Chaotic dephasing in a double-slit scattering experiment

TL;DR

This study explores how the classical integrability of a billiard shape influences quantum interference patterns in a double-slit scattering experiment, revealing a link between classical chaos and quantum dephasing.

Contribution

It demonstrates the impact of billiard geometry on quantum interference, highlighting the role of classical integrability in quantum dephasing phenomena.

Findings

Integrable billiards show constructive interference similar to standard double-slit experiments.

Non-integrable billiards produce asymmetric, low-visibility interference patterns.

Classical integrability correlates with quantum coherence and interference stability.

Abstract

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, pseudo-integrable, weak-mixing and strongly chaotic. In agreement with the earlier result by Casati and Prosen [1], 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, non-integrable 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, responsible for the destruction of interference.