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.

Noise spectroscopy through dynamical decoupling with a superconducting flux qubit


Quantum coherence in natural and artificial spin systems is fundamental to applications ranging from quantum information science to magnetic-resonance imaging and identification. Several multipulse control sequences targeting generalized noise models have been developed to extend coherence by dynamically decoupling a spin system from its noisy environment. In any particular implementation, however, the efficacy of these methods is sensitive to the specific frequency distribution of the noise, suggesting that these same pulse sequences could also be used to probe the noise spectrum directly. Here we demonstrate noise spectroscopy by means of dynamical decoupling using a superconducting qubit with energy-relaxation time T1=12 μs. We first demonstrate that dynamical decoupling improves the coherence time T2 in this system up to the T2=2 T1 limit (pure dephasing times exceeding 100 μs), and then leverage its filtering properties to probe the environmental noise over a frequency (f) range 0.2–20 MHz, observing a 1/fα distribution with α<1. The characterization of environmental noise has broad utility for spin-resonance applications, enabling the design of optimized coherent-control methods, promoting device and materials engineering, and generally improving coherence.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Qubit device and characterization.
Figure 2: Dynamical-decoupling pulse sequences.
Figure 3: Dephasing under the CPMG sequence.
Figure 4: Decoherence during driven dynamics.
Figure 5: Noise-power spectral density (PSD).


  1. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950).

    ADS  Article  Google Scholar 

  2. Carr, H. Y. & Purcell, E. M. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94, 630–638 (1954).

    ADS  Article  Google Scholar 

  3. Meiboom, S. & Gill, D. Modified spin-echo method for measuring nuclear relaxation times. Rev. Sci. Instrum. 29, 688–691 (1958).

    ADS  Article  Google Scholar 

  4. Slichter, C. P. Principles of Nuclear Magnetic Resonance 3rd edn (Springer, 1990).

    Book  Google Scholar 

  5. Biercuk, M. J. et al. Optimized dynamical decoupling in a model quantum memory. Nature 458, 996–1000 (2009).

    ADS  Article  Google Scholar 

  6. Biercuk, M. J. et al. Experimental Uhrig dynamical decoupling using trapped ions. Phys. Rev. A 79, 062324 (2009).

    ADS  Article  Google Scholar 

  7. Sagi, Y., Almog, I. & Davidson, N. Process tomography of dynamical decoupling in a dense cold atomic ensemble. Phys. Rev. Lett. 105, 053201 (2010).

    ADS  Article  Google Scholar 

  8. Szwer, D. J., Webster, S. C., Steane, A. M. & Lucas, D. M. Keeping a single qubit alive by experimental dynamic decoupling. J. Phys. B 44, 025501 (2011).

    ADS  Article  Google Scholar 

  9. Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature 461, 1265–1268 (2009).

    ADS  Article  Google Scholar 

  10. Barthel, C., Medford, J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Interlaced dynamical decoupling and coherent operation of a singlet–triplet qubit. Phys. Rev. Lett. 105, 266808 (2010).

    ADS  Article  Google Scholar 

  11. Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nature Phys. 7, 109–113 (2011).

    ADS  Article  Google Scholar 

  12. de Lange, G., Wang, Z. H., Riste, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010).

    ADS  Article  Google Scholar 

  13. Ryan, C. A., Hodges, J. S. & Cory, D. G. Robust decoupling techniques to extend quantum coherence in diamond. Phys. Rev. Lett. 105, 200402 (2010).

    ADS  Article  Google Scholar 

  14. Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  15. Faoro, L. & Viola, L. Dynamical suppression of 1/f noise processes in qubit systems. Phys. Rev. Lett. 92, 117905 (2004).

    ADS  Article  Google Scholar 

  16. Falci, G., D’Arrigo, A., Mastellone, A. & Paladino, E. Dynamical suppression of telegraph and 1/f noise due to quantum bistable fluctuators. Phys. Rev. A 70, 040101 (2004).

    ADS  Article  Google Scholar 

  17. Uhrig, G. S. Keeping a quantum bit alive by optimized π -pulse sequences. Phys. Rev. Lett. 98, 100504 (2007).

    ADS  Article  Google Scholar 

  18. Uhrig, G. S. Exact results on dynamical decoupling by π pulses in quantum information processes. New J. Phys. 10, 083024 (2008).

    ADS  Article  Google Scholar 

  19. Cywiński, L., Lutchyn, R. M., Nave, C. P. & Das Sarma, S. How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008).

    ADS  Article  Google Scholar 

  20. Pasini, S. & Uhrig, G. S. Optimized dynamical decoupling for power-law noise spectra. Phys. Rev. A 81, 012309 (2010).

    ADS  Article  Google Scholar 

  21. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

    ADS  Article  Google Scholar 

  22. Lasic, S., Stepisnik, J. & Mohoric, A. Displacement power spectrum measurement by CPMG in constant gradient. J. Magn. Reson. 182, 208–214 (2006).

