Phase-controlled robust quantum entanglement of remote mechanical oscillators

Quantum entanglement between distant massive mechanical oscillators has played a central role in building and engineering quantum devices for application in long-distance quantum communications, distributed quantum sensing, and synchronized quantum processing. Here we propose to control quantum entanglement of two spatially separated mechanical oscillators in a cascaded quantum system by applying two counterpropagating pump fields. In particular, we find that by adjusting the phase difference of pump lasers, quantum entanglement between such two mechanical oscillators can be significantly enhanced, together with improved robustness against environmental thermal noise. Our work opens up a well -accessible way to manipulate and protect mechanical entanglement, shedding light on a wide range of practical applications requiring robust purely quantum resources.