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Controlling spin relaxation with a cavity

Nature volume 531, pages 74–77 (2016)Cite this article

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Abstract

Spontaneous emission of radiation is one of the fundamental mechanisms by which an excited quantum system returns to equilibrium. For spins, however, spontaneous emission is generally negligible compared to other non-radiative relaxation processes because of the weak coupling between the magnetic dipole and the electromagnetic field. In 1946, Purcell realized1 that the rate of spontaneous emission can be greatly enhanced by placing the quantum system in a resonant cavity. This effect has since been used extensively to control the lifetime of atoms and semiconducting heterostructures coupled to microwave2 or optical3,4 cavities, and is essential for the realization of high-efficiency single-photon sources5. Here we report the application of this idea to spins in solids. By coupling donor spins in silicon to a superconducting microwave cavity with a high quality factor and a small mode volume, we reach the regime in which spontaneous emission constitutes the dominant mechanism of spin relaxation. The relaxation rate is increased by three orders of magnitude as the spins are tuned to the cavity resonance, demonstrating that energy relaxation can be controlled on demand. Our results provide a general way to initialize spin systems into their ground state and therefore have applications in magnetic resonance and quantum information processing6. They also demonstrate that the coupling between the magnetic dipole of a spin and the electromagnetic field can be enhanced up to the point at which quantum fluctuations have a marked effect on the spin dynamics; as such, they represent an important step towards the coherent magnetic coupling of individual spins to microwave photons.

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Figure 1: Purcell-enhanced spin relaxation and experimental set-up.
Figure 2: ESR spectroscopy and Purcell-limited T1 measurement.
Figure 3: Controlling Purcell relaxation by spin–cavity detuning.
Figure 4: Dependence of Purcell relaxation on spin–cavity coupling g.

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References

  1. Purcell, E. M. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946)

    Article  Google Scholar 

  2. Goy, P., Raimond, J. M., Gross, M. & Haroche, S. Observation of cavity-enhanced single-atom spontaneous emission. Phys. Rev. Lett. 50, 1903–1906 (1983)

    Article  ADS  CAS  Google Scholar 

  3. Heinzen, D. J., Childs, J. J., Thomas, J. E. & Feld, M. S. Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator. Phys. Rev. Lett. 58, 1320–1323 (1987)

    Article  ADS  CAS  Google Scholar 

  4. Yamamoto, Y., Machida, S., Horikoshi, Y., Igeta, K. & Bjork, G. Enhanced and inhibited spontaneous emission of free excitons in GaAs quantum wells in a microcavity. Opt. Commun. 80, 337–342 (1991)

    Article  ADS  CAS  Google Scholar 

  5. Gérard, J. M. et al. Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity. Phys. Rev. Lett. 81, 1110–1113 (1998)

    Article  ADS  Google Scholar 

  6. Butler, M. C. & Weitekamp, D. P. Polarization of nuclear spins by a cold nanoscale resonator. Phys. Rev. A 84, 063407 (2011)

    Article  ADS  Google Scholar 

  7. Sinova, J. & Žutić, I. New moves of the spintronics tango. Nature Mater. 11, 368–371 (2012)

    Article  ADS  CAS  Google Scholar 

  8. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010)

    Article  ADS  CAS  Google Scholar 

  9. Levitt, M. H. Spin Dynamics: Basics of Nuclear Magnetic Resonance (John Wiley & Sons, 2001)

  10. Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011)

    Article  ADS  CAS  Google Scholar 

  11. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012)

    Article  ADS  CAS  Google Scholar 

  12. Shapiro, M. G. et al. Directed evolution of a magnetic resonance imaging contrast agent for noninvasive imaging of dopamine. Nature Biotechnol. 28, 264–270 (2010)

    Article  CAS  Google Scholar 

  13. Wood, C. J., Borneman, T. W. & Cory, D. G. Cavity cooling of an ensemble spin system. Phys. Rev. Lett. 112, 050501 (2014)

    Article  ADS  Google Scholar 

  14. Sleator, T., Hahn, E. L., Hilbert, C. & Clarke, J. Nuclear-spin noise. Phys. Rev. Lett. 55, 1742–1745 (1985)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Zhou, X. et al. High-gain weakly nonlinear flux-modulated Josephson parametric amplifier using a SQUID array. Phys. Rev. B 89, 214517 (2014)

    Article  ADS  Google Scholar 

  17. Bienfait, A. et al. Reaching the quantum limit of sensitivity in electron spin resonance. Nature Nanotechnol. http://dx.doi.org/10.1038/nnano.2015.282 (2015)

  18. Feher, G. Electron spin resonance experiments on donors in silicon. I. Electronic structure of donors by the electron nuclear double resonance technique. Phys. Rev. 114, 1219–1244 (1959)

