Higher order correlations in a levitated nanoparticle phonon laser

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [Nat. Photonics 13, 402 (2019)10.1038/s41566-019-0395-5]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle’s position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.