A novel mechanism for probing the Planck scale with wavepackets following general distributions

TL;DR

This paper extends previous work on GUP-induced effects on wavepacket doubling times to arbitrary distributions, using a duality between quantum and statistical mechanics, and identifies optimal wavepacket shapes for probing Planck-scale physics.

Contribution

It generalizes the analysis of GUP effects to any wavepacket shape via a duality formalism, enabling broader experimental testing of minimal length signatures.

Findings

Generalized the formalism to arbitrary wavepacket distributions.

Identified a specific organic wavepacket shape as optimal for GUP detection.

Can probe minimal length scales down to hundreds of times the Planck length.

Abstract

It was also shown recently that GUP predicts potentially measurable corrections to the `doubling time' of freely moving Gaussian atomic and molecular wavepackets with a favorable combination of three parameters, {\it e.g.} mass, initial width and mean velocity of a travelling wavepacket. However, it is well known that such wavepackets can come with various shapes which correspond to variety of distributions. In this article, we generalize our earlier work for an {\it arbitrary distribution} and thereby accommodate any shape of the wavepacket. Mathematically, we build this formalism by exploiting a duality between quantum and statistical mechanics, by which (quantum mechanical) expectation values of the momentum operator can be expressed in terms of the derivatives of the characteristic functions of the dual statistical description. Equipped with this result, we go one step further and numerically study a few physical distributions. We find that large organic (TPPF152) wavepacket following the generalized normal distribution with parameter $\kappa=0.5$ offers one of the best-case scenarios, effectively scanning the whole GUP parameter space with current technologies. Although we do not say that the minimal length has to be near or at the Planck value, we mange improving our previous studies to scan the minimal length signatures down to hundred times the Planck value.