Analytical Study of the Non-Hermitian Semiclassical Rabi Model

TL;DR

This paper provides an analytical approach to the non-Hermitian semiclassical Rabi model, revealing phase boundaries, stable oscillations, and the Bloch-Siegert shift, thus deepening understanding of open quantum systems with non-Hermitian dynamics.

Contribution

It introduces a similarity transformation and analytical solutions for the PT-symmetric Rabi model, accurately describing phase transitions and dynamics in non-Hermitian atom-field interactions.

Findings

Analytical phase boundary matches numerical results.

Stable oscillations observed in excited-state populations.

Bloch-Siegert shift resembles the Hermitian case, with higher-order coupling effects.

Abstract

The $\mathcal{PT}$ symmetric semiclassical Rabi model explores the fundamental interaction between a two-level atom and a classical field, revealing novel phenomena in open systems through the inclusion of non-Hermitian terms. We propose a single similarity transformation that yields an effective Hamiltonian in rotating-wave approximation, enabling an analytical solution. The phase boundary of the $\mathcal{PT}$-broken phase, derived from the analytical eigenvalues, closely matches the numerical exact one over a wide range of atomic frequencies, demonstrating the effectiveness of the analytical approach, especially at the main resonance. The Floquet parity operator is also introduced, providing a deeper physical understanding of the emergence of the $\mathcal{PT}$-broken phase. Furthermore, by analyzing the dynamics of excited-state population, we observe several stable oscillations in the Fourier spectrum, demonstrating the applicability of the analytical method beyond the single-photon resonance region. The Bloch-Siegert shift is also discussed and, surprisingly, resembles its Hermitian counterpart, except for the higher-order terms in the coupling strength. The present analytical treatment provides a concise and accurate description of the main physics of this non-Hermitian atom-field interaction system.