Geometric Phase in the Interaction System of Three-Energy Atom with Double-Mode Radiation Field

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in the interaction system of three-energy atom with double-mode radiation field, respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.     

Geometric Phase of Quantum Dots in the Time-Dependent Isotropic Magnetic Field

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

Atomic Tunneling Effect in Two-Component Bose-Einstein Condensates with a Coupling Drive

In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.     

Inhomogeneous Inverse Differential Realization of Multimode SU(1, 1) Group

The generators and irreducible representationcoherent state of the multimode SU(1, 1) group inBargmann space are constructed by using the inverseoperators of the multimode bosonic harmonic oscillator, and the inhomogeneous inverse differentialrealization of the multimode SU(1, 1) group arederived.     

Geometric Phase in a Generalized Jaynes-Cummings Model with Double Mode Operators and Phase Operators

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

Geometric Phase in a Time-Dependent Bose-Fermi System

By using the Lewis-Riesenfeld invariant theory, the geometric phase in a time-dependent Bose-Fermi system has been studied. It is found that the geometric phase has nothing to do with the field frequency and the coupling coefficient between the Boson and Fermion.     

Geometric Phase in a Time-Dependent System with Laguerre Polynomial State

By using of the invariant theory, we have studied the geometric phase in a time-dependent system with Laguerre polynomial state, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Two-Parameter Deformed Multimode Usui Operators of Multimode SU(2)q,s and SU(1,1)q,s Algebras

The two-parameter deformed (q,s-deformed)multimode Usui operators of multimodeSU(2)_q,s and SU(1,1)_q,s algebrasare introduced and the multimode q,s-Dyson bosonrealizations of both algebras are also given.     

Interference of Two-Component Bose-Einstein Condensates with a Coupling Drive in Presence of Dissipation

The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωrf, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.     

Geometric Phase in a Λ-type <Emphasis Type="Italic">k</Emphasis>-photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in this process may be observed, and the geometric phases in this process have the observable physical effect.