Arbitrary Non-equilibrium Steady State Construction with a Levitated Nanoparticle

Non-equilibrium thermodynamics provides a general framework for understanding non-equilibrium processes, particularly in small systems that are typically far from equilibrium and dominated by fluctuations. However, the experimental investigation of non-equilibrium thermodynamics remains challenging due to the lack of approaches to precisely manipulate non-equilibrium states and dynamics. Here, by shaping the effective potential of energy, we propose a general method to construct a non-equilibrium 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 uHz. Such an arbitrary NESS construction method provides a new approach to manipulating the dynamics processes of micromechanical systems and paves the way for the systematic study of non-equilibrium dynamics in interdisciplinary research fields.