Dependence of fluorescence-level statistics on bin-time size in a few-atom magneto-optical trap

We have analyzed the statistical distribution of the fluorescence signal levels in a magneto-optical trap containing a few atoms and observed that it strongly depends on the relative size of the bin time with respect to the trap decay time. We derived analytic expressions for the signal distributions in two limiting cases, long and short bin time limits, and found good agreement with numerical simulations performed regardless of the size of the bin time. We found an optimal size of the bin time for minimizing the probability of indeterminate atom numbers while providing accurate information on the instantaneous number of atoms in the trap. These theoretical results are compared with actual experimental data. We observed super-Poisson counting statistics for the fluorescence from trapped atoms, which might be attributed to uncorrelated motion of trapped atoms in the inhomogeneous magnetic field in the trap.