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

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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.