Nonclassicality of the Harmonic-Oscillator Coherent State Persisting up to the Macroscopic Domain (NoHarmMacro)

所有量子态中最“类经典”的，也就是谐振子的薛定谔相干态，能表现出非经典行为吗？我们发现，对于一个振荡的对象最初在一个相干态，仅仅通过观察在不同的时刻，该对象是在哪个空间区域，Leggett-Garg不等式（LGI）可以违反通过一个真正的负结果测量，从而否定日常概念的宏观实在论。因此，这种违反揭示了量子描述中经典性的缩影，而这种状态的非经典性却未被注意到。研究发现，对于任意给定的质量和振子频率，通过适当地选择相干态波包的初始峰值动量，可以获得一个显著的LGI量子破坏。因此，它可能开辟了一种最简单的方法，（不与任何辅助量子系统耦合或使用非线性），用于测试各种最近设计和追求的宏观振荡器，如反馈冷却的热捕获纳米粒子，是否确实是真正的非经典物体。该项目的首要目标是进行悬浮光机械实验，通过对纳米粒子相干运动态的Leggett-Garg不等式（LGI）进行采样，在宏观现实主义预测的背景下直接探测量子非定域性。为了实现这一目标，我们将建立一个实验平台，实现以下目标：1）快速重复单粒子实验动力学轨迹，获得足够的计数统计，以重建离域量子态的独特特征; 2）捕获和操纵（冷却）足够大的颗粒（直径约100 nm），以使波函数演化有足够的时间，并以足够高的分辨率实现位置测量。该NoHarmMacro实验将打开大门，以一个新的宏观领域测试量子力学在低能量非相对论制度-非常制度，重力预计会影响量子系统的动力学。NoHarmMacro利用大量的专业知识，在实验悬浮光学力学技术（PI乌布利希在南安普顿）与开拓性的分析专业知识（Co-I玻色在伦敦大学学院），以最大限度地提高这两个目标的成功。

Can the most "classical-like" of all quantum states, namely the Schrödinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanoparticles, are indeed bona fide nonclassical objects.The overarching goal of this project is to perform a levitated optomechanical experiment that, by sampling the Leggett-Garg inequality (LGI) for a coherent motional state of a nanoparticle, directly probing quantum non-locality in the context of predictions made by macroscopic realism. In order to reach this goal, we will develop an experimental platform that will allow the following achievements: 1) To rapidly repeat single-particle experimental dynamical trajectories to gain sufficient counting statistics in order to reconstruct the unique features of the delocalized quantum state; 2) To trap and manipulate (cool) sufficiently large particles (around 100 nm in diameter), to enable sufficient time for the wavefunction evolution, and to realise position measurements at sufficient high resolution. The NoHarmMacro experiment will open the door to a new macroscopic domain for testing quantum mechanics in the low energy non-relativistic regime -- the very regime where gravity is expected to affect the dynamics of quantum systems.NoHarmMacro leverages substantial expertise in experimental levitated optomechanical techniques (PI Ulbricht at Southampton) with pioneering analytical expertise (Co-I Bose at UCL) to maximise the success of both objectives.