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arXiv:2004.02568 · Physical Review A

Stationary states, dynamical stability, and vorticity of Bose-Einstein condensates in tilted rotating harmonic traps

Srivatsa B. Prasad, Brendan C. Mulkerin, A. Martin

Published Jun 4, 2020• 7 citations
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Abstract

We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semianalytical prediction of their dynamical instability at high rotation frequencies against collective modes arising from environmental perturbations. Comparing the stationary states to direct simulations of the Gross-Pitaevskii equation, we predict the nucleation of quantum vortices in the dynamically unstable rotational regime. These vortex lines are aligned along the rotation axis despite the tilting of the rotating trap although the background density profile is tilted with respect to the trapping and rotation axes.

DOI
10.1103/physreva.101.063608

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We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semianalytical prediction of their dynamical instability at high rotation frequencies against collective modes arising from environmental perturbations. Comparing the stationary states to direct simulations of the Gross-Pitaevskii equation, we predict the nucleation of quantum vortices in the dynamically unstable rotational regime. These vortex lines are aligned along the rotation axis despite the tilting of the rotating trap although the background density profile is tilted with respect to the trapping and rotation axes.
We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semianalytical prediction of their dynamical instability at high rotation frequencies against collective modes arising from environmental perturbations. Comparing the stationary states to direct simulations of the Gross-Pitaevskii equation, we predict the nucleation of quantum vortices in the dynamically unstable rotational regime. These vortex lines are aligned along the rotation axis despite the tilting of the rotating trap although the background density profile is tilted with respect to the trapping and rotation axes.
We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches for any given dipole tilt angle. We also find that the tilt angle of the stationary state's body frame with respect to the rotation axis is a nontrivial function of the trapping geometry, rotation frequency, and dipole tilt angle. For rotation frequencies of at least an order of magnitude higher than the in-plane trapping frequency, the stationary state density profile is almost perfectly equivalent to the profile expected in a time-averaged dipolar potential that effectively vanishes when the dipoles are tilted along the “magic angle” 54.7 deg. However, by linearizing the fully time-dependent superfluid hydrodynamics about these stationary states, we find that they are dynamically unstable against the formation of collective modes, which we expect would result in turbulent decay.
We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches for any given dipole tilt angle. We also find that the tilt angle of the stationary state's body frame with respect to the rotation axis is a nontrivial function of the trapping geometry, rotation frequency, and dipole tilt angle. For rotation frequencies of at least an order of magnitude higher than the in-plane trapping frequency, the stationary state density profile is almost perfectly equivalent to the profile expected in a time-averaged dipolar potential that effectively vanishes when the dipoles are tilted along the ``magic angle'' 54.7 deg. However, by linearizing the fully time-dependent superfluid hydrodynamics about these stationary states, we find that they are dynamically unstable against the formation of collective modes, which we expect would result in turbulent decay.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancellation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.