Periodically-driven quantum matter: the case of resonant modulations

TL;DR

This paper develops a formalism for analyzing quantum systems under high-frequency, resonant periodic driving, revealing how micro-motion influences observable properties and enabling control of flux patterns in optical lattices.

Contribution

It introduces a general approach for systems with resonant driving frequencies, extending beyond traditional high-frequency approximations to include micro-motion effects.

Findings

Resonant modulations can generate artificial fluxes in cold-atom systems.

Micro-motion effects are scheme-dependent and significantly impact physical observables.

The formalism provides insights into band structures and flux patterns under resonant driving.

Abstract

Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micro-motion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micro-motion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time-evolution of the system.