Collective excitation frequencies and stationary states of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime

TL;DR

This paper introduces a method to exactly determine static states and collective excitation frequencies of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime, accounting for complex interactions and stability conditions.

Contribution

It provides an analytic approach to handle non-local dipolar interactions and maps static solutions and excitation modes, including stability analysis, for various trap geometries and interaction strengths.

Findings

Global collapse mediated by an anisotropic quadrupolar mode.

Existence of stable regimes even with infinite dipolar to s-wave interaction ratio.

Identification of long-range restoring forces in dipolar BECs.

Abstract

We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expressions for the dipolar potential of an arbitrary polynomial density profile, thereby reducing the problem of handling non-local dipolar interactions to the solution of algebraic equations. We comprehensively map out the static solutions and excitation modes, including non-cylindrically symmetric traps, and also the case of negative scattering length where dipolar interactions stabilize an otherwise unstable condensate. The dynamical stability of the excitation modes gives insight into the onset of collapse of a dipolar BEC. We find that global collapse is consistently mediated by an anisotropic quadrupolar collective mode, although there are two trapping regimes in which the BEC is stable against quadrupole fluctuations even as the ratio of the dipolar to s-wave interactions becomes infinite. Motivated by the possibility of fragmented BEC in a dipolar Bose gas due to the partially attractive interactions, we pay special attention to the scissors modes, which can provide a signature of superfluidity, and identify a long-range restoring force which is peculiar to dipolar systems. As part of the supporting material for this paper we provide the computer program used to make the calculations, including a graphical user interface.