Gouy phase and quantum interference with cross-Wigner functions for matter-waves

Abstract

Abstract The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.