Nonreciprocal enhancement of remote entanglement between nonidentical mechanical oscillators

Entanglement between distant massive mechanical oscillators is of particular interest in quantum-enabled devices due to its potential applications in distributed quantum information processing. Here we propose how to achieve nonreciprocal remote entanglement between two spatially separated mechanical oscillators within a cascaded optomechanical configuration, where the two optomechanical resonators are indirectly coupled through a telecommunication fiber. We show that by selectively spinning the optomechanical resonators, one can break the time reversal symmetry of this compound system via Sagnac effect, and more excitingly, enhance the indirect couplings between the mechanical oscillators via the individual optimizations of light-motion interaction in each optomechanical resonator. This ability allows us to generate and manipulate nonreciprocal entanglement between distant mechanical oscillators, that is, the entanglement could be achieved only through driving the system from one specific input direction but not the other. Moreover, in the case of two frequency-mismatched mechanical oscillators, it is also found that the degree of the generated nonreciprocal entanglement is counterintuitively enhanced in comparison with its reciprocal counterparts, which are otherwise unattainable in static cascaded systems with a single-tone driving laser. Our work, which is well within the feasibility of current experimental capabilities, provides an enticing new opportunity to explore the nonclassical correlations between distant massive objects and facilitates a variety of emerging quantum technologies ranging from quantum information processing to quantum sensing.