References & Citations
Quantum Physics
Title: Unified approach to the nonlinear Rabi models
(Submitted on 20 Jun 2022 (v1), last revised 25 Feb 2023 (this version, v2))
Abstract: An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry. There exist exact isolated solutions, which are located at the level crossings between different parities and correspond to eigenstates with finite dimension. Beyond the exact isolated solutions, the regular spectrum can be achieved by finding the roots of the G-function. The corresponding eigenstates are of infinite dimension. It is noteworthy that the expansion coefficients of the eigenstates present an exponential decay behavior. The decay rate decreases with increasing coupling strength. When the coupling strength tends to the spectral collapse point $g \rightarrow \omega / 2$, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of novel physics in nonlinear quantum optics.
Submission history
From: Liwei Duan [view email][v1] Mon, 20 Jun 2022 14:29:14 GMT (86kb)
[v2] Sat, 25 Feb 2023 01:23:18 GMT (124kb)
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