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

在所有量子状态中，最“经典”的状态，即谐振子的薛定谔相干态，能表现出非经典行为吗？我们发现，对于一个最初处于相干态的振荡对象，仅仅通过在不同时刻观察对象所在的空间区域，就可以通过真正的负结果度量来违反Leggett-Garg不等式(LGI)，从而否定了日常的宏观现实主义概念。因此，这种违反揭示了状态本身的一种未被注意的非经典，这是量子描述中经典的缩影。结果表明，对于任意给定的质量和振子频率，通过适当选择相干态波包的初始峰值动量，可以获得LGI的显著量子破坏。因此，它开辟了潜在的最简单的方法(不与任何辅助量子系统或使用非线性)来测试各种最近设计和寻找的宏观振荡器，如反馈冷却热陷阱纳米粒子，是否确实是真正的非经典物体。该项目的首要目标是执行悬浮光学机械实验，通过采样Leggett-Garg不等式(LGI)获得纳米粒子的相干运动状态，在宏观现实主义预测的背景下直接探测量子非定域性。为了达到这一目标，我们将开发一个实验平台，它将允许以下成就：1)快速重复单粒子实验动力学轨迹，以获得足够的计数统计数据，以重建离域量子态的独特特征；2)捕获和操纵(冷却)足够大的粒子(直径约100 nm)，以便有足够的时间进行波函数演化，并实现足够高分辨率的位置测量。NoHarmMacro实验将为在低能非相对论区域测试量子力学打开一扇新的宏观领域的大门，正是在这种区域，重力预计会影响量子系统的动力学。NoHarmMacro利用实验悬浮光学机械技术方面的丰富专业知识(南安普顿的Pi Ulbricht)和开创性的分析专业知识(UCL的Co-I Bose)来最大化这两个目标的成功。

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.