Probing fluctuations in a lattice of mesoscopic atomic ensembles

We experimentally probe intrinsic atom number fluctuations in trapped ensembles of ultracold atoms on a magnetic lattice atom chip. Advanced post-processing and optimal analysis techniques allow the detection of intrinsic fluctuations in the number of atoms in small atomic ensembles with absorption imaging. A fringe removal algorithm reduces imaging noise to the fundamental photon shot noise limit and proves beneficial even in the absence of fringes. Maximum-likelihood estimation is used to optimally detect the number of atoms in a single realisation of the experiment. Combined, these techniques offer a factor 3 improvement in signal to noise, to a minimum resolvable population difference of 17 atoms/shot in a double well experiment. In a lattice of tightly confining magnetic traps, atoms undergo density dependent three-body loss. This loss process naturally reduces the shot-to-shot atom number fluctuations to below the Poisson level. We directly observe sub-Poissonian atom number fluctuations in our lattice, and find a Fano factor of F = 0.53±0.22 for ensembles comprising between 50 and 300 atoms each, in very good agreement with an analytic theory, which predicts F = 3/5. Our results provide the basis for improved readout of atom interferometers and for the study of quantum information science with mesoscopic ensembles.