Analytical energy spectrum for hybrid mechanical systems

Abstract

We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level-crossings, which correspond to two-fold energy degeneracy.

17 pages, 2 figures

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• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
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• Universal dynamics of superradiant phase transition in the anisotropic quantum Rabi model
• The heat kernel of the asymmetric quantum Rabi model
• General symmetry operators of the asymmetric quantum Rabi model
• On the Origin of the Hidden Symmetry in the Asymmetric Quantum Rabi Model
• Symmetry operators of the asymmetric two-photon quantum Rabi model
• Tripartite quantum Rabi model with trapped Rydberg ions
• Anisotropic Rabi model with two-photon relaxation
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model