Superpositions of Free Electron Vortices and Measurement of Matter Wave Gouy Phase

I. G. da Paz, Maria Carolina Nemes, Sebastião Pádua +2 more

Alfredo Luis, I. G. da Paz, J. G. G. de Oliveira +3 more

Justin T. Schultz, Azure Hansen, Joseph D. Murphree +2 more

Lucas S. Marinho, Pedro R. Dieguez, Carlos H. S. Vieira +1 more

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.

George Paget Thomson

I. G. da Paz

In this thesis, we study theoretical and experimental aspects of the Gouy phase in matter waves. We show that this phase is related to the covariance between position and momentum and can be indirectly extracted from interferometric experiments. Next, we analyze a diffraction experiment with macro-molecules realized by Zeilingers group [1] and we show that the existence of a Gouy phase is compatible with those experimental data. Similar to the Gouy phase for classical electromagnetic waves, it is shown that a beam of matter waves suffers a phase anomaly around the focus of a quantum lens. An experimental proposal to measure this phase is presented with experimental parameters viable to current technology. We hope this work motivates studies of the theoretical problem, open a few years ago, and forexperiments that lead us to an understanding deeper and more realistic of the Gouy phase for mixed states of matter waves and light. At the end, we present our conclusions.