  We describe a mechanism for guiding the dynamical evolution of ultracold
atomic motional degrees of freedom toward multiparticle entangled
Dicke-squeezed states, via nonlinear self-organization under external driving.
Two examples of many-body models are investigated. In the first model, the
external drive is a temporally oscillating magnetic field leading to
self-organization by interatomic scattering. In the second model, the drive is
a pump laser leading to transverse self organization by photon-atom scattering
in a ring cavity. We numerically demonstrate the generation of multiparticle
entangled states of atomic motion and discuss prospective experimental
realizations of the models. For the cavity case, the calculations with
adiabatically eliminated photonic sidebands show significant momentum
entanglement generation can occur even in the "bad cavity" regime. The results
highlight the potential for using self-organization of atomic motion in quantum
technological applications.
