Applications of maximum likelihood estimations for analyzing photon counts in few atom experiments

TL;DR

This paper introduces a maximum likelihood estimation method to accurately determine atom number distributions in few-atom experiments, overcoming challenges posed by non-Poissonian fluorescence distributions caused by light-assisted collisions.

Contribution

The paper develops a maximum likelihood approach that accounts for atom loss and overlapping fluorescence distributions, enabling precise atom counting in tight optical traps.

Findings

Accurate atom number distributions obtained with about 600 experimental runs.

Method extends to unknown initial atom number distributions with more data.

Overcomes limitations of threshold techniques in non-Poissonian regimes.

Abstract

We present a method for determining the atom number distribution of few atoms in a tight optical tweezer from their fluorescence distributions. In the tight tweezer regime, the detection light causes rapid atom loss due to light-assisted collisions. This in turn leads to non-Poissonian and overlapping fluorescence distributions for different initial atom numbers, and commonly used threshold techniques fail. We use maximum likelihood estimation algorithms to fit model distributions that account for the atom loss. This gives accurate atom number distributions for relatively few experimental runs (about 600 is sufficient) to sample a photon number distribution. We show that the method can be extended to situations when the photon number distributions for known initial atom numbers cannot be modeled, at the cost of requiring a higher number of experimental runs.