Fast generation of spin squeezing via resonant spin-boson coupling

We propose protocols for the creation of useful entangled states in a system of spins collectively coupled to a bosonic mode, directly applicable to trapped- ion and cavity QED setups. The protocols use coherent manipulations of the resonant spin-boson interactions naturally arising in these systems to prepare spin squeezed states exponentially fast in time. The resonance condition harnesses the full spin-boson coupling and thus avoids the slower timescales when operating in the off-resonance regime.