  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 an unfavorable
factor for gain in a laser. Here we demonstrate a novel mechanism of 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
shows anti-parity-time (anti-PT) symmetry 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 new 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.
