Based on the SU(2) group for the Jaynes-Cummings model with time-dependent modul ation,we obtain its pancharatnam phase and analyse the phase changes during the whole process from adiabatically switching on to switching off of the interactio n of the atom with the field.Finally,we discuss the results in the semiclassical approximation.
The Pancharatnam phase of deformed Jaynes-Cummings(J-C) model was obtained analytically.The evolution of Pancharatnam phase for deformed Jaynes-Cummings model,was also discussed.The difference between the Pancharatnam phase evolution for deformed J-C model and that of conventional J-C model has been investigated.The results show that the Pancharatnam phase reveals some information of population reversion of an atom and the quantum nature of the cavity field.And the larger is the average photon number,the larger is the difference of Pancharatnam phase evolution between deformed J-C model and conventional J-C model.This exhibits that the evolution of Pancharatnam phase is closely relative to the quantum algebra structure of the system.
The Pancharatnam phase of a Tavis-Cummings model with the coherent state in Kerr medium is investigated theoretically and numerically. An exact expression of the Pancharatnam phase under this general system is obtained. The numerical results show that the dipole-dipole coupling strength between two atoms can change the quasi-period of the Pancharatnam phase evolution,and it is also proved that the Pancharatnam phase contains the information of atoms and the field. In the nonlinear interaction regime, the nonlinearity can cause the chaotic behavior of the Pancharatnam phase.