Bounds on quantum collapse models from matter-wave interferometry: calculational details

Abstract

We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse models: 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 Diósi–Penrose (DP) model. We discuss the separability of the dynamics of the collapse models along the three 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 recent matter-wave experiments: the 2012 far-field experiment of Juffmann T et al (2012 Nat. Nanotechnol. 7 297–300) and the 2013 Kapitza–Dirac–Talbot–Lau (KDTL) near-field experiment of Eibenberger et al (2013 Phys. Chem. Chem. Phys. 15 14696–700). We show the region of the parameter space for each collapse model that is excluded by these experiments. We show that matter-wave experiments provide model-insensitive bounds that are valid for a wide family of dissipative and non-Markovian generalizations.