  Coherent signal containing squeezed noise in a mixed state of radiation field
is considered here as a non-Gaussian mixture of a coherent state density
operator and a squeezed state density operator, as opposed to the usual well
known squeezed coherent state. Both these states are `quantum' noise-included
signal states. Effects of these two distinct ways of adding squeezing to a
coherent state are compared and contrasted. The main objective of this work is
to study the mixed state version of the Jaynes-Cummings model in the context of
a two-level atom interacting with a mixed field state of a squeezed vacuum and
a coherent state. The pure squeezed coherent state (PSCS) and the mixed
squeezed coherent state (MSCS) are used as the states of the radiation field.
The photon-counting distribution (PCD), the atomic inversion and the
entanglement dynamics of atom-field interaction for both the radiation fields
are investigated and compared with each other. We observe that depending on the
state of the field, squeezing has very different effects on coherent photons.
Mild squeezing on the coherent photons strongly localizes the PCD for PSCS;
however, for MSCS there is no such localization observed - instead squeezing
manifests for MSCS as oscillations in the PCD. The effects of squeezing on the
atomic inversion and the entanglement dynamics for MSCS are contrasting in
comparison with the corresponding quantities associated with PSCS. It is well
known in the literature that for PSCS, increasing the squeezing increases the
well-known ringing revivals in the atomic inversion, and also increases
irregularity in the entanglement dynamics. However, increasing the squeezing in
MSCS very significantly alters the collapse-revival pattern in the atomic
inversion and the entanglement dynamics of the Jaynes-Cummings model.
