  We consider a correlated Bose gas tightly confined into a ring shaped
lattice, in the presence of an artificial gauge potential inducing a persistent
current through it. A weak link painted on the ring acts as a source of
coherent back-scattering for the propagating gas, interfering with the forward
scattered current. This system defines an atomic counterpart of the rf-SQUID:
the atomtronics quantum interference device (AQUID). The goal of the present
study is to corroborate the emergence of an effective two-level system in such
a setup and to assess its quality, in terms of its inner resolution and its
separation from the rest of the many-body spectrum, across the different
physical regimes. In order to achieve this aim, we examine the dependence of
the qubit energy gap on the bosonic density, the interaction strength, and the
barrier depth, and we show how the superposition between current states appears
in the momentum distribution (time-of-flight) images. A mesoscopic ring lattice
with intermediate-to-strong interactions and weak barrier depth is found to be
a favorable candidate for setting up, manipulating and probing a qubit in the
next generation of atomic experiments.
