Atomtronic protocol designs for NOON states

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.