Atom correlations and spin squeezing near the Heisenberg limit: Finite-size effect and decoherence

We analyze a model for spin squeezing based on the so-called countertwisting Hamiltonian, including the effects of dissipation and finite system size. We discuss the conditions under which the Heisenberg limit, i.e., phase sensitivity $\propto 1/N,$ can be achieved. A specific implementation of this model based on atom-atom interactions via quantized photon exchange is presented in detail. The resulting excitation corresponds to the creation of spin-flipped atomic pairs and can be used for fast generation of entangled atomic ensembles, spin squeezing, and applications in quantum information processing. The conditions for achieving strong spin squeezing with this mechanism are also analyzed.