01502nas a2200109   4500008004100000022001400041245013300055210006900188300001000257520107000267856005501337       2024                        eng d  a1745-248100aPT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum0 aPTlike phase transition and limit cycle oscillations in nonrecip  a1–73 a<p>Nanoparticles levitated in an optical trap provide a versatile platform to study mechanical oscillators in a controlled environment with tuneable parameters. Recently, it has become possible to couple two of these optomechanical oscillators. Here we demonstrate the collective non-Hermitian dynamics of such a pair of non-conservatively coupled oscillators. We take advantage of the tunability of the optical interactions between the particles in our system and set the optical interaction between the particles to be purely non-reciprocal. By continuously varying the relative power of the trapping beams, we take the system through a transition similar to a parity–time phase transition. A Hopf bifurcation at a critical point results in the formation of collective limit cycle oscillations, resembling those observed in phonon lasers. These coupled levitated oscillators provide a platform for exceptional point optomechanical sensing and can be extended to multi-particle systems, paving the way for the development of topological optomechanical media.</p>  uhttps://www.nature.com/articles/s41567-024-02590-1