Nonlinear Hall response in the driving dynamics of ultracold atoms in optical lattices

TL;DR

This paper predicts a nonlinear Hall effect in ultracold atoms within optical lattices, revealing second-order responses in Bloch oscillations under both dc and ac driving fields, linked to Berry curvature dipoles.

Contribution

It introduces the concept of nonlinear Hall response in ultracold atom systems and connects it to Berry curvature dipoles, expanding understanding of nonlinear transport phenomena.

Findings

Nonlinear Hall current dominates in short-time Bloch oscillations.

Berry curvature dipole can be extracted from atomic oscillations.

Double frequency nonlinear response observed under ac driving.

Abstract

We propose that a nonlinear Hall response can be observed in Bloch oscillations of ultracold atoms in optical lattices under the condition of preserved time-reversal symmetry. In the short-time limit of Bloch oscillations driven by a direct current (dc) field, the nonlinear Hall current dominates, being a second-order response to the external field strength. The associated Berry curvature dipole, which is a second-order nonlinear coefficient of the driving field, can be obtained from the oscillation of atoms. In an alternating current (ac) driving field, the nonlinear Hall response has a double frequency of the driving force in the case of time-reversal symmetry.