Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{PT}$-symmetric circuit QED
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| Format: | Preprint |
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2023
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| _version_ | 1866913230287273984 |
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| author | Starkov, Grigory A. Fistul, Mikhail V. Eremin, Ilya M. |
| author_facet | Starkov, Grigory A. Fistul, Mikhail V. Eremin, Ilya M. |
| contents | Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate \textit{non-Hermitian} systems. We apply our results to an exemplary $\mathcal{PT}$--symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as $|ω_r-Ω| \ll ω_r$, where $Ω$ and $ω_r$ are qubits and resonator frequencies, respectively, providing well-defined groups of quasi-degenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator, $g$, and the gain (loss) parameter $γ$, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify $\mathcal{PT}$--symmetry broken and unbroken phases, trace the formation of Exceptional Points of the second and the third order, and provide a complete phase diagram $g-γ$ of low-lying resonant states. We relate the formation of Exceptional Points to the additional $\mathcal{P}$-pseudo-Hermitian symmetry of the system and show that non-hermiticity mixes the "dark" and the "bright" states, which has a direct experimental consequence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_09829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{PT}$-symmetric circuit QED Starkov, Grigory A. Fistul, Mikhail V. Eremin, Ilya M. Quantum Physics Mesoscale and Nanoscale Physics Superconductivity Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate \textit{non-Hermitian} systems. We apply our results to an exemplary $\mathcal{PT}$--symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as $|ω_r-Ω| \ll ω_r$, where $Ω$ and $ω_r$ are qubits and resonator frequencies, respectively, providing well-defined groups of quasi-degenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator, $g$, and the gain (loss) parameter $γ$, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify $\mathcal{PT}$--symmetry broken and unbroken phases, trace the formation of Exceptional Points of the second and the third order, and provide a complete phase diagram $g-γ$ of low-lying resonant states. We relate the formation of Exceptional Points to the additional $\mathcal{P}$-pseudo-Hermitian symmetry of the system and show that non-hermiticity mixes the "dark" and the "bright" states, which has a direct experimental consequence. |
| title | Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{PT}$-symmetric circuit QED |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2309.09829 |