Controllable photon and phonon localization in optomechanical Lieb lattices.

The Lieb lattice featuring flat band is not only important in strongly-correlated many-body physics, but also can be utilized to inspire new quantum devices. Here we propose an optomechanical Lieb lattice, where the flat-band physics of photon-phonon polaritons is demonstrated. The tunability of the band structure of the optomechanical arrays allows one to obtain an approximate photon or phonon flat band as well as the transition between them. This ultimately leads to the result that the controllable photon or phonon localization could be realized by the path interference effects. This study offers an alternative approach to explore the exotic photon and phonon many-body effects, which has potential applications in the future hybrid-photon-phonon quantum network and engineering new type solid-state quantum devices.