Nonequilibrium dynamics of optically levitated particles

This paper reviews the nonequilibrium dynamics of nanoparticles optically levitated in a vacuum, a platform that minimizes mechanical dissipation and reveals complex inertial behaviors driven by nonconservative optical forces. We demonstrate that while traditional optical traps are often modeled as conservative potential wells, the total optical force field generally includes rotational components that cannot be represented by a scalar potential. By linearizing the dynamics near stationary positions, we show that these nonconservative contributions manifest as a nonsymmetrical stiffness matrix. As environmental damping is reduced, the system can cross a non-Hermitian exceptional point where eigenvalues become complex, leading to a Hopf bifurcation and the autonomous formation of stable, coherent limit cycles in multidimensional phase space. We further explore collective phenomena in coupled multi-particle systems, including the emergence of synchronized in-phase and antiphase modes in two optically coupled particles. Finally, we discuss the statistical inevitability of instabilities in large photonic clusters, positioning levitated optomechanics as a versatile arena for engineering non-Hermitian many-body dynamics and exploring emergent temporal order.