Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles

We show that three-body loss of trapped atoms leads to sub-Poissonian atom-number fluctuations. We prepare hundreds of dense ultracold ensembles in an array of magnetic microtraps which undergo rapid three-body decay. The shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian, for ensembles comprising 50–300 atoms. The measured relative variance or Fano factor $F=0.53\pm 0.22$ agrees very well with the prediction by an analytic theory ($F=3/5$) and numerical calculations. These results will facilitate studies of quantum information science with mesoscopic ensembles.

Figure 1

(a) Subsection of an optical density (OD) image for $t=25\mathrm{ms}$ for a single realization of the experiment. (b) Decay of the mean atom number in a selected site [highlighted in (a)]. A fit to Eq. (2) is shown (solid line) together with the corresponding one-body loss (dashed line). The shaded region indicates the range of atom numbers in our data for all traps. The residuals from the fit and standard errors on the measurement of $⟨N⟩$ are shown below, demonstrating agreement at the level of $\pm 3$ atoms.

Figure 2

Atom-number fluctuations measured for each of 245 lattice sites during three-body decay. (a),(b) Number distributions for one specific trap ($m=138$) at two hold times. Histograms correspond to 19 measurements and each bin is 5 atoms wide. The lines indicate Gaussian fits to the data (solid line), Poisson distributions (dashed line), and combined Poisson and detection noise contributions (dash-dotted line). (c) The relative variance versus $⟨N_m⟩$ for each lattice site and for each hold time (points). Open circles indicate the measurements for the selected trap, with a fit (including detection noise) for a constant Fano factor $F=0.57$ (solid line). Arrows highlight the two data points corresponding to the histograms (a),(b).

Figure 3

Lattice-averaged Fano factor $\overline{F}$ as a function of the mean number of atoms $⟨\overline{N}⟩$. Horizontal lines correspond to $F=1$ (dashed line) and to $F=3/5$ (dotted line) for strong three-body loss. The solid line is a model including three-body and one-body loss terms. The shaded region indicates systematic uncertainties described in the text. The inset shows an example fluctuation correlation function $⟨\chi (\mathit{\delta })⟩$ for $t=25\mathrm{ms}$.