Quantum treatment of atom-field interaction via the quadratic invariant

We introduce a new quantum treatment for the problem of the interaction between a two-level atom and field, which is expressed by the Jaynes-Cummings model. The treatment is built up on the construction of a quadratic invariant for the free-field Hamiltonian and used to reformulate the interaction term. We concentrate our study on atomic inversion as well as the phenomenon of squeezing. For the atomic inversion there is a delay during the revival period beside a period of partial collapse. The phenomenon of squeezing is also observed in the normal, the variance, and the entropy squeezing. However, the maximum value of the squeezing beside its period depends in general on the variation of the field frequency. as well as the mu-parameter, both of which play a crucial role to control this phenomenon. (C) 2012 Optical Society of America