Chaotic dephasing in a double-slit scattering experiment.

We design a computational experiment in which a quantum particle tunnels into a billiard of variable shape and scatters out of it through a double-slit opening on the billiard's base. The interference patterns produced by the scattered probability currents for a range of energies are investigated in relation to the billiard's geometry which is connected to its classical integrability. Four billiards with hierarchical integrability levels are considered: integrable, pseudointegrable, weak-mixing, and strongly chaotic. In agreement with the earlier result by Casati and Prosen [Phys. Rev. A 72, 032111 (2005)], we find the billiard's integrability to have a crucial influence on the properties of the interference patterns. In the integrable case, most experiment outcomes are found to be consistent with the constructive interference occurring in the usual double-slit experiment. In contrast to this, nonintegrable billiards typically display asymmetric interference patterns of smaller visibility characterized by weakly correlated wave function values at the two slits. Our findings indicate an intrinsic connection between the classical integrability and the quantum dephasing, which is responsible for the destruction of interference.