  We discuss a Rydberg atom chain with a tunable blockade radius from the gauge
theoretic perspective. When the blockade radius is one lattice spacing, this
system can be formulated in terms of the PXP model, and there is a
$\mathbb{Z}_2$ Ising phase transition known to be equivalent to a
confinement-deconfinement transition in a gauge theory, the lattice Schwinger
model. Further increasing the blockade radius, one can add a next-nearest
neighbor (NNN) interaction into the PXP model. We discuss the interpretation of
NNN interaction in terms of the gauge theory and how finite NNN interaction
alters the deconfinement behavior and propose a corresponding experimental
protocol. When the blockade radius reaches two lattice spacing, the model
reduces to the PPXPP model. A novel gauge theory equivalent to the PPXPP model
is formulated, and the phases in the two formulations are delineated. These
results are readily explored experimentally in Rydberg quantum simulators.
