NOON states via a quantum walk of bound particles

Tight-binding lattice models allow the creation of bound composite objects which, in the strong-interacting regime, are protected against dissociation. We show that a local impurity in the lattice potential can generate a coherent split of an incoming bound particle wave packet which consequently produces a NOON state between the endpoints. This is nontrivial because, when finite lattices are involved, edge-localization effects render challenging their use for nonclassical state generation and information transfer. We derive an effective model to describe the propagation of bound particles in a Bose–Hubbard chain. We introduce local impurities in the lattice potential to inhibit localization effects and to split the propagating bound particle, thus enabling the generation of distant NOON states. We analyze how minimal engineering transfer schemes improve the transfer fidelity and we quantify the robustness to typical decoherence effects in optical lattice implementations. Our scheme potentially has an impact on quantum-enhanced atomic interferometry in a lattice.