Two-photon Jaynes-Cummings model interacting with the squeezed vacuum state solved by dressed-state method

We reconsider the problem on a two-photon Jaynes-Cummings model interacting with the squeezed vacuum state, which has been studied by Gerry in 1988 [Phys. Rev. A 37, 2683-2686 (1988)]. By another different way (i.e. dressed state method), we cleverly deal with the dynamic evolution of more properties for the atom and the field in this process. The population inversion of the atom and the photon statistics of the optical field, in terms of photon number distribution, mean photon number, Mandel Q parameter and quadrature squeezing, are discussed in detail. Specially, we derive the analytic expressions and make the numerical simulation for these properties. Some interesting results involving in Gerry's paper are obtained.