Dispersion and fidelity in quantum interferometry

TL;DR

This paper analyzes how dispersion affects phase measurement sensitivity in quantum interferometers using various nonclassical light states, providing quantitative comparisons of their effectiveness.

Contribution

It introduces a detailed analysis of dispersion effects on different quantum states in interferometry and offers a simplified analytical model for parametric downconversion.

Findings

Dispersion reduces phase measurement sensitivity for certain quantum states.

N00N states show higher sensitivity but are more affected by dispersion.

The simplified downconversion model allows explicit probability calculations.

Abstract

We consider Mach-Zehnder and Hong-Ou-Mandel interferometers with nonclassical states of light as input, and study the effect that dispersion inside the interferometer has on the sensitivity of phase measurements. We study in detail a number of different one- and two-photon input states, including Fock, dual Fock, N00N states, and photon pairs from parametric downconversion. Assuming there is a phase shift $\phi_0$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of $\phi_0$, and then compute the Shannon mutual information between $\phi_0$ and the measurements. This provides a means of quantitatively comparing the utility of various input states for determining the phase in the presence of dispersion. In addition, we consider a simplified model of parametric downconversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic downconversion model.