Abstract
An analytical description for the dynamical evolution of a qubit interacting with two nonlinear Kerr oscillators pumped by optical parametric process is derived through Su (1, 1)-algebraic treatment. The role of intrinsic damping, detuning and Kerr-like Medium on the squeezing phenomenon is elucidated via information entropy squeezing. The evolutions of the interaction of the qubit with two-mode Kerr nonlinear coupler lead to the appearance the regular squeezing phenomenon during the chosen time-interval. The preserving and protecting of the qubit components from the squeezing can be controlled by the intrinsic decoherence, detuning and the Kerr-like medium effects. Where the squeezing phenomenon deteriorates with increasing the decoherence rate, whereas, the Kerr-like medium can not protect some qubit components from the squeezing.