Title: Fermat's Spiral-Based Characterization of Squeezed Nonlinear Motional States of Levitated Nanoparticle Show Chinese title

Title: 基于费马螺旋的悬浮纳米粒子压缩非线性运动状态表征

Abstract: Controlling the state of motion of optically levitated nanoparticles is crucial for the advancement of precision sensing, fundamental tests of physics, and the development of hybrid classical-quantum technologies. Experimentally, such control can be achieved by pulsed modifications of the optical potential confining the nanoparticle. Most frequently, the applied potential pulses are parabolic in nanoparticle position, and they expand/squeeze or displace the initial Gaussian state of motion to a modified Gaussian state. The time-dependent mean values and covariance matrix of the phase-space variables can fully characterize such a state. However, quasi-parabolic optical potentials with added weak Duffing-type nonlinearity, encountered in real-world experiments, can generally distort the state of motion to a non-Gaussian one, for which the description based solely on the mean values and covariance matrix fails. Here, we introduce a nonlinear transformation of the phase-space coordinates using the concept of Fermat's spiral, which effectively removes the state distortion induced by the Duffing-type nonlinearity and enables characterization of the state of motion by the standard Gaussian-state metrics. Comparisons of the experimental data with theoretical models show that the proposed coordinate transformation can recover the ideal behavior of a harmonic oscillator even after extended evolution of the system in the nonlinear potential. The presented scheme enables the separation of the effects of the applied state manipulation, the system's gradual thermalization, and the nonlinearity of the confinement on the experimentally observed dynamics of the system, thereby facilitating the design of advanced protocols for levitated optomechanics. Show Chinese abstract

Abstract: 控制光学悬浮纳米粒子的运动状态对于精密传感、物理学基础测试以及混合经典-量子技术的发展至关重要。 实验上，可以通过对限制纳米粒子的光学势进行脉冲修改来实现这种控制。 通常，施加的势脉冲在纳米粒子位置上是抛物线形的，它们可以扩展/压缩或位移初始的高斯运动状态，使其变为修改后的高斯状态。 相空间变量的时间依赖均值和协方差矩阵可以完全表征这样的状态。 然而，在实际实验中遇到的带有弱杜芬型非线性的准抛物线光学势通常会将运动状态扭曲为非高斯状态，此时仅基于均值和协方差矩阵的描述方法会失效。 在这里，我们引入了一种基于费马螺旋概念的相空间坐标非线性变换，该变换能有效消除由杜芬型非线性引起的状态失真，并通过标准的高斯态度量来表征运动状态。 实验数据与理论模型的比较表明，所提出的坐标变换即使在系统在非线性势中长时间演化后，也能恢复简谐振子的理想行为。 所提出的方案能够将施加的状态操控效应、系统的逐渐热化以及约束的非线性对系统实验观测动力学的影响分离开来，从而有助于设计先进的悬浮光机械协议。