Floquet Engineering of Lie Algebraic Quantum Systems

TL;DR

This paper introduces a Floquet engineering method for designing periodic drives in Lie algebraic quantum systems, enabling precise control over the Floquet Hamiltonian at any frequency, including regimes beyond fast or slow driving.

Contribution

It develops a systematic Floquet engineering formalism applicable to Lie algebraic quantum systems, utilizing the Wei-Norman ansatz to design driving protocols at arbitrary frequencies.

Findings

Successfully engineered the cross-stitched lattice model.

Demonstrated control over micro-motion dynamics.

Applicable to systems with underlying Lie algebraic structures.

Abstract

We propose a `Floquet engineering' formalism to systematically design a periodic driving protocol in order to stroboscopically realize the desired system starting from a given static Hamiltonian. The formalism is applicable to quantum systems which have an underlying closed Lie-algebraic structure, for example, solid-state systems with noninteracting particles moving on a lattice or its variant described by the ultra-cold atoms moving on an optical lattice. Unlike previous attempts at Floquet engineering, our method produces the desired Floquet Hamiltonian at any driving frequency and is not restricted to the fast or slow driving regimes. The approach is based on Wei-Norman ansatz, which was originally proposed to construct a time-evolution operator for any arbitrary driving. Here, we apply this ansatz to the micro-motion dynamics, defined within one period of the driving, and obtain the driving protocol by fixing the gauge of the micro-motion. To illustrate our idea, we use a two-band system or the systems consisting of two sub-lattices as a testbed. Particularly, we focus on engineering the cross-stitched lattice model that has been a paradigmatic flat-band model.