Chaos, Coherence and the Double-Slit Experiment

TL;DR

This paper explores how classical dynamics influence quantum interference patterns in coherence experiments, showing that chaos suppresses fringes in probability currents but not in conductance, and analyzing dephasing effects in ballistic systems.

Contribution

It demonstrates the impact of classical chaos on interference fringes and conductance in Aharonov-Bohm setups, extending dephasing analysis to multi-channel ballistic systems.

Findings

Interference fringes disappear in chaotic systems with small openings.

Flux-sensitive conductance component remains and becomes universal in chaotic cavities.

Dephasing causes exponential damping of conductance oscillations with traversal and dephasing times.

Abstract

We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected ballistic cavity, both in an Aharonov-Bohm geometry with forward scattering only. We show how interference fringes in the probability current generically disappear in the case of a chaotic system with small openings, and how they may persist in the case of an integrable cavity. Simultaneously, the typical, sample dependent amplitude of the flux-sensitive part $g(\phi)$ of the conductance survives in all cases, and becomes universal in the case of a chaotic cavity. In presence of dephasing by fluctuations of the electric potential in one arm of the Aharonov-Bohm loop, we find an exponential damping of the flux-dependent part of the conductance, $g(\phi) \propto \exp[-\tau_{\rm L}/\tau_\phi]$, in term of the traversal time $\tau_{\rm L}$ through the arm and the dephasing time $\tau_\phi$. This extends previous works on dephasing in ballistic systems to the case of many conducting channels.