Level crossings and new exact solutions of the two-photon Rabi model

Abstract

An infinite family of exact solutions of the two-photon Rabi model was found by investigating the differential algebraic properties of the Hamiltonian. This family corresponds to energy level crossings not covered by the Juddian class, which is given by elemetary functions. In contrast, the new states are expressible in terms of parabolic cylinder or Bessel functions. We discuss three approaches for discovering this hidden structure: factorization of differential equations, Kimura transformation, and a doubly-infinite, transcendental basis of the Bargmann space.

arXiv commentAccepted for publication in Journal of Physics A; 17 pages, 1 color figure

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Cited by in corpus (5)

• Symmetry breaking patterns, tricriticalities and quadruple points in quantum Rabi model with bias and nonlinear interaction
• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
• Spectral determinant of the two-photon quantum Rabi model
• Two-photon Rabi-Stark model
• Bound states of two-photon Rabi model at the collapse point