Algebraic approach to the Tavis-Cummings model with three modes of oscillation

Abstract

We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the $SU(1,1)$ and $SU(2)$ groups. The algebraic method based on the Bogoliubov transformation and the normal-mode operators let us obtain the energy spectrum and eigenfunctions of a particular case of the Tavis-Cummings model, while with the tilting transformation we are able to solve the most general case of this Hamiltonian. Finally, we compute some expectation values of this problem by means of the $SU(1,1)$ and $SU(2)$ group theory.

17 pages. arXiv admin note: text overlap with arXiv:1704.05778

References in corpus (6)

• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Progressive field-state collapse and quantum non-demolition photon counting
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Two-photon entanglement in multi-qubit bi-directional waveguide QED
• Landau-Zener extension of the Tavis-Cummings model: structure of the solution
• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models

Cited by in corpus (4)

• Generalization of the Tavis-Cummings model for multi-level anharmonic systems: insights on the second excitation manifold
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Berry phase of the Tavis-Cummings model with three modes of oscillation