Fig. 4: Ultra-fast high-fidelity imaging via binarization of Electron Multiplying (EM) CCD counts.

EM noise on the EM CCD camera can negatively affect the signal-to-noise ratio (a). Pixels with 0, 1, or 2 initial electrons (left top 3 panels) are amplified via EM, resulting in overlapping probability distributions that make it impossible to precisely distinguish the initial electron number (right top 3 panels). Assuming a Poisson distribution of the initial electron number (left lowest panel in orange), the EM process results in a factor of two more variance (right lowest panel in orange). However, when the photon density per pixel is less than one (the blue panels dominate) setting a binarization threshold (brown dashed line) to each camera pixel enables a near-perfect distinction between 0 and 1 initial electrons. This effectively removes the EM noise and increases the signal-to-noise ratio. An example of binarization is shown in (b), where only 15 photons are collected on the camera within 2.4 μs (3 μm accordion lattice spacing). The histograms are fitted with two skew-normal distributions and a constant offset between the peaks to account for the branching ratio in (c). The infidelity at different cutoffs is estimated based on the fit, assuming the overlapping distributions are accurate representations of the probability distribution in the tails. Binarization increases the estimated fidelity from 97.7% to 99.4% on our EM CCD camera. The maximum fidelity of more than 99.5% can be achieved with only 3 μs imaging duration as shown in (d). The fidelity is mainly limited by the atom transitioning into a dark state during imaging, which we estimate in (e) by preparing a cloud with mostly one atom per site and then performing imaging for 8.8 μs at 4 μm accordion lattice spacing. In addition to two peaks corresponding to 0 and 1 atom per site, we identify significant counts between the peaks with this long imaging duration. The simulated histograms assuming different branching ratios are laid on top of the data, showing an estimated branching ratio of slightly below 5 × 10⁻⁵.