    ADS  Article  Google Scholar 

  23. Jenista, E. R., Stokes, A. M., Branca, R. T. & Warren, W. S. Optimized, unequal pulse spacing in multiple echo sequences improves refocusing in magnetic resonance. J. Chem. Phys. 131, 204510 (2009).

    ADS  Article  Google Scholar 

  24. Orlando, T. et al. Superconducting persistent-current qubit. Phys. Rev. B 60, 15398–15413 (1999).

    ADS  Article  Google Scholar 

  25. Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).

    Article  Google Scholar 

  26. Astafiev, O., Pashkin, Y. A., Nakamura, Y., Yamamoto, T. & Tsai, J. S. Quantum noise in the Josephson charge qubit. Phys. Rev. Lett. 93, 267007 (2004).

    ADS  Article  Google Scholar 

  27. Averin, D. V. Quantum computing and quantum measurement with mesoscopic Josephson junctions. Fortschr. Phys. 48, 1055–1074 (2000).

    Article  Google Scholar 

  28. Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

    ADS  Article  Google Scholar 

  29. Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005).

    ADS  Article  Google Scholar 

  30. Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).

    ADS  MathSciNet  MATH  Google Scholar 

  31. Yoshihara, F., Harrabi, K., Niskanen, A. O., Nakamura, Y. & Tsai, J. S. Decoherence of flux qubits due to 1/f flux noise. Phys. Rev. Lett. 97, 167001 (2006).

    ADS  Article  Google Scholar 

  32. Martinis, J. M., Nam, S., Aumentado, J., Lang, K. M. & Urbina, C. Decoherence of a superconducting qubit due to bias noise. Phys. Rev. B 67, 094510 (2003).

    ADS  Article  Google Scholar 

  33. Borneman, T. W., Hurlimann, M. D. & Cory, D. G. Application of optimal control to CPMG refocusing pulse design. J. Magn. Reson. 207, 220–233 (2010).

    ADS  Article  Google Scholar 

  34. Wellstood, F. C., Urbina, C. & Clarke, J. Low-frequency noise in dc superconducting quantum interference devices below 1 K. Appl. Phys. Lett. 50, 772–774 (1987).

    ADS  Article  Google Scholar 

  35. Geva, E., Kosloff, R. & Skinner, J. L. On the relaxation of a two-level system driven by a strong electromagnetic field. J. Chem. Phys. 102, 8541–8561 (1995).

    ADS  Article  Google Scholar 

  36. Van der Wal, C. H., Wilhelm, F. K., Harmans, C. J. P. M. & Mooij, J. E. Engineering decoherence in Josephson persistent-current qubits. Eur. Phys. J. B 31, 111–123 (2003).

    ADS  Article  Google Scholar 

  37. Shnirman, A., Schön, G., Martin, I. & Makhlin, Y. Low- and high-frequency noise from coherent two-level systems. Phys. Rev. Lett. 94, 127002 (2005).

    ADS  Article  Google Scholar 

  38. Kerman, A. J. & Oliver, W. D. High-fidelity quantum operations on superconducting qubits in the presence of noise. Phys. Rev. Lett. 101, 070501 (2008).

    ADS  Article  Google Scholar 

  39. Van Harlingen, D. J. et al. Decoherence in Josephson-junction qubits due to critical-current fluctuations. Phys. Rev. B 70, 064517 (2004).

    ADS  Article  Google Scholar 

Download references


We gratefully acknowledge T. Orlando for support in all aspects of this work. We appreciate M. Biercuk, J. Clarke, L. Levitov and S. Lloyd for discussions, and P. Forn-Diaz and S. Valenzuela for comments on the manuscript. We thank P. Murphy and the LTSE team at MIT Lincoln Laboratory for technical assistance. This work was sponsored by the US Government, the Laboratory for Physical Sciences, the National Science Foundation and the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST), CREST-JST, MEXT kakenhi ‘Quantum Cybernetics’. Opinions, interpretations, conclusions and recommendations are those of the author(s) and are not necessarily endorsed by the US Government.

Author information

Authors and Affiliations



F. Yoshihara, K.H., Y.N. and J-S.T. designed and fabricated the device. J.B. and S.G. carried out the experiments. G.F., S.G. and J.B. contributed to the software infrastructure. J.B., F. Yan, W.D.O. and Y.N. analysed the data and F. Yoshihara and D.G.C. provided feedback. J.B. and W.D.O. wrote the paper with feedback from all authors. W.D.O. supervised the project. All authors contributed to discussions during the conception, execution and interpretation of the experiments.

Corresponding author

Correspondence to Jonas Bylander.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 909 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bylander, J., Gustavsson, S., Yan, F. et al. Noise spectroscopy through dynamical decoupling with a superconducting flux qubit. Nature Phys 7, 565–570 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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