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Preserving electron spin coherence in solids by optimal dynamical decoupling


To exploit the quantum coherence of electron spins in solids in future technologies such as quantum computing1,2, it is first vital to overcome the problem of spin decoherence due to their coupling to the noisy environment. Dynamical decoupling3,4,5,6,7,8,9, which uses stroboscopic spin flips to give an average coupling to the environment that is effectively zero, is a particularly promising strategy for combating decoherence because it can be naturally integrated with other desired functionalities, such as quantum gates. Errors are inevitably introduced in each spin flip, so it is desirable to minimize the number of control pulses used to realize dynamical decoupling having a given level of precision. Such optimal dynamical decoupling sequences have recently been explored9,10,11,12. The experimental realization of optimal dynamical decoupling in solid-state systems, however, remains elusive. Here we use pulsed electron paramagnetic resonance to demonstrate experimentally optimal dynamical decoupling for preserving electron spin coherence in irradiated malonic acid crystals at temperatures from 50 K to room temperature. Using a seven-pulse optimal dynamical decoupling sequence, we prolonged the spin coherence time to about 30 μs; it would otherwise be about 0.04 μs without control or 6.2 μs under one-pulse control. By comparing experiments with microscopic theories, we have identified the relevant electron spin decoherence mechanisms in the solid. Optimal dynamical decoupling may be applied to other solid-state systems, such as diamonds with nitrogen-vacancy centres13,14,15, and so lay the foundation for quantum coherence control of spins in solids at room temperature.

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Figure 1: System and methods for the dynamical decoupling experiments.
Figure 2: Electron spin decoherence under UDD and PDD control.
Figure 3: Effects of various decoherence mechanisms in malonic acid crystals.

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  1. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    Article  CAS  ADS  Google Scholar 

  2. Awschalom, D. D., Loss, D. & Samarth, N. Semiconductor Spintronics and Quantum Computation (Springer, 2002)

    Book  Google Scholar 

  3. Viola, L., Knill, E. & Lloyd, S. Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417–2421 (1999)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  4. Kern, O. & Alber, G. Controlling quantum systems by embedded dynamical decoupling schemes. Phys. Rev. Lett. 95, 250501 (2005)

    Article  CAS  ADS  Google Scholar 

  5. Khodjasteh, K. & Lidar, D. A. Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett. 95, 180501 (2005)

    Article  CAS  ADS  Google Scholar 

  6. Santos, L. F. & Viola, L. Enhanced convergence and robust performance of randomized dynamical decoupling. Phys. Rev. Lett. 97, 150501 (2006)

    Article  ADS  Google Scholar 

  7. Yao, W., Liu, R. B. & Sham, L. J. Restoring coherence lost to a slow interacting mesoscopic spin bath. Phys. Rev. Lett. 98, 077602 (2007)

    Article  ADS  Google Scholar 

  8. Witzel, W. M. & Das Sarma, S. Concatenated dynamical decoupling in a solid-state spin bath. Phys. Rev. B 76, 241303 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Lee, B., Witzel, W. M. & Das Sarma, S. Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem. Phys. Rev. Lett. 100, 160505 (2008)

    Article  CAS  ADS  Google Scholar 

  11. Yang, W. & Liu, R. B. Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation. Phys. Rev. Lett. 101, 180403 (2008)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  13. Jelezko, F. et al. Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004)

    Article  CAS  ADS  Google Scholar 

  14. Gaebel, T. et al. Room-temperature coherent coupling of single spins in diamond. Nature Phys. 2, 408–413 (2006)

    Article  CAS  ADS  Google Scholar 

  15. Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281–285 (2006)

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Schweiger, A. & Jeschke, G. Principles of Pulse Electron Paramagnetic Resonance (Oxford Univ. Press, 2001)

    Google Scholar 

  18. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  CAS  ADS  Google Scholar 

  19. Berezovsky, J., Mikkelsen, M. H., Stoltz, N. G., Coldren, L. A. & Awschalom, D. D. Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science 320, 349–352 (2008)

    Article  CAS  ADS  Google Scholar 

  20. Tyryshkin, A. M., Lyon, S. A., Astashkin, A. V. & Raitsimring, A. M. Electron spin relaxation times of phosphorus donors in silicon. Phys. Rev. B 68, 193207 (2003)

    Article  ADS  Google Scholar 

  21. Morton, J. J. L. et al. Bang-bang control of fullerene qubits using ultrafast phase gates. Nature Phys. 2, 40–43 (2006)

    Article  CAS  ADS  Google Scholar 

  22. McConnell, H. M., Heller, C., Cole, T. & Fressenden, R. W. Radiation damage in organic crystals. I. CH(COOH)2 in malonic acid. J. Am. Chem. Soc. 82, 766–775 (1960)

    Article  CAS  Google Scholar 

  23. Hodges, J. S., Yang, J. C., Remanathan, C. & Cory, D. G. Universal control of nuclear spins via anisotropic hyperfine interactions. Phys. Rev. A 78, 010303(R) (2008)

    Article  ADS  Google Scholar 

  24. Dalton, L. R., Kwiram, A. L. & Cowen, J. A. Electron spin-lattice and cross relaxation in irradiated malonic acid. Chem. Phys. Lett. 14, 77–81 (1972)

    Article  CAS  ADS  Google Scholar 

  25. Prokof’ev, N. V. & Stamp, P. C. E. Theory of the spin bath. Rep. Prog. Phys. 63, 669–726 (2000)

    Article  ADS  Google Scholar 

  26. de Sousa, R. & Das Sarma, S. Theory of nuclear-induced spectral diffusion: spin decoherence of phosphorus donors in Si and GaAs quantum dots. Phys. Rev. B 68, 115322 (2003)

    Article  ADS  Google Scholar 

  27. Witzel, W. M. & Das Sarma, S. Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: spectral diffusion of localized electron spins in the nuclear solid-state environment. Phys. Rev. B 74, 035322 (2006)

    Article  ADS  Google Scholar 

  28. Yao, W., Liu, R. B. & Sham, L. J. Theory of electron spin decoherence by interacting nuclear spins in a quantum dot. Phys. Rev. B 74, 195301 (2006)

    Article  ADS  Google Scholar 

  29. Yang, W. & Liu, R. B. Quantum many-body theory of qubit decoherence in a finite-size spin bath. Phys. Rev. B 78, 085315 (2008)

    Article  ADS  Google Scholar 

  30. McCalley, R. C. & Kwiram, A. L. ENDOR studies at 4.2 K of the radicals in malonic acid single crystals. J. Chem. Phys. 97, 2888–2903 (1993)

    Article  CAS  Google Scholar 

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J.D. thanks J. F. Chen for discussions on sample preparation. This work was supported by the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Ministry of Education of PRC, the National Fundamental Research Program 2007CB925200, and Hong Kong GRF Projects CUHK401906 and CUHK402209.

Author Contributions J.D. conceived and designed the experiment; J.D., X.R. and Y.W. performed the EPR measurements; J.D. and J.Y. prepared the samples; R.B.L. and N.Z. formulated the theory; N.Z. performed the calculations; J.D. and R.B.L. analysed the experimental and theoretical data; and R.B.L. wrote the paper. All authors discussed the results and commented on the manuscript.

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Correspondence to Jiangfeng Du or R. B. Liu.

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

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