Bounds on Collapse Models from Matter-Wave Interferometry: Calculational details

TL;DR

This paper derives interference patterns in matter-wave interferometry for various collapse models, compares predictions with experiments, and establishes bounds on model parameters, enhancing understanding of quantum collapse mechanisms.

Contribution

It provides a unified derivation of collapse model effects on matter-wave interference and compares theoretical bounds with experimental data.

Findings

Experimental data exclude certain parameter regions of collapse models.

Matter-wave experiments set model-insensitive bounds on collapse parameters.

Analytical expressions derived for both far-field and near-field regimes.

Abstract

We present a simple derivation of the interference pattern in matter-wave interferometry as predicted by a class of master equations, by using the density matrix formalism. We apply the obtained formulae to the most relevant collapse models, namely the Ghirardi-Rimini-Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL) and the Di\'{o}si-Penrose (DP) model. We discuss the separability of the collapse models dynamics along the 3 spatial directions, the validity of the paraxial approximation and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two relevant matter-wave experiments: the 2012 far-field experiment and the 2013 Kapitza Dirac Talbot Lau (KDTL) near-field experiment of Arndt's group. We show the region of the parameter space for each collapse model, which is excluded by these experiments. We show that matter-wave experiments provide model insensitive bounds, valid for a wide family of dissipative and non-markovian generalizations.