Arbitrary nonequilibrium steady-state construction with a levitated nanoparticle

Nonequilibrium thermodynamics provides a general framework for understanding nonequilibrium processes, particularly in small systems that are typically far from equilibrium and dominated by fluctuations. However, the experimental investigation of nonequilibrium thermodynamics remains challenging due to the lack of approaches to precisely manipulate nonequilibrium states and dynamics. Here, by shaping the effective potential of energy, we propose a general method to construct a nonequilibrium steady state (NESS) with arbitrary energy distribution. Using a well-designed energy-dependent feedback damping, the dynamics of an optically levitated nanoparticle in vacuum is manipulated and driven into a NESS with the desired energy distribution. Based on this approach, a phonon laser state is constructed with an ultra-narrow linewidth of 6.40 & mu;Hz. Such an arbitrary NESS construction method provides an approach to manipulating the dynamics processes of micromechanical systems and paves the way for the systematic study of nonequilibrium dynamics in interdisciplinary research fields.