Sub-Planck structure quantification in non-Gaussian probability densities

TL;DR

This paper introduces a universal, experimentally accessible method to identify and quantify sub-Planck structures in non-Gaussian phase space densities of bosonic quantum systems, demonstrated on high-order Fock states.

Contribution

The authors develop a new method for quantifying sub-Planck structures directly from measurable probability densities, applicable across various quantum states and dynamics.

Findings

Finer sub-Planck structures are observed with increasing Fock occupation.

The method is effective on experimental data from a single-atom mechanical oscillator.

Sub-Planck structures are prevalent in nonlinear quantum dynamics and measurements.

Abstract

Sub-Planck structures in non-Gaussian probability densities of phase space variables are pervasive in bosonic quantum systems. They are almost universally present if the bosonic system evolves via nonlinear dynamics or nonlinear measurements. So far, identification and comparison of such structures remains qualitative. Here we provide a universally applicable and experimentally friendly method to identify, quantify and compare sub-Planck structures from directly measurable or estimated probability densities of single phase space variables. We demonstrate the efficacy of this method on experimental high order Fock states of a single-atom mechanical oscillator, showing provably finer sub-Planck structures as the Fock occupation increases despite the accompanying uncertainty increase in the phonon, position, and momentum bases.