Single-atom counting in a two-color magneto-optical trap

Open Access

Single-atom counting in a two-color magneto-optical trap

Martin Schlederer, Alexandra Mozdzen, Thomas Lompe, and Henning Moritz

Phys. Rev. A 103, 033308 – Published 12 March 2021

Abstract

Recording the fluorescence of a magneto-optical trap (MOT) is a standard tool for measuring atom numbers in experiments with ultracold atoms. When trapping few atoms in a small MOT, the emitted fluorescence increases with the atom number in discrete steps, which allows one to measure the atom number with single-particle resolution. Achieving such single-particle resolution requires stringent minimization of stray light from the MOT beams, which is very difficult to achieve in experimental setups that require in-vacuum components close to the atoms. Here, we present a modified scheme that addresses this issue: Instead of collecting the fluorescence on the MOT (D2) transition, we scatter light on an additional probing (D1) transition and collect this fluorescence with a high-resolution microscope while filtering out the intense MOT light. Using this scheme, we are able to reliably distinguish up to 17 ${}^{40}K$ atoms with classification fidelities of $\sim 98 %$ for up to 5 atom numbers and fidelities of more than 85% for up to 17 atoms.

Received 19 November 2020
Accepted 5 February 2021

DOI:https://doi.org/10.1103/PhysRevA.103.033308

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atom & ion cooling Cold atoms & matter waves Cooling & trapping

Atomic, Molecular & Optical

Authors & Affiliations

Martin Schlederer ^*, Alexandra Mozdzen, Thomas Lompe, and Henning Moritz

Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, 22761 Hamburg, Germany

^*Corresponding author: mschlede@physnet.uni-hamburg.de

Article Text

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Issue

Vol. 103, Iss. 3 — March 2021

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Images

Figure 1
(a) Sketch of the experimental setup. The detection MOT is formed by three pairs of D2 trapping beams (dark red), while a pair of D1 beams (light blue) generates D1 fluorescence for detection. The D1 fluorescence light is collected by an in-vacuum microscope objective (NA = 0.75, $f = 20$ mm), separated from the D2 trapping beams using dielectric filters, and finally imaged on an sCMOS camera. (b) Simplified level scheme showing the atomic transitions utilized in the detection MOT: The D2 line is used for cooling and trapping the atoms, while the D1 repumper addresses atoms that decay into the $F = 7 / 2$ state. The D1 mF-pumper excites atoms from the ground state to the ${}^{2}P_{1 / 2}$ manifold and thereby enhances the D1 fluorescence. (c) Typical fluorescence images containing zero, one, and five atoms.
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Figure 2
(a) Timeline of the fluorescence level over $\sim 10$ 000 experiment runs, where each dot shows the result of a single experiment run. The red dots to the left of the vertical dotted line show the raw fluorescence levels without correcting for time-dependent changes in offset and scattering rate; the black dots are corrected for these effects. (b) Histogram of the corrected fluorescence levels. The red line shows a fit to the data, consisting of a sum of 20 Gaussians with independent centers $x_{N}$ , widths $σ_{N}$ , and amplitudes. We can reliably determine the atom number for systems with up to about 17 atoms. Above this number, both the limited statistics of the data set and the width of the distributions prevent a reliable classification.
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Figure 3
(a) Mean value $x_{N}$ and (b) width $σ_{N}$ of the fluorescence signal as a function of atom number, as determined from the fit to the histogram shown in Fig. 2. The mean fluorescence increases linearly with atom number (red solid line), indicating that density-dependent effects are negligible. The error bars represent the $\pm 2 σ_{N}$ confidence intervals. The widths $σ_{N}$ of the peaks in the histogram are normalized to the average fluorescence per atom and shown in (b). We assume the peak widths to be a quadratic sum of a constant background noise, photon shot noise scaling with $\sqrt{N}$ , and a linear noise contribution due to short-term variations in the intensity and detuning of the imaging light. Fitting the data with this model (red curve) shows that the noise is dominated by the linear term. The dotted line shows the point where the $\pm 2 σ_{N}$ classification regions of two neighboring peaks start to overlap, which roughly indicates the point where we can no longer reliably assign an atom number to an event.
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Figure 4
Simulated classification fidelities for systems with different atom numbers using the noise characteristics determined in Fig. 2 and an independent measurement of the MOT lifetime (see inset; assuming an exponential decay of the atom number). The classification fidelity is limited by the ratio of imaging time to lifetime: loss events during the imaging time reduce the number of collected fluorescence photons and thus can cause the fluorescence signal to fall into the classification bin of a lower atom number.
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