High-resolution adaptive imaging of a single atom

Journal name:
Nature Photonics
Volume:
10,
Pages:
606–610
Year published:
DOI:
doi:10.1038/nphoton.2016.136
Received
Accepted
Published online

Abstract

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

Figures

  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
    results.
    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).

References

  1. Moerner, W. Nobel lecture. Single-molecule spectroscopy, imaging, and photocontrol: foundations for super-resolution microscopy. Rev. Mod. Phys. 87, 11831212 (2015).
  2. Betzig, E. Nobel lecture. Single molecules, cells, and super-resolution optics. Rev. Mod. Phys. 87, 11531168 (2015).
  3. Eva, R. et al. STED microscopy reveals crystal colour centres. Nature Photon. 3, 144147 (2009).
  4. Betzig, E. et al. Imaging intracellular fluorescent proteins at nanometer resolution. Science 313, 16421645 (2006).
  5. Bakr, W., Gillen, J., Peng, A., Fölling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 7477 (2009).
  6. Blatt, R. & Wineland, D. Entangled states of trapped atomic ions. Nature 453, 10081015 (2008).
  7. Hell, S. Nobel lecture. Nanoscopy with freely propagating light. Rev. Mod. Phys. 87, 11691182 (2015).
  8. Monroe, C. et al. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014).
  9. Eschner, J., Raab, Ch., Schmidt-Kaler, F. & Blatt, R. Light interference from single atoms and their mirror images. Nature 413, 495498 (2001).
  10. Biercuk, M., Uys, H., Britton, J., VanDevender, A. & Bollinger, J. Ultrasensitive detection of force and displacement using trapped ions. Nature Nanotech. 5, 646650 (2010).
  11. Schlosser, N., Reymond, G., Protsenko, I. & Grangier, P. Sub-Poissonian loading of single atoms in a microscopic dipole trap. Nature 411, 10241027 (2001).
  12. Karpa, L., Bylinskii, A., Gangloff, D., Cetina, M. & Vuletić, V. Suppression of ion transport due to long-lived subwavelength localization by an optical lattice. Phys. Rev. Lett. 111, 163002 (2013).
  13. Schmiegelow, C. et al. Phase-stable free-space optical lattices for trapped ions. Phys. Rev. Lett. 116, 033002 (2016).
  14. Alberti, A. et al. Super-resolution microscopy of single atoms in optical lattices. New J. Phys. 18, 053010 (2016).
  15. Noek, R. et al. High speed, high fidelity detection of an atomic hyperfine qubit. Opt. Lett. 38, 47354738 (2013).
  16. Burrell, A., Szwer, D., Webster, S. & Lucas, D. Scalable simultaneous multiqubit readout with 99.99% single-shot fidelity. Phys. Rev. A 81, 040302 (2010).
  17. Streed, E., Norton, B., Jechow, A., Weinhold, T. & Kielpinski, D. Imaging of trapped ions with a microfabricated optic for quantum information processing. Phys. Rev. Lett. 106, 010502 (2011).
  18. Shu, G., Chou, C., Kurz, N., Dietrich, M. & Blinov, B. Efficient fluorescence collection and ion imaging with the ‘tack’ ion trap. J. Opt. Soc. Am. B 28, 28652870 (2011).
  19. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281324 (2003).
  20. Goodman, J. Introduction to Fourier Optics (McGraw-Hill, 1996).
  21. Iglesias, I. Parametric wave-aberration retrieval from point-spread function data by use of a pyramidal recursive algorithm. Appl. Opt. 37, 54275430 (1998).
  22. Barakat, R. & Sandler, B. Determination of the wave-front aberration function from measured values of the point-spread function: a two-dimensional phase retrieval problem. J. Opt. Soc. Am. A 9, 17151723 (1992).
  23. Avoort, C., Braat, J., Dirksen, P. & Janssen, A. Aberration retrieval from the intensity point-spread function in the focal region using the extended Nijboer–Zernike approach. J. Mod. Opt. 52, 16951728 (2005).
  24. Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, 2006).
  25. Speidel, M., Jonáš, A. & Florin, E. Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging. Opt. Lett. 28, 6971 (2003).
  26. Nelson, K., Li, X. & Weiss, D. Imaging single atoms in a three-dimensional array. Nature Phys. 3, 556560 (2007).
  27. Riley, W. Handbook of Frequency Stability Analysis Special Publication 1065 (NIST, 2008).
  28. Barnes, J. & Allan, D. Variances Based on Data with Dead Time Between the Measurements Technical Note 1318 (NIST, 1990).
  29. Thompson, R., Larson, D. & Webb, W. Precise nanometer localization analysis for individual fluorescent probes. Biophys. J. 82, 27752783 (2002).
  30. Quan, T., Zeng, S. & Huang, Z. Localization capability and limitation of electron-multiplying charge-coupled, scientific complementary metal-oxide semiconductor, and charge-coupled devices for superresolution imaging. J. Biomed. Opt. 15, 066005 (2010).
  31. Major, F. & Dehmelt, H. Exchange-collision technique for rf spectroscopy of stored ions. Phys. Rev. 170, 91107 (1968).
  32. Berkeland, D., Miller, J., Bergquist, J., Itano, W. & Wineland, D. Minimization of ion micromotion in a Paul trap. J. Appl. Phys. 83, 50255033 (1998).
  33. Keller, J., Partner, H., Burgermeister, T. & Mehlstäubler, T. Precise determination of micromotion for trapped-ion optical clocks. J. Appl. Phys. 118, 104501 (2015).
  34. Anderson, D. Alignment of resonant optical cavities. Appl. Opt. 23, 29442949 (1984).
  35. Wyant, J. & Creath, K. Applied Optics and Optical Engineering Vol. XI (Academic, 1992).

Download references

Author information

Affiliations

  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

Contributions

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.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary information (440 KB)

    Supplementary information

Additional data