Realization of programmable nanomechanical lattice with both nearest-neighboring and next-nearest-neighboring couplings

The programmable artificial lattice, based on the controllability of coupling strengths and the scalability of multiple sites, is desperately desired in engineering metamaterials and exploring fundamental physics. In this work, we experimentally present a programmable lattice consisting of multiple paralleled nanomechanical resonators, whose internal interactions can be linearly manipulated by external voltages. Flexural modes of nearest-neighboring (NN) and next-nearest-neighboring (NNN) resonators are parametrically coupled through modulated electrostatic interactions. Particularly, in a wide range up to deep strong coupling regimes, both the NN and NNN coupling strengths are precisely proportional to manipulation voltage. The realization of long-range coupling provides a promising prospect in constructing a complex lattice structure, which is essential for investigating mechanical logic devices, topological physics, and coherent phononic dynamics.