Knowing "where the photons have been"

TL;DR

This paper offers a clear, intuitive explanation of a complex quantum optics experiment, demonstrating that the observed results align with classical physics and proposing a more reliable method to determine photon paths.

Contribution

It introduces a simple one-state vector formalism for interpreting nested Mach-Zehnder interferometer experiments and proposes a more reliable which-path witness.

Findings

The formalism agrees with classical physics models.

The new which-path witness provides consistent results.

The experiment's seemingly counter-intuitive results are explained logically.

Abstract

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness producing seemingly contra-intuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well expected outcomes of the experiment.