The phonon dispersion relation of a Bose-Einstein condensate

TL;DR

This paper experimentally measures the phonon dispersion relation in a Bose-Einstein condensate using a novel short Bragg pulse technique, revealing a 3D to 1D transition and features affecting superfluid properties.

Contribution

It introduces a new method for measuring phonon dispersion in BECs and characterizes the 3D-1D transition and its impact on superfluid behavior.

Findings

Observation of phonon oscillations and dispersion relation

Identification of 3D to 1D transition affecting phonon properties

Measurement of static structure factor in long-wavelength regime

Abstract

We measure the oscillations of a standing wave of phonons in a Bose-Einstein condensate, thus obtaining the dispersion relation. We present the technique of short Bragg pulses, which stimulates the standing wave. The subsequent oscillations are observed in situ. It is seen that the phonons undergo a 3D to 1D transition, when their wavelength becomes longer than the transverse radius of the condensate. The 1D regime contains an inflection point in the dispersion relation, which should decrease the superfluid critical velocity according to the Landau criterion. The inflection point also represents a minimum in the group velocity, although the minimum is not deep enough to result in a roton. The 3D-1D transition also results in an increase in the lifetime of the standing-wave oscillations, and a breakdown of the local density approximation. In addition, the static structure factor is measured in the long-wavelength regime. The measurements are enabled by the high sensitivity of the new technique.