Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology

TL;DR

This paper develops tools to analyze multimode N-photon states from nonlinear waveguide decays, deriving a simple expression for quantum Fisher information in optical interferometry, enhancing quantum metrology techniques.

Contribution

It introduces general methods for characterizing multimode photon states and provides a simplified formula for quantum Fisher information applicable to multi-mode quantum metrology.

Findings

Derived a simple expression for Quantum Fisher Information in multi-mode interferometry.

Showed that number-resolved photon measurements can saturate the quantum Fisher information bound.

Provided efficient computational tools for multimode N-photon states in waveguides.

Abstract

We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.