Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials
arXiv (Cornell University)(2023)
Abstract
We derive an analytical expression of a Wigner function that approximately
describes the time evolution of the one-dimensional motion of a particle in a
nonharmonic potential. Our method involves two exact frame transformations,
accounting for both the classical dynamics of the centroid of the initial state
and the rotation and squeezing about that trajectory. Subsequently, we employ
two crucial approximations, namely the constant-angle and
linearized-decoherence approximations. These approximations are effective in
the regime of wide potentials and small fluctuations, namely potentials that
enable spatial expansions orders of magnitude larger than the one of the
initial state but that remain smaller compared to the relevant dynamical length
scale (e.g., distance between turning points). Our analytical result elucidates
the interplay between classical and quantum physics and the impact of
decoherence during nonlinear dynamics. This analytical result is instrumental
to design, optimize and understand proposals using nonlinear dynamics to
generate macroscopic quantum states of massive particles.
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Key words
wide nonharmonic potentials,particle dynamics
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