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- W4386876145 abstract "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 $|omega_r-Omega| ll omega_r$, where $Omega$ and $omega_r$ 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 $gamma$, 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 $g-gamma$ 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." @default.
- W4386876145 created "2023-09-20" @default.
- W4386876145 creator A5015173100 @default.
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- W4386876145 date "2023-09-18" @default.
- W4386876145 modified "2023-09-27" @default.
- W4386876145 title "Schrieffer-Wolff transformation for non-Hermitian systems: application for $mathcal{PT}$-symmetric circuit QED" @default.
- W4386876145 doi "https://doi.org/10.48550/arxiv.2309.09829" @default.
- W4386876145 hasPublicationYear "2023" @default.
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