  We study the interplay between superfluid Meissner response, localization
dynamics from impurities and gauge theories. The superfluidity is formed in the
rung-Mott phase of the bosonic ladder model producing spin-Meissner currents
induced by a $\mathbb{U}(1)$ gauge field or a uniform magnetic field.
Impurities are described through two-state systems which act as a two-peak
random potential. An impurity sits either at the top or at the bottom of the
ladder on each rung equally, producing a telegraph signal. The
impurities-matter coupling gives rise to an intrinsic $\mathbb{Z}_2$ gauge
theory. Through analytical approaches and numerical exact diagonalization, we
address both the weakly-coupled and strongly-coupled rungs limits for
impurities. In the weakly-coupled rungs situation, we find a smooth power-law
localization whereas the strongly-coupled rungs limit produces a steep
localization or insulating phase for various configurations of the potential.
We describe the superfluid response relying on quantum spin models showing
four-particles coupling in the strongly-interacting regime with impurities and
linking with the persistent current limit. Through entanglement and bipartite
fluctuation measures, we also identify a many-body localization regime in time
after a quench of the system when prepared in a N\' eel state.
