High-resolution adaptive imaging of a single atom

Journal name:
Nature Photonics
Year published:
Published online


Optical imaging systems are used extensively in the life and physical sciences because of their ability to non-invasively capture details on the microscopic and nanoscopic scales. Such systems are often limited by source or detector noise, image distortions and human operator misjudgement. Here, we report a general, quantitative method to analyse and correct these errors. We use this method to identify and correct optical aberrations in an imaging system for single atoms and realize an atomic position sensitivity of ∼0.5 nm Hz−1/2 with a minimum uncertainty of 1.7 nm, allowing the direct imaging of atomic motion. This is the highest position sensitivity ever measured for an isolated atom and opens up the possibility of performing out-of-focus three-dimensional particle tracking, imaging of atoms in three-dimensional optical lattices or sensing forces at the yoctonewton (10−24 N) scale.

At a glance


  1. Schematic of the imaging system.
    Figure 1: Schematic of the imaging system.

    a, Atomic energy diagram for 174Yb+. The atom is excited with laser radiation at 369.5 nm, driving the 2S1/22P1/2 cycling transition, and the resulting fluorescence is collected by the imaging system. b, Transverse cut of the optical set-up depicting the source, vacuum window, 0.6 NA objective lens, pinhole, short-focal-length lens, cylindrical lens and camera. c, Image of two atomic ions separated by 5 μm.

  2. Aberration retrieval
    Figure 2: Aberration retrieval results.

    ac, Single-shot images of the misaligned system. df, The optimally aligned system at various distances from the focal plane, with the best focus shown in f. In d,e, a high contribution from the defocus term is evident, with low contributions of astigmatism and coma (right). Large contributions of coma and astigmatism (ac) are corrected with a five-axis stage and cylindrical lens (Supplementary Section I). The goodness of fit obtained for these examples approaches unity at coefficients of determination of 0.989, 0.965, 0.958, 0.957, 0.983 and 0.994 for images af, respectively. These images are integrated for ∼0.5 s. Further analysis of the coefficients error bars is provided in Supplementary Section II.

  3. Measured position uncertainty δx of the trapped ion centroid position versus image integration time τ.
    Figure 3: Measured position uncertainty δx of the trapped ion centroid position versus image integration time τ.

    The blue line shows the expected uncertainty limited by photon counting shot noise in the imaging system. A sensitivity of ∼0.5 nm Hz−1/2 is measured for τ <0.1 s, which is approximately three times higher than the shot noise, presumably from camera noise. The ultimate position sensitivity is found to be 1.7(3) nm at τ =0.2 s. These measurements include small corrections for dead time bias, as described in the Methods. Error bars on each point indicate root-mean-square error.

  4. Micromotion position measurement.
    Figure 4: Micromotion position measurement.

    a, The ion's velocity v (solid black arrows) is colinear with the direction k of the detection light, taken to be the x axis. Fluorescence is modulated from the micromotion of the ion along x by the first-order Doppler effect as well as the obscuration by a mask with variable position a along the x axis. b, Contributions of the velocity (left y axis) and position (right y axis) of a single atom when a mask is scanned along one transversal direction x. The solid and dashed lines depict fits to the data for the velocity and position components, respectively, of equation (5), given respectively by the cosine and sine terms alone. All values are normalized with the signal amplitude at a =–∞. Horizontal error bars represent the uncertainty of the scanning stage (0.01 mm) and vertical errors are computed from the uncertainty propagation using equation (5).


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  1. Joint Quantum Institute, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA

    • J. D. Wong-Campos,
    • K. G. Johnson,
    • B. Neyenhuis,
    • J. Mizrahi &
    • C. Monroe


All authors contributed to the design, construction and carrying out of the experiment, discussed the results and commented on the manuscript. J.D.W.-C. and K.G.J. analysed the data and performed the simulations. J.D.W.-C., K.G.J. and C.M. wrote the manuscript. B.N. and J.M. contributed equally to both the design and construction of the experiment.

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