Phonon lasers, as the counterpart of photonic lasers, have been intensively studied in a large variety of systems; however, (all) most of them are based on the directly coherent pumping. Intuitively, dissipation is unfavorable for lasing. Here, we experimentally demonstrate a mechanism of generating phonon lasing from the dissipative coupling in a multimode optomechanical system. By precisely engineering the dissipations of two membranes and tuning the intensity modulation of the cavity light, the two-membrane-in-the-middle system exhibits non-Hermitian characteristics and the cavity-mediated interaction between two nanomechanical resonators becomes purely dissipative. The level attraction and damping repulsion are clearly exhibited as the signature of dissipative coupling. After the exceptional point, a non-Hermitian phase transition, where eigenvalues and the corresponding eigenmodes coalesce, two phonon modes are simultaneously excited into the self-sustained oscillation regime by increasing the interaction strength over a critical value (threshold). In distinct contrast to conventional phonon lasers, the measurement of the second-order phonon correlation reveals the oscillatory and biexponential phases in the nonlasing regime as well as the coherence phase in the lasing regime. Our study provides a method to study phonon lasers in a non-Hermitian open system and could be applied to a wide range of disciplines, including optics, acoustics, and quantum many-body physics.
Keywords: dissipative coupling; multimode phonon laser; non-Hermitian phase transition.