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Solid-state electron spin lifetime limited by phononic vacuum modes

Abstract

Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems, relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum1,2,3,4,5,6,7,8,9. In the quantum limit, the spin lifetime is determined by phononic vacuum fluctuations10. However, this limit was not observed in previous studies due to thermal phonon contributions11,12,13 or phonon-bottleneck processes10, 14,15. Here we use a dispersive detection scheme16,17 based on cavity quantum electrodynamics18,19,20,21 to observe this quantum limit of spin relaxation of the negatively charged nitrogen vacancy (NV) centre22 in diamond. Diamond possesses high thermal conductivity even at low temperatures23, which eliminates phonon-bottleneck processes. We observe exceptionally long longitudinal relaxation times T1 of up to 8 h. To understand the fundamental mechanism of spin–phonon coupling in this system we develop a theoretical model and calculate the relaxation time ab initio. The calculations confirm that the low phononic density of states at the NV transition frequency enables the spin polarization to survive over macroscopic timescales.

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Fig. 1: Experimental set-up for measuring spin relaxation.
Fig. 2: Measured time dependence and thermal steady state of \(\left\langle {\boldsymbol{S}}_{\boldsymbol{z}}^{\boldsymbol{2}}\right\rangle\).
Fig. 3: Temperature dependence of the spin–lattice relaxation rate.

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Acknowledgements

We thank W. J. Munro, K. Streltsov, J. Redinger and W. Mayr-Schmoelzer for fruitful discussions. The experimental effort has been supported by the TOP grant of TU Wien and the Japan Society for the Promotion of Science KAKENHI (No. 26246001, 26220903). T.A., A.A. and S.P. acknowledge support by the Austrian Science Fund (FWF) in the framework of the Doctoral School Building Solids for Function (Project W1243). J.G., J.M., N.M. and P.M. acknowledge support by the FWF SFB VICOM (Project F4109-N28). J.S. and N.M. further acknowledge support by the WWTF project SEQUEX (Project MA16-066).

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Contributions

T.A., J.S., N.M., S.P. and J.M designed and set up the experiment. T.A., A.A. and S.W. carried out the measurements under the supervision of J.M., while J.G. and P.M. devised the theoretical framework and provided the theoretical model for spin-lattice relaxation. J.I., S.O., H.S. and M.T. characterized and provided the diamond samples. T.A., J.G. and A.A. wrote the manuscript, to which all authors suggested improvements.

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Correspondence to T. Astner or J. Majer.

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Supplementary information

Phonon Oscillation

In this movie an optical vibrational mode of the NV centre is shown. The coloured surface depicts the spin density of the electrons. For illustrational purposes the amplitude of the ionic displacements is chosen to be ten times as large as in reality.

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Astner, T., Gugler, J., Angerer, A. et al. Solid-state electron spin lifetime limited by phononic vacuum modes. Nature Mater 17, 313–317 (2018). https://doi.org/10.1038/s41563-017-0008-y

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