Two-dimensional Thouless pumping in time-space crystalline structures

TL;DR

This paper demonstrates a novel form of Thouless pumping in time-space crystalline structures by using resonantly driven quantum wells and optical lattices, enabling adiabatic transport in both temporal and spatial dimensions.

Contribution

It introduces a new realization of Thouless pumping in time-space crystals and extends the concept to 2D structures using driven optical lattices.

Findings

Realization of Thouless pumping in time crystalline structures.

Extension to 2D time-space crystalline structures.

Simulation of simultaneous time-space pumping.

Abstract

Dynamics of particle in a resonantly driven quantum well can be interpreted as that of a particle in a crystal-like structure, with the time playing the role of the coordinate. By introducing an adiabatically varied phase in the driving protocol, we demonstrate a realization of the Thouless pumping in such a time crystalline structure. Next, we extend the analysis beyond a single quantum well by considering a driven one-dimensional optical lattice, thereby engineering a 2D time-space crystalline structure. Such a setup allows us to explore adiabatic pumping in the spatial and the temporal dimensions separately, as well as to simulate simultaneous time-space pumping.