Phonon laser in an optomechanical system with nonreciprocal coupling

Phonon lasers, which are analogous to optical lasers, have garnered significant attention in various research fields. Here, we propose a phonon laser based on a three-cavity optomechanical system in which a dissipative cavity is simultaneously coupled to two optical cavities. By adiabatically eliminating the degrees of freedom associated with the dissipative cavity, we derive an effective non-Hermitian dual-cavity optomechanical model with tunable nonreciprocal coupling. We show that tuning the nonreciprocal coupling strength under an optimal coupling ratio condition significantly modifies phonon laser thresholds and mechanical gain. In contrast to conventional symmetric coupling systems, we introduce what we believe to be a novel supermode orthogonalization method based on coupling strength weighting. Numerical simulations reveal that the tunability of phonon lasing dynamics originates from the photon population asymmetry induced by supermode symmetry breaking. Our approach establishes a new paradigm for exploring phonon laser effects in non-Hermitian open systems and provides an innovative platform for integrating optomechanics with non-Hermitian photonics theory.