Collective oscillations of dipolar Bose-Einstein condensates and accurate comparison between contact and dipolar interaction

TL;DR

This paper introduces a method to precisely measure the s-wave scattering length in dipolar Bose-Einstein condensates by analyzing polarization-dependent shifts in collective oscillation frequencies.

Contribution

It presents a novel scheme to determine the scattering length using collective oscillation frequency shifts caused by dipole interactions, with optimized trap geometries for enhanced accuracy.

Findings

Frequency shifts depend on dipolar interaction strength and polarization.

Optimal trap geometries maximize the measurable frequency shifts.

The method achieves percent-level accuracy in measuring the scattering length.

Abstract

We propose a scheme for the measurement of the s-wave scattering length $a$ of an atom or molecule with significant dipole-dipole interaction with an accuracy at the percent level. The frequencies of the collective oscillations of a Bose-Einstein condensate are shifted by the magnetic dipole interaction. The shift is polarization dependent and proportional to the ratio $\epsilon_{dd}$ of dipolar and s-wave coupling constants. Measuring the differences in the frequencies for different polarization we can extract the value of $\epsilon_{dd}$ and thus measure $a$. We calculate the frequency shifts for a large variety of non-axisymmetric harmonic traps in the Thomas-Fermi limit and find optimal trapping geometries to maximize the shifts.