True photo-counting statistics of multiple on-off detectors

TL;DR

This paper derives a comprehensive photo-counting formula for on-off detectors that accounts for noise and efficiency, enabling accurate comparison between measured and true photon statistics in quantum optics experiments.

Contribution

It provides the first closed-form photo-counting formula for on-off detectors that includes noise and efficiency, applicable to various detection schemes.

Findings

The formula accurately models photon counting in array and multiplexing detectors.

It allows for correct interpretation of quantum states like Fock, squeezed, and coherent states.

Application demonstrates improved analysis of quantum effects in experiments.

Abstract

We derive a closed photo-counting formula, including noise counts and a finite quantum efficiency, for photon number resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photo-counting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indispensable for the correct interpretation of quantum effects observed with such devices.