PT-symmetric Rabi model: Perturbation theory

TL;DR

This paper analyzes a non-Hermitian, PT-symmetric version of the Rabi model, deriving phase boundaries and shifts using perturbation theory, with potential experimental realizations in waveguides and atomic systems.

Contribution

It introduces a perturbative approach to determine PT phase boundaries in a non-Hermitian Rabi model beyond the rotating-wave approximation.

Findings

Identifies PT-breaking boundaries for main and higher-order resonances.

Derives the non-Hermitian Bloch-Siegert shift at maximal PT-breaking.

Maps high-frequency regime to Wannier-Stark ladder.

Abstract

We study a non-Hermitian version of the Rabi model, where a two-level system is periodically driven with an imaginary-valued drive strength, leading to alternating gain and loss. In the Floquet picture, the model exhibits PT symmetry, which can be broken when the drive is sufficiently strong. We derive the boundaries of the PT phase diagram for the different resonances by doing perturbation theory beyond the rotating-wave approximation. For the main resonance, we show that the non-Hermitian analog of the Bloch-Siegert shift corresponds to maximal PT-breaking. For the higher-order resonances, we capture the boundaries to lowest order. We also solve the regime of high frequency by mapping to the Wannier-Stark ladder. Our model can be experimentally realized in waveguides with spatially-modulated loss or in atoms with time-modulated spontaneous decay.