  The ability to reliably prepare non-classical states will play a major role
in the realization of quantum technology. NOON states, belonging to the class
of Schroedinger cat states, have emerged as a leading candidate for several
applications. Starting from a model of dipolar bosons confined to a closed
circuit of four sites, we show how to generate NOON states. This is achieved by
designing protocols to transform initial Fock states to NOON states through use
of time evolution, application of an external field, and local projective
measurements. By variation of the external field strength, we demonstrate how
the system can be controlled to encode a phase into a NOON state. We also
discuss the physical feasibility, via an optical lattice setup. Our proposal
illuminates the benefits of quantum integrable systems in the design of
atomtronic protocols.
