Floquet dynamical quantum phase transitions under synchronized periodic driving

TL;DR

This paper investigates how synchronized periodic driving affects dynamical quantum phase transitions in fermionic two-band models, revealing nonperiodic patterns, geometric phase quantization, and potential experimental realizations.

Contribution

It introduces the study of synchronized periodic drives on fermionic models, showing nonperiodic transition patterns and proposing an experimental setup with Rydberg atoms.

Findings

Nonperiodic dynamical quantum phase transition patterns observed.

Quantized geometric phases enable an effective dynamical order parameter.

Transitions are detectable even with slight initial state perturbations.

Abstract

We study a generic class of fermionic two-band models under synchronized periodic driving, i.e., with the different terms in a Hamiltonian subject to periodic drives with the same frequency and phase. With all modes initially in a maximally mixed state, the synchronized drive is found to produce nonperiodic patterns of dynamical quantum phase transitions, with their appearance determined by an interplay of the band structure and the frequency of the drive. A case study of the anisotropic XY chain in a transverse magnetic field, transcribed to an effective two-band model, shows that the modes come with quantized geometric phases, allowing for the construction of an effective dynamical order parameter. Numerical studies in the limit of a strong magnetic field reveal distinct signals of precursors of dynamical quantum phase transitions also when the initial state of the XY chain is perturbed slightly away from maximal mixing, suggesting that the transitions may be accessible experimentally. A blueprint for an experiment built around laser-trapped circular Rydberg atoms is proposed.