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We explore the collective non-Hermitian dynamics of a pair ofnon-conservatively coupled optomechanical oscillators. The oscillators consistof silica nanoparticles optically levitated in vacuum in two parallel pairs ofinterfering counter-propagating laser beams. By adjusting the relative phase,polarization, and separation of the trapping laser beams, we set the opticalinteraction between the particles to be purely non-reciprocal. Continuouslyvarying the relative power of the trapping beams over a predefined range takesthe system through transition, analogous to a parity-time (PT) phasetransition. Decreasing the dissipation rate within the non-equilibrium phaseinduces a Hopf bifurcation resulting in the formation of collective limit cycleoscillations similar to those observed in phonon lasers. Such systems provide anovel platform for exceptional point optomechanical sensing and due to theirwide flexibility and tunability of the interactions can be extended tomulti-particle systems, paving the way for the development of topologicaloptomechanical media.

Observations of a PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum