  We chart out the ground state phase diagram and demonstrate the presence of a
many-body localized (MBL) phase for an experimentally realizable
one-dimensional (1D) constrained dipole boson model in the presence of an
Aubry-Andre (AA) potential whose strength $\lambda_0$ can be tuned to
precipitate an ergodic-MBL transition. We discuss the signature of such a
transition in the quantum dynamics of the model by computing its response
subsequent to a sudden quench of $\lambda_0$. We show that the MBL and the
ergodic phases can be clearly distinguished by study of post-quench dynamics
and provide an estimate for minimal time up to which experiments need to track
the response of the system to confirm the onset of the MBL phase. We suggest
experiments which can test our theory.
