Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi models
Abstract
We prove that the non-commutative harmonic oscillator on L2(R)2 introduced by Parmeggiani and Wakayama is equivalent to the two-photon quantum Rabi model, and they are also equivalent to a holomorphic differential equation on the unit disk. The confluence process of this differential equation and the relation with the one-photon quantum Rabi model are also discussed.
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