Reconstruction of the photon distribution in a micromaser

TL;DR

This paper introduces an iterative maximum-likelihood method to accurately reconstruct the photon number distribution in a micromaser cavity using atomic statistics, effective even with limited data.

Contribution

It presents a novel, efficient reconstruction technique based on atomic measurements, applicable across various micromaser regimes with high fidelity.

Findings

Method reliably reconstructs single-peaked distributions

Effective for double-peaked and trapping states

Works with limited atomic samples

Abstract

We suggest an iterative, maximum-likelihood-based, method to reconstruct the photon number distribution of the steady state cavity field of a micromaser starting from the statistics of the atoms leaving the cavity after the interaction. The scheme is based on measuring the atomic populations of probe atoms for different interaction times and works effectively using a small number of atoms and a limited sampling of the interaction times. The method has been tested by numerically simulated experiments showing that it may be reliably used in any micromaser regime leading to high-fidelity reconstructions for single-peaked distributions as well as for double-peaked ones and for trapping states.