citations

Generalized yrast states of a Bose-Einstein condensate in a harmonic trap for a universality class of interactions

Mahir Saleh Hussein, Oleg Vorov

For a system of N bosons in a two-dimensional harmonic trap with frequency $\ensuremath{\omega},$ interacting via forces $V\ensuremath{\ll}\ensuremath{\Elzxh}\ensuremath{\omega},$ we develop a method to find the ground states of rotating Bose condensate as a function of two quantum numbers, the total angular momentum and the angular momentum of internal excitations (generalized yrast states). The energies of these condensed vortex states are expressed through the single two-body matrix element of interaction, $V.$ A broad universality class of predominantly repulsive interactions for which these results hold is described by a simple integral condition on $V.$ It includes Gaussian, $\ensuremath{\delta}$ function, and log-Coulomb forces.

arXiv:cond-mat/0102505•Physical Review A•Feb 13, 2002•11 citations
Trapped bosonic atoms with manipulated interaction strength near the sign flip of the scattering length are considered. Analytic solutions for the rotating ground states are obtained within algebraic approach, using permutation symmetry and group-theoretical properties of Bose operators. It is shown that the form of the ground states at any angular momentum is universal, and it does not depend on the details of the interaction. The ground states are either “collective rotations” or “condensed vortex states”, depending on the sign of the “modified Born scattering length”.
In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.
In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.
We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.
By numerically solving the single-particle stationary Schrödinger equation and the Gross-Pitaevskii equation with mean-field interactions at zero temperature, the ground state properties of the rotating spin-orbital-angular-momentum coupled Bose-Einstein condensates in a harmonic trapping potential are investigated in this work. The results show that the rotation lifts the double degeneracy of the single-particle energy spectrum in the angular momentum space, and leads to the vortex state. The angular momentum of the vortex depends on the rotating frequency, the intensity of the laser beam, and the spin-orbital-angular-momentum coupling. In particular, if the rotating frequency is below a critical value, the angular momentum of the ground state vortex remains unaffected by the rotating frequency. When the rotating frequency exceeds the critical value, the angular momentum of the ground state vortex will increase with the rotating frequency increasing. By assuming that the system is confined in a ring trap, the expression of the single-particle energy spectrum in the angular momentum space can be obtained, which clarifies how the rotation frequency affects the angular momentum of the ground state. In the presence of atomic interactions, similar phenomena can also be observed in the mean-field ground state at zero temperature.
We study the lowest energy states of a weakly interacting trapped atomic Bose-Einstein condensate in both quantum and classical cases. An analytic expression for the ground-state wavefunction of a rotating Gross-Pitaevskii condensate of trapped atoms describes the onset of vorticity in an accelerated trap, starting from the vortex entry followed by formation of growing symmetric Wigner molecules. Within a unified picture, it explains the staircase of the angular momentum jumps and the behavior of the bosonic occupancies observed in numerical and variational studies. The similarity of this behavior and mesoscopic superconductors is discussed.
For a system of N bosons in a two-dimensional harmonic trap with frequency $\ensuremath{\omega},$ interacting via forces $V\ensuremath{\ll}\ensuremath{\Elzxh}\ensuremath{\omega},$ we develop a method to find the ground states of rotating Bose condensate as a function of two quantum numbers, the total angular momentum and the angular momentum of internal excitations (generalized yrast states). The energies of these condensed vortex states are expressed through the single two-body matrix element of interaction, V.V.V. A broad universality class of predominantly repulsive interactions for which these results hold is described by a simple integral condition on V.V.V. It includes Gaussian, $\ensuremath{\delta}$ function, and log-Coulomb forces.