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We theoretically investigate the problem of position detection of an optically levitated Mie particle. The information radiation field (IRF) is proposed and defined to characterize the scattered light carrying complete information about the center-of-mass (c.m.) motion of the particle. Based on the IRF, we suggest an optimal detection scheme for the position of arbitrary particles. We calculate both the information losses of objective collection and mode-matching in levitated optomechanical experiments. Our results conclude that the backward detection scheme, using an incident Gaussian beam focused by a high numerical aperture lens, provides sufficient information to achieve the quantum ground state through cooling of the three-dimensional c.m. motion of the Mie particle.

Accurate measurement of pressure with a wide dynamic range holds significant importance for various applications. This issue can be realized with a mechanical nano-oscillator, where the pressure-related collisions with surrounding molecules induce its energy dissipation. However, this energy dissipation of the nano-oscillator may be overshadowed by other processes. Here, we apply the second-order coherence analysis to accurately characterize those distinct dissipation processes. Based on an optically levitated nano-oscillator, we successfully obtain precise measurements of the air pressure surrounding the particles from atmosphere to 7E-6 mbar, over 8 orders of magnitude. It proves that the mechanical nano-oscillator is an extremely promising candidate for precision pressure sensing applications. Moreover, the second-order coherence analysis method on a classical system can pave the way to characterize the dynamic properties of an oscillator, which will benefit microscopic thermodynamics, precision measurement, and macroscopic quantum research., Comment: 6 pages. 4 figures

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.