Abstract
Linearized stochastic nanomechanical systems operating at nonzero temperatures and constant frequency and damping are restricted in their capacity to reduce noise in nonlinear combinations of the canonical variables. Nonlinear dynamics are then required in order to overcome these limits. Here we demonstrate how to make these limits explicit in the form of a threshold for nonlinear squeezing of the motional variables. Noise suppression below the threshold cannot be explained by linearized dynamics and is helpful in low-noise nonlinear devices at an ambient temperature. We predict that a state of the art levitating particle, exposed to cubic or quartic trapping potentials for a short interval will display nonlinear squeezing of stochastic motion that cannot be replicated by linear motion.
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