Generalized Rabi model in quantum-information processing including the (A)over-right-arrow2 term

We consider the effect of the quadratic term (A) over right arrow (2) on quantum state transfer, nonclassical state preparation, and collapse-revival dynamics in the strong and ultrastrong coupling regime. Using the Bogoliubov transformation, we define a field mode which allows us to reduce the Hamiltonian to the original Rabi form without the (A) over right arrow (2) term. We calculate the error introduced by the (A) over right arrow (2) term in quantum state transfer and find it cannot be neglected in the strong coupling regime. We also study how it impacts the characteristics of the prepared nonclassical states and collapse-revival dynamics. The double-peak characteristic of the revival dynamics can be experimentally observed as manifestation of the effect of the (A) over right arrow (2) term.