  The manuscript investigates the entropy squeezing of a qubit (two-level atom)
interacting with the cavity field in the Schr\"odinger cat states. The effects
of the Schr\"odinger cat states of the field on the squeezing are examined. Our
results suggest that entropy squeezing is not sensitive to the superposition
features of two coherent states of the Schr\"odinger cat states. Furthermore,
it is found that entropy squeezing occurs as the qubit initially close to its
maximally coherent state, and the qubit initially in the maximally coherent
state can generate optimal squeezing. This also demonstrates that the atomic
coherence has a remarkable effect on the atomic squeezing. On the other hand,
we also show how the entropy squeezing is related to the intensity of the
initial field.
