Tight-binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. How to harness this mobility in a many-site lattice for useful operations is still an open question. We show how effective linear opticslike operations between arbitrary lattice sites can be implemented by a minimal local control which introduces a local impurity in the middle of the lattice. In particular we show how striking is the difference of the two possible correlations with and without the impurity. Our scheme enables the observation of the Hong-Ou-Mandel effect between distant wells without moving them next to each other with, e.g., tweezers. Moreover, we show that a tunable Mach-Zehnder interferometer is implemented adding a steplike potential, and we prove the robustness of our linear optics scheme to interparticle interactions.

• Received 2 September 2014

DOI:https://doi.org/10.1103/PhysRevA.92.022701