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arXiv · 1504.04701

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

Shuai Cui·Jun-Peng Cao·Heng Fan·Luigi Amico
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Abstract

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying $su(1,1)$ Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions.

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Shuai Cui, Jun-Peng Cao, Heng Fan, Luigi Amico. 2015-04-18. Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model. https://arxiv.org/abs/1504.04701

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