  We theoretically investigate the effect of optical-force-mediated
interactions onto the quantum dynamics of a pair of dielectric nanospheres
optically trapped in two neighboring optical tweezers. Thanks to the
interference between the tweezer beams and the elastically scattered light by
the other nanosphere, the effective inter nanosphere coupling can reach the
ultrastrong coupling regime. Experimentally accessible signatures of the
entangled nature of the quantum ground state are highlighted, including
entanglement witnesses based on position/momentum correlation functions and a
sizable dynamical Casimir excitation upon a fast modulation of the tweezer's
properties.
