Anomalous Doppler effect in superfluid and supersolid atomic gases

TL;DR

This paper predicts and analyzes the anomalous Doppler effect in superfluid and supersolid atomic gases, highlighting how broken Galilean invariance influences sound propagation and Doppler shifts, with quantitative estimates for Bose-Einstein condensates.

Contribution

It provides new analytic predictions for the Doppler effect in superfluids with broken Galilean invariance, including supersolids, using hydrodynamics and simulations.

Findings

Doppler shifts are affected by superfluid fraction and broken Galilean invariance.

Distinct sound modes in supersolids exhibit different Doppler effects.

Quantitative estimates align with hydrodynamic and simulation results.

Abstract

By employing the formalism of hydrodynamics, we derive novel analytic predictions for the Doppler effect in superfluids with broken Galilean invariance and hosting persistent currents at zero temperature. We consider two scenarios: when Galilean invariance is broken explicitly (by external potentials) and spontaneously, as it happens in a supersolid. In the former case, the presence of a stationary current affects the propagation of sound via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound. Quantitative estimates of the Doppler shifts are obtained for Bose-Einstein condensed atomic gases, described by Gross-Pitaevskii theory. The estimates are obtained both calculating the thermodynamic parameters entering the hydrodynamic results, and from full time-dependent simulations.