Free evolution of a mixture of quantum states with classical space and momentum uncertainties

Abstract

This article continues and completes a recent one regarding a quantum version of van Cittert–Zernike's theorem (Fabre et al 2018 Eur. J. Phys. 39 015401). In that paper, we considered a mixture of quantum states that only differed in their initial positions, but not on their momenta. Here, we relax this nonphysical assumption and analyse how the inclusion of both classical uncertainties in the initial position and momentum of a mixture of—otherwise identical—free quantum states which do not interact with an environment, affects its quantum coherence length. We show that the mathematical development and the final result are simple enough to make possible the incorporation of this subject into a basic course of quantum physics. Furthermore, we demonstrate that these results provide a comprehensive solution to a recent controversy in atomic collision physics.