Nonlinear coherent state generation in the two-photon Jaynes-Cummings model

We show that the two-photon Jaynes-Cummings model, feasible of experimental realization in cavity or ion-trap quantum electrodynamics, can approximately produce nonlinear coherent states of the field. We introduce these nonlinear coherent states of the field as $2m$-photon added or subtracted coherent states in terms of raising and lowering field operators, also known as London phase operators or Susskind-Glogower operators.