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:1005.3081 · Physical Review A

Fluctuations and correlations in rotating Bose-Einstein condensates

Soheil Baharian, Gordon Baym

Published Dec 6, 2010• 9 citations
arXivHTMLPDF

Abstract

We investigate the effects of correlations on the properties of the ground state of the rotating harmonically trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an $N$-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus pointing to a better state for slow rotation. We construct mean-field ground states of zero-, one-, and two-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.

DOI
10.1103/physreva.82.063606

Related papers

Properties of rotating ultracold bosonic quantum gases

Soheil Baharian

In this dissertation, we study rotational properties of ultracold bosonic quantum gases in two trapped configurations, a quasi-two-dimensional gas in a harmonic trap and a quasi-one-dimensional gas in a toroidal trap. First, we investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an N-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud. Then, we show how the configuration-space form of the above-mentioned Bogoliubov ground-state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at a high angular momentum per particle. Finally, we study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the eigenstates of the system. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.

•Dec 1, 2013•0 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

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

Anssi Collin

We study the rotational properties of an attractively interacting Bose gas in an anharmonic potential. Low-energy excitations for the two possible rotational ground-state configurations (vortex and the center-of-mass rotating state) are analyzed. The vortex excitation spectrum is all positive for weak couplings, but as the interactions become stronger, the energy of the lowest mode decreases rapidly to a negative value. The broken rotational symmetry involved in the center-of-mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center-of-mass rotational state also demonstrate the coupling between the center of mass and relative motions.

arXiv:cond-mat/0509256•Physical Review A•Jan 12, 2006•18 citations

Phases of a rotating Bose-Einstein condensate trapped in a hard-wall potential

Hélène Perrin, G. M. Kavoulakis

We investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.

cond-mat.quant-gasCross-listedarXiv:2610.18527•Oct 14, 2026•0 citations

Diffusive instability of a vortex in a rotating Bose gas

Ashton S. Bradley, Crispin W. Gardiner

The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.

arXiv:cond-mat/0509592•Sep 23, 2005•1 citation

Applications of rotational excitations in Bose-Einstein condensates

Anssi Collin

This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.

Työväentutkimus Vuosikirja•Mar 1, 2006•0 citations
We investigate the effects of correlations on the properties of the ground state of the rotating harmonically trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an NNN-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus pointing to a better state for slow rotation. We construct mean-field ground states of zero-, one-, and two-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.
In this dissertation, we study rotational properties of ultracold bosonic quantum gases in two trapped configurations, a quasi-two-dimensional gas in a harmonic trap and a quasi-one-dimensional gas in a toroidal trap. First, we investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an N-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud. Then, we show how the configuration-space form of the above-mentioned Bogoliubov ground-state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at a high angular momentum per particle. Finally, we study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the eigenstates of the system. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.
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 rotational properties of an attractively interacting Bose gas in an anharmonic potential. Low-energy excitations for the two possible rotational ground-state configurations (vortex and the center-of-mass rotating state) are analyzed. The vortex excitation spectrum is all positive for weak couplings, but as the interactions become stronger, the energy of the lowest mode decreases rapidly to a negative value. The broken rotational symmetry involved in the center-of-mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center-of-mass rotational state also demonstrate the coupling between the center of mass and relative motions.
We investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.
This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.