Hierarchy of quantum non-Gaussian conservative motion.

Mechanical quantum systems embedded in an external nonlinear potential currently offer the first deep excursion into quantum non-Gaussian motion. The Gaussian statistics of the motion of a linear mechanical quantum system, characterised by its mass and a linear-and-quadratic potential, possess a limited capacity to reduce noise in nonlinear variables. This limitation induces thresholds for noise reduction in nonlinear variables beyond which linear mechanical oscillators cannot pass. Squeezing below the thresholds for such variables is relevant for the implementation of nonlinear mechanical devices, such as sensors, processors or engines. First however, quantum non-Gaussian conservative motion must be identified in experiments with diverse nonlinear potentials. For this purpose, we provide sufficient criteria for quantum non-Gaussian motional states in conservative systems based on the observation of squeezing in nonlinear variables. We further extend these criteria to a hierarchy able to recognise the quantum non-Gaussian motion induced via diverse nonlinear potentials through their various capacities to produce nonlinear squeezing. Gaussian systems are useful for many quantum technologies but new applications will require control over nonlinear systems generating quantum non-Gaussian states. The authors present a method for the detection of quantum non-Gaussian states of mechanical particles which may be applied for future experiments in optomechanics and levitated nanoparticles in the quantum regime. [ABSTRACT FROM AUTHOR]