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

@article{Choreno2019BerryPO,
  title={Berry phase of the Tavis-Cummings model with three modes of oscillation},
  author={E. Choreno and D. Ojeda-Guill'en and R. Valencia and V. D. Granados},
  journal={Journal of Mathematical Physics},
  year={2019}
}
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. 
1 Citations
Algebraic approach and Berry phase of a Hamiltonian with a general SU(1, 1) symmetry
In this paper we study a general Hamiltonian with a linear structure given in terms of two different realizations of the $SU(1,1)$ group. We diagonalize this Hamiltonian by using the similarity

References

SHOWING 1-10 OF 87 REFERENCES
Algebraic approach to the Tavis-Cummings model with three modes of oscillation
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
Algebraic approach to the Tavis-Cummings problem
An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings Hamiltonian, based on polynomially deformed su(2), i.e., su{sub n}(2) algebras. In this
Landau-Zener extension of the Tavis-Cummings model: Structure of the solution
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly
Generalized two-mode harmonic oscillator model: squeezed number state solutions and nonadiabatic Berry’s phase
Abstract.A generalized two-mode harmonic oscillator model is investigated within the framework of its general dynamical algebra so(3,2). Two types of eigenstates, formulated as extended su(1,1),
SU(1, 1) and SU(2) Perelomov number coherent states: algebraic approach for general systems
We study some properties of the SU(1, 1) Perelomov number coherent states. The Schrödinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie
Berry phase in arbitrary dimensions
We study the properties of the Berry phase in quantum systems where momentum and position operators satisfy the R-deformed Heisenberg relations and the noninteger dimension d and angular momentum ℓ
SU(2) and SU(1,1) phase states.
  • Vourdas
  • Mathematics, Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1990
TLDR
In the SU(1,1) case the exponential of the phase operators is nonunitary, and the phase states form an overcomplete set which is used to formulate an analytic representation.
Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model
Abstract We study and exactly solve the two-photon and k-photon Jaynes–Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the
The su(1,1) Tavis-Cummings model
A generic su(1,1) Tavis-Cummings model is solved both by the quantum inverse method and within a conventional quantum-mechanical approach. Examples of corresponding quantum dynamics including
...
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