Classical billiards and double-slit quantum interference

Abstract

We carry out a numerical simulation about the occurrence of interference fringes in experiments where an initial Gaussian wave packet evolves inside a billiard domain with two slits on the boundary. Our simulation extends a previous work by Casati and Prosen and it is aimed to test their surprising conclusion that the fringes disappear in the experiments with fully chaotic billiards. According to the results found, we are led to reassess this remarkable effect of classical dynamics on quantum interference. Actually, we highlight another factor which acts on interference: a symmetry condition (SC) concerning the experimental set-up. This condition seems even to play a role more important than classical chaos. Indeed, when the SC is verified, classical chaos has no effect, whereas when the SC is violated classical chaos turns out to be an additional factor that causes dephasing at the slits. We explain the respective roles of these two factors, by specifying the physical mechanism through which they influence the interference patterns. This mechanism depends both on the position and direction of the initial wave packet and on certain its recurrences which occur especially in the regular billiards.