Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate

TL;DR

This paper investigates how a rotating magnetic field at arbitrary angles affects the shape and stability of dipolar Bose-Einstein condensates, revealing new stationary states and their instability leading to turbulence.

Contribution

It introduces a semi-analytical approach to study tilted dipolar BECs under rotation, uncovering new stationary solutions and analyzing their stability.

Findings

Stationary solutions depend nontrivially on tilt angle and trap geometry.

At high rotation frequencies, density profiles match time-averaged dipolar potentials.

Stationary states are dynamically unstable, leading to potential turbulence.

Abstract

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.