Phase transition between linear and nonlinear motion in a quadrupole-trap-based levitodynamic system with massive particles

We have experimentally investigated the nonlinear nature of massive particle dynamics in a quadrupole trap under atmospheric pressure. We have studied our levitated system over a wide range of trapping parameters and determined four distinct dynamical states of the trapped particle motion, which are associated with the retaining force and drag force nonlinearities. Like any other nonlinear system, the considered one possesses a phase transition in its behavior that demarcates linear and nonlinear regimes of motion. The nonlinear regime manifests itself as the formation of a specific limit cycle of the trapped particle motion also known as an extended orbit. We have shown that the birth of the extended orbits is foretold by the appearance of half-integer trapping frequency multiples in the particle motion oscillation. These half-integer multiples are highly sensitive to trapping parameters and external perturbation. We have demonstrated that the phase transition is a continuous process over a range of system parameters and can be exploited to detect small influences on the levitated system. We have tested the system response in the transient state to the external optical perturbation. The strong sensitivity to perturbation laser power has been shown for both the spectral composition of the trapped particle translational oscillations and extended orbit formation point. We believe in the potential to apply the nonlinear state of the levitodynamic system with massive particles to the field of precision measurements and nonequilibrium physics investigation.