Two sites coherence and visibility

TL;DR

This paper investigates quantum coherence and visibility in a two-site electron system, analyzing how wave-particle duality manifests through oscillatory behavior and decoherence effects.

Contribution

It provides a detailed calculation of coherence and visibility dynamics for electrons on two sites, highlighting their oscillatory and complementary nature.

Findings

Visibility and predictability oscillate over time.

Neither measure depends on single particle energy.

Decoherence reduces visibility, emphasizing wave-particle duality.

Abstract

Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.