Hysteresis effects in rotating Bose-Einstein condensates

We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.

arXiv:cond-mat/0602334Physical Review AOct 25, 200610 citations

B. Jackson, Carlo Barenghi

We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system. © 2006 The American Physical Society.We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system. © 2006 The American Physical Society.

Dec 31, 20060 citations

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate

Kenichi Kasamatsu, Makoto Tsubota, Masahito Ueda

We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.

arXiv:cond-mat/0211394Physical Review AMar 26, 2003201 citations

Pinning of hidden vortices in Bose-Einstein condensates

Thudiyangal Mithun, Kuppuswamy Porsezian, Bishwajyoti Dey

We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensates in a rotating double-well trap potential and corotating optical lattice. We show that the vortex number does not diverge when the rotational frequency $\ensuremath{\Omega}\ensuremath{\rightarrow}1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value $\sqrt{l}/l$ for $l=4$ , which supports the conjecture that surface modes with angular momentum $l=4$ are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensates in a rotating double-well trap potential and corotating optical lattice. We show that the vortex number does not diverge when the rotational frequency $\ensuremath{\Omega}\ensuremath{\rightarrow}1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value $\sqrt{l}/l$ for $l=4$, which supports the conjecture that surface modes with angular momentum $l=4$ are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.

arXiv:1408.5218Physical Review AMay 28, 201432 citations

Vortices and hysteresis in a rotating Bose-Einstein condensate with anharmonic confinement

Andrew David Jackson, G. M. Kavoulakis

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply and singly quantized vortex states. We also show that states of different circulation can be metastable and, as a result, the gas can exhibit hysteresis as the angular frequency of rotation of the trap is varied. The simplicity of the picture that emerges for small coupling strengths suggests that this system may be attractive for studies of phase transitions.We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply and singly quantized vortex states. We also show that states of different circulation can be metastable and, as a result, the gas can exhibit hysteresis as the angular frequency of rotation of the trap is varied. The simplicity of the picture that emerges for small coupling strengths suggests that this system may be attractive for studies of phase transitions.

arXiv:cond-mat/0311066Physical Review AAug 4, 200437 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.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/0309613Physical Review AFeb 26, 200452 citations

\sqrt{l}/l

for

l=4

, which supports the conjecture that surface modes with angular momentum

l=4

are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.