Effects of Berry Curvature on the Collective Modes of Ultracold Gases

TL;DR

This paper demonstrates how Berry curvature influences the collective modes of ultracold gases, altering their frequencies and providing a method to experimentally probe the geometrical properties of energy bands.

Contribution

It introduces a theoretical framework showing Berry curvature modifies hydrodynamic equations and collective modes in Bose-Einstein condensates, with potential experimental detection.

Findings

Berry curvature affects collective mode frequencies

Modifications are significant and experimentally detectable

Provides a method to measure geometrical properties of energy bands

Abstract

Topological energy bands have important geometrical properties described by the Berry curvature. We show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field. Using an operator approach, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of energy bands.