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. *

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

“…where the term D(ξ) ab |ϕ ′′ can be identified as the SU (1, 1) Perelomov number coherent states for the twodimensional harmonic oscillator [38].…”

“…Since its introduction, it has been extensively studied in several quantum systems [31][32][33]. We recently have applied the theory of the SU (1, 1) and SU (2) groups to obtain the energy spectrum, eigenfunctions and the Berry phase of some of these Quantum Optics models [34][35][36][37][38]. In reference [39], an algebraic method based on the Sp(4, R) group (and contains the SU (1, 1) and SU (2) groups) was introduced to solve exactly the interaction part of the most general Hamiltonian of a two-level system in two-dimensional geometry.…”