# Radiative cooling of a spin ensemble

## Abstract

Physical systems reach thermal equilibrium through energy exchange with their environment, and for spins in solids the relevant environment is almost always their host lattice. However, recent studies1 motivated by observations by Purcell2 have shown how radiative emission into a microwave cavity can become the dominant relaxation path for spins if the spin–cavity coupling is sufficiently large (such as for small-mode-volume cavities). In this regime, the cavity electromagnetic field overrides the lattice as the dominant environment, inviting the prospect of controlling the spin temperature independently from that of the lattice, by engineering a suitable cavity field. Here, we report on precisely such control over spin temperature, illustrating a novel and universal method to increase the electron spin polarization above its thermal equilibrium value (termed hyperpolarization). By switching the cavity input between resistive loads at different temperatures we can control the electron spin polarization, cooling it below the lattice temperature. Our demonstration uses donor spins in silicon coupled to a superconducting microresonator and we observe more than a twofold increase in spin polarization. This approach provides a general route to signal enhancement in electron spin resonance, or nuclear magnetic resonance through dynamical nuclear spin polarization3,4.

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## Data availability

Source data are available for this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank P. Sénat, D. Duet and J.-C. Tack for technical support, and are grateful for discussions within the Quantronics group. We acknowledge IARPA and Lincoln Labs for providing a Josephson travelling-wave parametric amplifier. We acknowledge support from the European Research Council through grant no. 615767 (CIRQUSS) and through the Superconducting Quantum Networks project, the Agence Nationale de la Rercherche under the Chaire Industrielle NASNIQ, the Region Ile-de-France via DIM SIRTEQ, the Engineering and Physical Sciences Research Council (EPSRC) through grant no. EP/K025945/1, the Horizon 2020 research and innovation programme through grant no. 771493 (LOQO-MOTIONS), the National Centre of Competence in Reseach ‘Quantum Science and Technology’, a research instrument of the Swiss National Science Foundation, and the ETH Zurich.

## Author information

Authors

### Contributions

B.A., S.P. and P.B. designed the experiment. J.J.L.M. and C.W.Z. provided and characterized the implanted Si sample, on which B.A. and S.P. fabricated the Nb resonator. B.A. performed the measurements, with help from S.P. and V.R. B.A. and P.B. analysed the data. B.A. and V.R. performed the simulations. M.P. realized and tested the superconducting switch in a project guided by A.W. B.A. and P.B. wrote the manuscript. S.P., V.R., A.W., J.J.L.M., D.V., D.E. and E.F. contributed useful input to the manuscript.

### Corresponding author

Correspondence to P. Bertet.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Stefan Putz and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Noise power spectral density measurement.

a, Frequency dependence of the noise power spectral density S measured at Tphon=840 mK for the hot (red circles) and cold (blue circles) switch configurations. Solid lines are fit (see Methods). The blue dashed line indicates the expected Scold(ω)for α=0. b, Still temperature Tphon dependence of S measured at ω = ω0 (open circles) and at ωω0 = − 2.7 MHz (open triangles) for both hot (red) and cold (blue) configurations. Solid lines are plot of Shot (red) and Scold (blue) with parameters obtained from the frequency dependence fits performed at all Tphon, and with nTWPA = 0.75. Source data

### Extended Data Fig. 2 Temperature dependence of polarization.

Equilibrium polarization of transitions 4, − 1 > ↔ 5, 0 > and 4, 0 > ↔ 5, − 1 > measured at B0=62.5 mT (red circles). Several hours are waited at each temperature before recording Ae. Red line is the calculated ΔN(T) for the considered transition at B0=62.5 mT. A second polarisation measurement of the same transitions (black circles) is reported. In this experiment, for each temperature value, B0 is first set to 9.3 mT during 20 min, then it is set to 62.5 mT and finally after 4 min Ae is recorded. The black line is the calculated ΔN(T)for the considered transition at B0=9.3 mT. The polarisation p(T)=$$\tanh (\frac{\hslash {\omega }_{0}}{2kT})$$ of a spin 1/2 is also shown for comparison (green). Ae as a function of time (inset) is measured at T=83 mK and B0=62.5 mT after B0 has been set to 9.3 mT for 20 min. The same data are represented in the main plot with the blue arrow. Source data

### Extended Data Fig. 3 Simulation of Rabi oscillations.

a, Distribution of the spin-cavity coupling g obtained from the spatial distribution of δB1. b, Rabi oscillations measured at B0=62.5 mT and T =850 mK by varying the amplitude of the second pulse in the Hahn echo sequence (blue circles). The pulse amplitude is normalized to the value $${{\mathrm{P}}_{\pi }}^{\frac{1}{2}}$$ corresponding to the maximum in detected signal. The solid green line is the result of the numerical simulation of a spin ensemble described by ρ(g). Source data

## Supplementary information

### Source Data Fig. 1

Cartesian measurement data.

### Source Data Fig. 2

Cartesian measurement data.

### Source Data Fig. 3

Cartesian measurement data.

### Source Data Fig. 4

Cartesian measurement data.

### Source Data Extended Data Fig. 1

Cartesian measurement data.

### Source Data Extended Data Fig. 2

Cartesian measurement data.

### Source Data Extended Data Fig. 3

Cartesian measurement data.

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Albanese, B., Probst, S., Ranjan, V. et al. Radiative cooling of a spin ensemble. Nat. Phys. 16, 751–755 (2020). https://doi.org/10.1038/s41567-020-0872-2

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