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We investigate theoretically the dynamics of two quasidegenerate mechanicalmodes coupled through an open quantum two-level system. A mean-field approachshows that by engineering the retarded response of the two-level system with acoherent drive, the non-Hermitian mechanical spectrum exhibits an exceptionaldegeneracy point where the two modes coalesce. We show that this degeneracy canbe exploited to manipulate the vectorial polarization of the mechanicaloscillations. We find that adiabatically varying the detuning and the intensityof the drive induces a rotation of the mechanical polarization, which enablesthe topological and chiral actuation of one mode from the other. Thistopological manifestation of the degeneracy is further supported byquantum-jump Monte Carlo simulations to account for the strong quantumfluctuations due to the spontaneous emission of the two-level system. Ourpresentation focuses on a promising realization based on flexural modes of acarbon-nanotube cantilever coupled to a single-molecule electric dipoleirradiated by a laser.

Two-level system as topological actuator for nanomechanical modes