Berry phase of the Tavis-Cummings model with three modes of oscillation

Abstract

In this paper we develop a general method to obtain the Berry phase of time-dependent Hamiltonians with a linear structure given in terms of the $SU(1,1)$ and $SU(2)$ groups. This method is based on the similarity transformations of the displacement operator performed to the generators of each group, and let us diagonalize these Hamiltonians. Then, we introduce a trilinear form of the Tavis-Cummings model to compute the $SU(1,1)$ and $SU(2)$ Berry phases of this model.

arXiv comment11 pages

References in corpus (16)

• Quantum simulation of the Dirac equation
• Progressive field-state collapse and quantum non-demolition photon counting
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Tavis-Cummings model and collective multi-qubit entanglement in trapped ions
• Relativistic quantum mechanics with trapped ions
• Landau-Zener extension of the Tavis-Cummings model: structure of the solution
• An algebraic approach to the Tavis-Cummings problem
• Dissipative Two-Mode Tavis-Cummings Model with Time-Delayed Feedback Control
• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
• A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
• Berry Phase in a Two-atom Jaynes-Cummings Model with Kerr Medium
• Algebraic treatments of the problems of the spin-1/2 particles in the one and two-dimensional geometry: a systematic study
• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation
• $SU(1,1)$ and $SU(2)$ Perelomov number coherent states: algebraic approach for general systems
• Solution of spin-boson systems in one and two-dimensional geometry via the asymptotic iteration method

Cited by in corpus (1)

• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry