Following Floquet states in high-dimensional Hilbert spaces

TL;DR

The paper introduces an iterative algorithm for computing and tracking Floquet states in high-dimensional many-body systems, demonstrated on a driven Bose-Hubbard chain, enabling efficient state preparation and analysis.

Contribution

A novel iterative method for calculating and following Floquet states in complex many-body systems, extending capabilities beyond conventional approaches.

Findings

Successful computation of Floquet states in high-dimensional systems.

Demonstration of pseudoadiabatic Floquet state following in a Bose-Hubbard chain.

High-efficiency population of a Floquet Mott insulator state with smooth driving.

Abstract

An iterative algorithm is established which enables one to compute individual Floquet states even for many-body systems with high-dimensional Hilbert spaces that are not accessible to commonly employed conventional methods. A strategy is proposed for following a Floquet state in response to small changes of a given system's Hamiltonian. The scheme is applied to a periodically driven Bose-Hubbard chain, verifying the possibility of pseudoadiabatic Floquet state following. In particular, it is demonstrated that a driving-induced Mott insulatorlike target Floquet state can be populated with high efficiency if the driving amplitude is turned on smoothly but not too slowly. We conclude that the algorithm constitutes a powerful tool for the future investigation of many-body Floquet systems.