    Article  ADS  CAS  Google Scholar 

  19. Wolfowicz, G. et al. Decoherence mechanisms of 209 Bi donor electron spins in isotopically pure 28Si. Phys. Rev. B 86, 245301 (2012)

    Article  ADS  Google Scholar 

  20. Morley, G. W. et al. The initialization and manipulation of quantum information stored in silicon by bismuth dopants. Nature Mater. 9, 725–729 (2010)

    Article  ADS  CAS  Google Scholar 

  21. George, R. E. et al. Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si. Phys. Rev. Lett. 105, 067601 (2010)

    Article  ADS  Google Scholar 

  22. Schweiger, A. & Jeschke, G. Principles of Pulse Electron Paramagnetic Resonance 225 (Oxford Univ. Press, 2001)

  23. Feher, G. & Gere, E. A. Electron spin resonance experiments on donors in silicon. II. Electron spin relaxation effects. Phys. Rev. 114, 1245–1256 (1959)

    Article  ADS  CAS  Google Scholar 

  24. Bloembergen, N. & Pound, R. V. Radiation damping in magnetic resonance experiments. Phys. Rev. 95, 8–12 (1954)

    Article  ADS  Google Scholar 

  25. Wood, C. J. & Cory, D. G. Cavity cooling to the ground state of an ensemble quantum system. Preprint at http://arXiv.org/abs/1506.03007 (2015)

  26. Feher, G., Gordon, J. P., Buehler, E., Gere, E. A. & Thurmond, C. D. Spontaneous emission of radiation from an electron spin system. Phys. Rev. 109, 221–222 (1958)

    Article  ADS  CAS  Google Scholar 

  27. Temnov, V. V. & Woggon, U. Superradiance and subradiance in an inhomogeneously broadened ensemble of two-level systems coupled to a low-Q cavity. Phys. Rev. Lett. 95, 243602 (2005)

    Article  ADS  Google Scholar 

  28. Carver, T. R. & Slichter, C. P. Polarization of nuclear spins in metals. Phys. Rev. 92, 212–213 (1953)

    Article  ADS  CAS  Google Scholar 

  29. Abragam, A. & Goldman, M. Principles of dynamic nuclear polarisation. Rep. Prog. Phys. 41, 395–467 (1978)

    Article  ADS  CAS  Google Scholar 

  30. Bloembergen, N., Shapiro, S., Pershan, P. S. & Artman, J. O. Cross-relaxation in spin systems. Phys. Rev. 114, 445–459 (1959)

    Article  ADS  CAS  Google Scholar 

  31. Wolfowicz, G. et al. Atomic clock transitions in silicon-based spin qubits. Nature Nanotechnol. 8, 561–564 (2013)

    Article  ADS  CAS  Google Scholar 

  32. Van Duzer, T. & Turner, C. W. Principles of Superconductive Devices and Circuits 2nd edn (Prentice-Hall PTR, 1999)

  33. Palacios-Laloy, A. Superconducting Qubit in a Resonator: Test of the Leggett-Garg Inequality and Single-shot Readout. PhD thesis, Université Pierre et Marie Curie — Paris VI (2010)

  34. Mentink-Vigier, F. et al. Increasing sensitivity of pulse EPR experiments using echo train detection schemes. J. Magn. Reson. 236, 117–125 (2013)

    Article  ADS  CAS  Google Scholar 

  35. Bloembergen, N. On the interaction of nuclear spins in a crystalline lattice. Physica 15, 386–426 (1949)

    Article  ADS  CAS  Google Scholar 

  36. Abragam, A. Principles of Nuclear Magnetism Ch. IX (Oxford Univ. Press, 1983)

  37. de Graaf, S. E., Davidovikj, D., Adamyan, A., Kubatkin, S. E. & Danilov, A. V. Galvanically split superconducting microwave resonators for introducing internal voltage bias. Appl. Phys. Lett. 104, 052601 (2014)

    Article  ADS  Google Scholar 

  38. Wisby, I. et al. Coupling of a locally implanted rare-earth ion ensemble to a superconducting micro-resonator. Appl. Phys. Lett. 105, 102601 (2014)

    Article  ADS  Google Scholar 

  39. Samkharadze, N. et al. High kinetic inductance superconducting nanowire resonators for circuit QED in a magnetic field. Preprint at http://arXiv.org/abs/1511.01760 (2015)

  40. Can, T. V. et al. Overhauser effects in insulating solids. J. Chem. Phys. 141, 064202 (2014)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge technical support from P. Sénat, D. Duet, J.-C. Tack, P. Pari and P. Forget, as well as discussions within the Quantronics group. We acknowledge support of the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) through grant agreements No. 615767 (CIRQUSS), 279781 (ASCENT) and 630070 (quRAM), and of the C’Nano IdF project QUANTROCRYO. J.J.L.M. is supported by the Royal Society. C.C.L. is supported by the Royal Commission for the Exhibition of 1851. T.S. and C.D.W. were supported by the US Department of Energy under contract DE-AC02-05CH11231.

