  Spin squeezing via atom-field interactions is considered within the context
of the Tavis-Cummings model. An ensemble of N two-level atoms interacts with a
quantized cavity field. For all the atoms initially in their ground states, it
is shown that spin squeezing of both the atoms and the field can be achieved
provided the initial state of the cavity field has coherence between number
states differing by 2. Most of the discussion is restricted to the case of a
cavity field initially in a coherent state, but initial squeezed states for the
field are also discussed. Optimal conditions for obtaining squeezing are
obtained. An analytic solution is found that is valid in the limit that the
number of atoms is much greater than unity and is also much larger than the
average number of photons, inititally in the coherent state of the cavity
field. In this limit, the degree of spin squeezing increases with increasing a,
even though the field more closely resembles a classical field for which no
spin squeezing could be achieved.
