Floquet engineering with quasienergy bands of periodically driven optical lattices

TL;DR

This paper explains Floquet theory for periodically driven quantum systems and demonstrates how to engineer quasienergy bands in ultracold atoms within optical lattices, enabling control over their quantum dynamics.

Contribution

It provides a comprehensive tutorial on applying Floquet theory to optical lattices and illustrates how to manipulate quasienergy bands for quantum control.

Findings

Floquet theory effectively describes driven optical lattice systems.

Quasienergy bands can be engineered using ac-Stark shifts and multiphoton resonances.

Numerical methods for calculating quasienergy structures are demonstrated.

Abstract

A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temporal Bloch waves whose dispersion relations can be manipulated at will by exploiting ac-Stark shifts and multiphoton resonances. The elements required for numerical calculations are introduced in a tutorial manner, and some example calculations are discussed in detail, thereby illustrating future prospects of Floquet engineering.