  We theoretically investigate PT symmetry, induced mechanical lasing and force
sensing in an optically levitated nanoparticle with coupled oscillation modes.
The coupling in the levitated system is created by the modulation of an
asymmetric optical potential in the plane transverse to the beam trapping the
nanoparticle. We show that such a coupling can lead to PT-symmetric mechanical
behavior for experimentally realistic parameters. Further, by examining the
phonon dynamics and the second-order coherence of the nanoparticle modes, we
determine that induced mechanical lasing is also possible. Finally, we
demonstrate that tunable ultra-sensitive force sensing can be engineered in the
system. Our studies represent an advance in the fields of coherent manipulation
of coupled degrees of freedom of levitated mechanical oscillators and their
application for sensing.
