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

We explore the collective non-Hermitian dynamics of a pair of non-conservatively coupled optomechanical oscillators. The oscillators consist of silica nanoparticles optically levitated in vacuum in two parallel pairs of interfering counter-propagating laser beams. By adjusting the relative phase, polarization, and separation of the trapping laser beams, we set the optical interaction between the particles to be purely non-reciprocal. Continuously varying the relative power of the trapping beams over a predefined range takes the system through transition, analogous to a parity-time (PT) phase transition. Decreasing the dissipation rate within the non-equilibrium phase induces a Hopf bifurcation resulting in the formation of collective limit cycle oscillations similar to those observed in phonon lasers. Such systems provide a novel platform for exceptional point optomechanical sensing and due to their wide flexibility and tunability of the interactions can be extended to multi-particle systems, paving the way for the development of topological optomechanical media