  Spin squeezing is one of the most attractive methods for realizing
high-precision metrology. In this paper, we propose a protocol for generating
spin squeezing in an atomic ensemble via a fully quantum degenerate parametric
amplifier. We discuss the properties of generating spin squeezing with and
without driving the pump cavity. Numerical simulation results show that the
generated spin squeezing strength is sizable, and is able to be comparable to
that obtained using a two-axis twisting (TAT) model. Moreover, we demonstrate
that the protocol is experimentally feasible by introducing the corresponding
experimental parameters. Therefore, the proposed protocol provides a promising
approach to realize spin squeezing in photon-spin coupling systems.
