Quasienergy operators and general squeezed states for systems of trapped ions (original) (raw)

Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated, for a dynamical system that exhibits multiple degrees of liberty, that is a combined (Paul and Penning) trap. We introduce the generators of the Lie algebra of the symplectic group SL(2,R), which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators, and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, as well as the total energy. We also infer the dispersions for the coordinate and momentum, the asymmetry and the flatness parametre for the distribution. The system interaction with the laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is obtain...