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Author notes

  1. J. J. Pla & Y. Kubo

    Present address: † Present addresses: School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, New South Wales 2052, Australia (J.J.P.); Okinawa Institute of Science and Technology (OIST) Graduate University, Onna, Okinawa 904-0495, Japan (Y.K.).,

Authors and Affiliations

  1. Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, Gif-sur-Yvette, 91191, France

    A. Bienfait, Y. Kubo, X. Zhou, M. Stern, D. Vion, D. Esteve & P. Bertet

  2. London Centre for Nanotechnology, University College London, London, WC1H 0AH, UK

    J. J. Pla, C. C. Lo & J. J. L. Morton

  3. ISEN Department, Institute of Electronics Microelectronics and Nanotechnology, CNRS UMR 8520, Avenue Poincaré, CS 60069, Villeneuve d’Ascq Cedex, 59652, France

    X. Zhou

  4. Quantum Nanoelectronics Laboratory, BINA, Bar Ilan University, Ramat Gan, Israel

    M. Stern

  5. Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA

    C. D. Weis & T. Schenkel

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Contributions

A.B., J.J.P., J.J.L.M. and P.B. designed the experiment. X.Z. and D.V. designed and fabricated the Josephson Parametric Amplifier. C.C.L., C.D.W. and T.S. provided the bismuth-implanted isotopically purified silicon sample. A.B., J.J.P. and Y.K. fabricated the sample and performed the measurements. A.B., J.J.P., Y.K., J.J.L.M. and P.B. analysed the data. J.J.L.M., D.E., D.V. and P.B. supervised the project. A.B., J.J.P., Y.K., M.S., D.V., D.E., J.J.L.M. and P.B. contributed to writing the paper.

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Correspondence to P. Bertet.

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Extended data figures and tables

Extended Data Figure 1 Effect of excitation-pulse bandwidth on the measurement of T1.

a, The red and blue lines shown the computed pulse bandwidth (‘normalized response’) for a 5-μs π pulse and a 100-μs π pulse, respectively, incident on a cavity with κ/(2π) = 23 kHz (green dashes). To illustrate the averaging effect of the pulse bandwidth on T1 measurements, the expected Purcell T1 curve (black line) as a function of spin–cavity detuning is plotted on the right axis, with T1(0) = 0.35 s and κ/(2π) = 23 kHz. b, T1 measurements for two different π-pulse lengths (see insets), measured on resonance with resonator A. Spin polarization is measured with a Hahn echo sequence and AQ is rescaled by its value for T ≫T1 (‘AQ(T = ∞)’). Symbols are data and solid lines are exponential fits. The 100-μs π pulse (blue) yields T1 = 0.35 s, which is in agreement with the Purcell rate. The 5-μs π pulse (red) yields T1 = 0.65 s, a factor of two greater than the accurate value.

Extended Data Figure 2 Spectral spin diffusion.

a–c, T1 measurement sequence when spins are detuned from the cavity by applying a magnetic field Bδ , providing a detuning of δ = ωs − ω0 = 2πγeffBδ , with γeff = df/dB(B0) the effective gyromagnetic ratio, evaluated as the derivative of f = 2πωs with respect to the applied magnetic field B at a given magnetic field B0. In a, a 5-μs π pulse is used to realize an inversion-recovery sequence; in b, a 1-s-long strong microwave pulse sent at cavity resonance is used to realize a saturation-recovery sequence; in c, a magnetic field scan (bottom panel) is used in addition to a 6-s-long strong microwave pulse to realize a saturation-recovery sequence. The expected magnetic field profile due to the coil filtering, assuming that the coil is an order-one low-pass filter with a bandwidth of 1 Hz, is shown in orange (c, bottom panel). d, T1 measurements for sequences shown in a (green), b (red) and c (blue) for δ/(2π) = 3.8 MHz. The fits (black lines) to the green and red data have a double-exponential decay, whereas the fit to the blue data is a simple exponential. We attribute the double-exponential decay (with extracted characteristic times T1A and T1B) to spin diffusion. e, Spectral profiles of the excitation pulse sequences shown in a (green), b (red) and c (blue). The sequence is as follows: send the excitation pulse, detune the spins and measure AQ(ωs). The black line is the reference profile without any excitation pulse, yielding the reference polarization . When an excitation pulse is sent, we can access . To conserve the line shape profile, we plotted AQ(ωs)/AQ0(ω0) instead of AQ(ωs)/AQ0(ωs). Neither the π profile nor the saturation profiles reach the full inversion +1 or the full saturation 0 at resonance; this is an artefact due to the coil transient time.

Extended Data Table 1 Relevant Bi:Si transitions and their characteristics
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Extended Data Table 2 Resonator characteristics
Full size table

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Bienfait, A., Pla, J., Kubo, Y. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016). https://doi.org/10.1038/nature16944

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