  In this paper, we study the interaction between a moving $\Lambda$-type
three-level atom and a single-mode cavity field in the presence of
intensity-dependent atom-field coupling. After obtaining the state vector of
the entire system explicitly, we study the nonclassical features of the system
such as quantum entanglement, position-momentum entropic squeezing, quadrature
squeezing and sub-Poissonian statistics. According to the obtained numerical
results we illustrate that the squeezed period, the duration of entropy
squeezing and the maximal squeezing can be controlled by choosing the
appropriate nonlinearity function together with entering the atomic motion
effect by suitably selection of the field-mode structure parameter. Also, the
atomic motion, as well as the nonlinearity function leads to the oscillatory
behaviour of the degree of entanglement between the atom and field.
