  False vacuum decay and nucleation offer the opportunity to study
non-equilibrium dynamical phenomena in quantum many-body systems with
confinement. Recent work has examined false vacuum decay in 1D ferromagnetic
Ising spins and superfluids. In this paper, we study false vacuum nucleation
dynamics in 1D antiferromagnetic neutral atom chains with Rydberg interactions,
using both numerical simulations and analytic modeling. We apply a staggered
local detuning field to generate the false and true vacuum states. Our efforts
focus on two dynamical regimes: decay and annealing. In the first, we
corroborate the phenomenological decay rate scaling and determine the
associated parameter range for the decay process; in the second, we uncover and
elucidate a procedure to anneal the false vacuum from the initial to the final
system, with intermediate nucleation events. We further propose experimental
protocols to prepare the required states and perform quenches on near-term
neutral atom quantum simulators, examining the experimental feasibility of our
proposed setup and parameter regime.
