Higher order weak values for paths in nested Mach-Zender interferometers

TL;DR

This paper explores the interpretation of weak values in nested Mach-Zender interferometers using path integrals, deriving models for sequences of weak measurements and analyzing probe shifts in different experimental setups.

Contribution

It extends path integral approaches for weak values by deriving expressions for sequential weak measurements and analyzing probe shifts in nested interferometer experiments.

Findings

Derived expressions for modeling sequences of weak measurements.

Analyzed probe shifts across different branches of the interferometer.

Provided insights into the interpretation of particle paths in weak value experiments.

Abstract

We consider weak values in the Feynman propagator framework, to gain a broader understanding of their interpretation in terms of path integrals. In particular, we examine the phenomenon of seemingly discontinuous paths that particles take in nested Mach-Zender interferometer experiments. We extend on existing path integral approaches for weak values by deriving expressions to model a sequence of weak measurements, and study the probe shifts across the different branches of a weak value interferometer. We apply this to scrutinise two scenarios of interest, one which treats photons as measurement apparatus via their spatial projection operators, and the second treating mirrors as probes.