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Controlling spin relaxation with a cavity


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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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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Authors and Affiliations



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 TT1 (‘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.

ac, 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
Extended Data Table 2 Resonator characteristics

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Bienfait, A., Pla, J., Kubo, Y. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016).

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