Analytical Study of the Non-Hermitian Semiclassical Rabi Model
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| Format: | Preprint |
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2024
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| _version_ | 1866909566108696576 |
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| author | Liu, Yibo Duan, Liwei Chen, Qing-Hu |
| author_facet | Liu, Yibo Duan, Liwei Chen, Qing-Hu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical Study of the Non-Hermitian Semiclassical Rabi Model Liu, Yibo Duan, Liwei Chen, Qing-Hu Quantum Physics 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. |
| title | Analytical Study of the Non-Hermitian Semiclassical Rabi Model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.02918 |