  We investigate spin squeezing (SS) and the quantum Fisher information (QFI)
for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic
Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions
for spin squeezing and the reciprocal of the quantum Fisher information per
particle (RMQFI) are derived using the frozen spin approximation. It is shown
that in the superradiant phase near the critical point, maximum squeezing and
maximum quantum entanglement occurs. The present study is relevant to quantum
information processing and precision spectroscopy.
