Light-matter correlations in Quantum Floquet engineering of cavity quantum materials

TL;DR

This paper develops a gauge-invariant, non-perturbative approach to quantum Floquet engineering in cavity-QED systems, revealing how light-matter correlations influence topological properties and edge states even at high frequencies.

Contribution

It introduces a novel non-perturbative truncation scheme for the Hamiltonian that captures light-matter correlations at arbitrary coupling strengths, advancing the understanding of quantum Floquet engineering.

Findings

Light-matter correlations are crucial for topological properties.

Correlations can break chiral symmetry in SSH chains.

Spectral functions encode light-matter correlation effects.

Abstract

Quantum Floquet engineering (QFE) seeks to generalize the control of quantum systems with classical external fields, widely known as Semi-Classical Floquet engineering (SCFE), to quantum fields. However, to faithfully capture the physics at arbitrary coupling, a gauge-invariant description of light-matter interaction in cavity-QED materials is required, which makes the Hamiltonian highly non-linear in photonic operators. We provide a non-perturbative truncation scheme of the Hamiltonian, which is valid or arbitrary coupling strength, and use it to investigate the role of light-matter correlations, which are absent in SCFE. We find that even in the high-frequency regime, light-matter correlations can be crucial, in particular for the topological properties of a system. As an example, we show that for a SSH chain coupled to a cavity, light-matter correlations break the original chiral symmetry of the chain, strongly affecting the robustness of its edge states. In addition, we show how light-matter correlations are imprinted in the photonic spectral function and discuss their relation with the topology of the bands.