Analytical Study of the Non-Hermitian Semiclassical Rabi Model

• URL: http://arxiv.org/abs/2412.02918v2
• Date: Tue, 24 Dec 2024 11:02:34 GMT
• Title: Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Authors: Yibo Liu, Liwei Duan, Qing-Hu Chen,
• Abstract summary: The $mathcalPT$-broken phase closely matches the numerical exact one over a wide range of atomic frequencies. By analyzing the dynamics of excited-state population, we observe several stable oscillations in the Fourier spectrum. The present analytical treatment provides a concise and accurate description of the main physics of this non-Hermitian atom-field interaction system.
• Score: 0.6554326244334868
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• 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.

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