  In our preceding serial works, we have investigated the generation of
higher-order atomic dipole squeezing (HOADS) in a high-Q micromaser cavity,
discussing the effects of dynamic Stark shift, atomic damping, atomic coherence
and nonlinear one-photon processes and different initial states (for example,
correlated and uncorrelated states, superposition states, squeezed vacuum). In
this paper, we continue to study HOADS in a high-Q micromaser cavity, but
consider that the atom interacts with the optical field via a multi-photon
transition process and that the initial atom is arbitrarily prepared. For a
vacuum initial field, we demonstrate that HOADS cannot occur if the atom is
initially prepared in a chaotic state and that a coherent atomic state
generates less efficient and stable HOADS than an arbitrary one. It is found
that large detuning may lead to enhanced and strong HOADS.
