Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Stern–Gerlach detection of neutral-atom qubits in a state-dependent optical lattice


Qubit state measurements are an essential part of any quantum computer, constituting the readout. Accurate measurements are also an integral component of one-way quantum computation and of error correction, which is needed for fault-tolerant quantum computation1. Here, we present a state measurement for neutral-atom qubits based on coherent spatial splitting of the atoms’ wavefunctions. It is reminiscent of the Stern–Gerlach experiment2, but carried out in light traps. For around 160 qubits in a three-dimensional array, we achieve a measurement fidelity of 0.9994, which is roughly 20 times lower error than in previous measurements of neutral-atom arrays3,4. It also greatly exceeds the measurement fidelity of other arrays with more than four qubits, including those with ion and superconducting qubits5,6. Our measurement fidelity is essentially independent of the number of qubits measured, and since the measurement causes no loss, we can reuse the atoms. We also demonstrate that we can replace atoms lost to background gas collisions during the experiment7.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Overview of lossless state detection.
Fig. 2: Displacement distributions and state assignment.
Fig. 3: Demonstration of re-initialization of a 3D qubit array.
Fig. 4: State-selective detection from the clock states.

Similar content being viewed by others

Data availability

The data that support the plots in this paper are available from the corresponding author upon reasonable request.


  1. Bruss, D. & Leuchs, G. Lectures on Quantum Information (Wiley, 2007).

  2. Gerlach, W. & Stern, O. Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Z. Phys. 9, 349–352 (1922).

    Article  ADS  Google Scholar 

  3. Kwon, M., Ebert, M. F., Walker, T. G. & Saffman, M. Parallel low-loss measurement of multiple atomic qubits. Phys. Rev. Lett. 119, 180504 (2017).

    Article  ADS  Google Scholar 

  4. Martinez-Dorantes, M. et al. Fast nondestructive parallel readout of neutral atom registers in optical potentials. Phys. Rev. Lett. 119, 180503 (2017).

    Article  ADS  Google Scholar 

  5. Debnath, S. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016).

    Article  ADS  Google Scholar 

  6. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014).

    Article  ADS  Google Scholar 

  7. Kumar, A., Wu, T.-Y., Giraldo Mejia, F. & Weiss, D. S. Sorting ultracold atoms in a 3D optical lattice in a realization of Maxwell’s demon. Nature 561, 83–87 (2018).

    Article  ADS  Google Scholar 

  8. Weiss, D. & Saffman, M. Quantum computing with neutral atoms. Phys. Today 70, 45–50 (2017).

    Article  Google Scholar 

  9. Nelson, K. D., Li, X. & Weiss, D. S. Imaging single atoms in a three-dimensional array. Nat. Phys. 3, 556–560 (2007).

    Article  Google Scholar 

  10. Gibbons, M. J., Hamley, C. D., Shih, C. Y. & Chapman, M. S. Nondestructive fluorescent state detection of single neutral atom qubits. Phys. Rev. Lett. 106, 133002 (2011).

    Article  ADS  Google Scholar 

  11. Fuhrmanek, A., Bourgain, R., Sortais, Y. R. P. & Browaeys, A. Free-space lossless state detection of a single trapped atom. Phys. Rev. Lett. 106, 133003 (2011).

    Article  ADS  Google Scholar 

  12. Covey, J. P., Madjarov, I. S., Cooper, A. & Endres, M. 2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays. Preprint at (2018).

  13. Bochmann, J. et al. Lossless state detection of single neutral atoms. Phys. Rev. Lett. 104, 203601 (2010).

    Article  ADS  Google Scholar 

  14. Gehr, R. et al. Cavity-based single atom preparation and high-fidelity hyperfine state readout. Phys. Rev. Lett. 104, 203602 (2010).

    Article  ADS  Google Scholar 

  15. Boll, M. et al. Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains. Science 353, 1257–1260 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  16. Deutsch, I. H. & Jessen, P. S. Quantum-state control in optical lattices. Phys. Rev. A 57, 1972–1986 (1998).

    Article  ADS  Google Scholar 

  17. Robens, C. et al. Low-entropy states of neutral atoms in polarization-synthesized optical lattices. Phys. Rev. Lett. 118, 065302 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  18. Li, X., Corcovilos, T. A., Wang, Y. & Weiss, D. S. 3D projection sideband cooling. Phys. Rev. Lett. 108, 103001 (2012).

    Article  ADS  Google Scholar 

  19. Wang, Y., Zhang, X. L., Corcovilos, T. A., Kumar, A. & Weiss, D. S. Coherent addressing of individual neutral atoms in a 3D optical lattice. Phys. Rev. Lett. 115, 043003 (2015).

    Article  ADS  Google Scholar 

  20. Wang, Y., Kumar, A., Wu, T. Y. & Weiss, D. S. Single-qubit gates based on targeted phase shifts in a 3D neutral atom array. Science 352, 1562–1565 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  21. Barredo, D., Lienhard, V., De Leseleuc, S., Lahaye, T. & Browaeys, A. Synthetic three-dimensional atomic structures assembled atom by atom. Nature 561, 79–82 (2018).

    Article  ADS  Google Scholar 

  22. Endres, M. et al. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science 354, 1024–1027 (2016).

    Article  ADS  Google Scholar 

  23. Kim, H. et al. In situ single-atom array synthesis using dynamic holographic optical tweezers. Nat. Commun. 7, 13317 (2016).

    Article  ADS  Google Scholar 

  24. Lester, B. J., Luick, N., Kaufman, A. M., Reynolds, C. M. & Regal, C. A. Rapid production of uniformly filled arrays of neutral atoms. Phys. Rev. Lett. 115, 073003 (2015).

    Article  ADS  Google Scholar 

  25. Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011).

    Article  ADS  Google Scholar 

  26. Linke, N. M. et al. Fault-tolerant quantum error detection. Sci. Adv. 3, e1701074 (2017).

    Article  ADS  Google Scholar 

  27. Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519, 66–69 (2015).

    Article  ADS  Google Scholar 

  28. Yamamoto, R. et al. Site-resolved imaging of single atoms with a Faraday quantum gas microscope. Phys. Rev. A 96, 033610 (2017).

    Article  ADS  Google Scholar 

  29. Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).

    Article  ADS  Google Scholar 

  30. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article  ADS  Google Scholar 

  31. Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007).

    Article  ADS  Google Scholar 

Download references


This work was supported by US National Science Foundation grant numbers PHY-1520976 and PHY-1820849.

Author information

Authors and Affiliations



All authors contributed to the design, execution and analysis of the experiment and the writing of the manuscript. A.K., T.-Y.W. and F.G. collected all the data.

Corresponding author

Correspondence to David S. Weiss.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Text and Supplementary Figures 1–3.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, TY., Kumar, A., Giraldo, F. et al. Stern–Gerlach detection of neutral-atom qubits in a state-dependent optical lattice. Nat. Phys. 15, 538–542 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing