Quantum Phase and Field Purification for Quantum System in Coherent States Based on Generalized Heisenberg Algebra

In this paper, we consider the interaction between the two-level atom and the electromagnetic field modes initially prepared in coherent states associated with the generalized Heisenberg algebra (GHA). We investigate the dynamical behavior of the field purity, Pancharatnam phase, and atomic-population inversion. Based on the GHA, we study the statistical properties of the field state through the evolution of the Mandel parameter and examine the effects of the initial atomic state setting and the number of transiting photons. The results show that the GHA-coherent-state strength has the potential to affect the time evolution of the field purification, the Pancharatnam phase, and the Mandel parameter.