Complementarity and uncertainty relations for matter wave interferometry

TL;DR

This paper establishes a rigorous quantitative link between interferometric duality and Heisenberg's uncertainty, applying it to atom interferometry and resolving longstanding interpretational challenges.

Contribution

It introduces a formal connection between duality relations and uncertainty principles, advancing understanding of matter wave interferometry.

Findings

Quantitative relation between duality and uncertainty established

Application to atom interferometry with photon-based which-way detection

Resolution of the perfect lens challenge to complementarity

Abstract

We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which way information, and unambiguously resolve the challenge posed by the metamaterial `perfect lens' to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.