Two-dimensional nonlinear Thouless pumping of matter waves

TL;DR

This paper theoretically investigates nonlinear quantized Thouless pumping of Bose-Einstein condensates in 2D optical lattices, revealing different transport regimes, the role of interactions, and the influence of topological band properties.

Contribution

It introduces a comprehensive analysis of nonlinear 2D Thouless pumping, including soliton dynamics, multi-soliton regimes, and effects of fractional Chern numbers in PT-symmetric potentials.

Findings

Identified three pumping scenarios: quasi-linear, single-soliton, and multi-soliton regimes.

Demonstrated that wavepacket displacement depends on Chern numbers and inter-band transitions.

Showed solitonic pumping occurs at various amplitudes, with complex behaviors at intermediate amplitudes.

Abstract

We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in a two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: quasi-linear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and multi-soliton regime when initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wavepacket are determined by Chern numbers of the populated energy bands and by the inter-band transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wavepacket, while at intermediate amplitudes the transport is multi-solitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.