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# Spin-cooling of the motion of a trapped diamond

## Abstract

Observing and controlling macroscopic quantum systems has long been a driving force in quantum physics research. In particular, strong coupling between individual quantum systems and mechanical oscillators is being actively studied1,2,3. Whereas both read-out of mechanical motion using coherent control of spin systems4,5,6,7,8,9 and single-spin read-out using pristine oscillators have been demonstrated10,11, temperature control of the motion of a macroscopic object using long-lived electronic spins has not been reported. Here we observe a spin-dependent torque and spin-cooling of the motion of a trapped microdiamond. Using a combination of microwave and laser excitation enables the spins of nitrogen–vacancy centres to act on the diamond orientation and to cool the diamond libration via a dynamical back-action. Furthermore, by driving the system in the nonlinear regime, we demonstrate bistability and self-sustained coherent oscillations stimulated by spin–mechanical coupling, which offers the prospect of spin-driven generation of non-classical states of motion. Such a levitating diamond—held in position by electric field gradients   under vacuum—can operate as a ‘compass’ with controlled dissipation and has potential use in high-precision torque sensing12,13,14, emulation of the spin-boson problem15 and probing of quantum phase transitions16. In the single-spin limit17 and using ultrapure nanoscale diamonds, it could allow quantum non-demolition read-out of the spin of nitrogen–vacancy centres at ambient conditions, deterministic entanglement between distant individual spins18 and matter-wave interferometry16,19,20.

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## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank R. Blatt, C. Voisin, Y. Chassagneux, E. Baudin and S. Deléglise for discussions.

## Author information

Authors

### Contributions

T.D. and P.H. contributed equally to this work. T.D., P. H., L.N. and G.H. performed the spin-torque experiments; T.D., P.H. and G.H. analysed the data and performed the modelling with assistance from L.N., and G.H., T. D. and P.H. wrote the manuscript. All authors contributed to the interpretation of the data and commented on the manuscript.

### Corresponding author

Correspondence to G. Hétet.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Ashok Ajoy and the 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 figures and tables

### Extended Data Fig. 1 Parametric spin-excitation of the librational mode.

a, Detection principle of the librational modes using microwave parametric excitation (top). Reflected light field amplitude as a function of time for one low-frequency librational mode (170 Hz) at 1 mbar (bottom). b, Spin-mechanical resonance for two different microwave powers: trace i, 20 dBm; trace ii, −10 dBm. c, Reflected light field amplitude as a function of time, for the three microwave frequencies 2.617 GHz (red thin curve), 2.623 GHz (green) and 2.634 GHz (blue) corresponding to the points 1, 2 and 3 in b, respectively. Plain thicker lines show the slow envelope of the fit to the data (see Methods) using two sines at the frequency of the parametrically excited librational mode (480 Hz) and of the closest librational mode (590 Hz) with an amplitude that is 30 times smaller.

### Extended Data Fig. 2 Numerical simulations in the nonlinear regime.

a, Effective damping and spring constants as a function of microwave detuning deduced by a numerical fit to the ring-down curves (see Methods). Traces i, ii, iii and iv correspond to increasing microwave Rabi frequencies Ω/2π = 50, 150, 200 and 250 kHz, respectively. b, Evolution of the angle as a function of time after turning on a microwave frequency to the blue of the spin resonance at a time t = 20 ms, showing amplification and finally lasing at t = 120 ms. c, Librational mode velocity as a function of microwave Rabi frequency, for three different values of the spin–lattice relaxation rate 1/T1 = 1, 2 and 3 kHz for traces i, ii and iii, respectively.

### Extended Data Fig. 3 Phonon-lasing as a function of time.

Shown is the reflected light field amplitude as a function of time on sudden switch-on of a microwave signal at a time t = 0.02 s to the blue side of the spin transition. The microwave power is above threshold so lasing can be observed after the Brownian motion signal (seen before t = 0.02 s). This curve was used to plot the histogram of Fig. 3C in the main text.

### Extended Data Fig. 4 Calibration of sensitivity using NV magnetometry.

a, Upper panel, mechanically detected spin resonance for three different microwave powers. The dashed line is the locus of the signal minima. Lower panel, angle between the NV axis and magnetic field direction versus NV spin transition frequency. ∆S is the maximal change of the optical signal. ∆θNV is the maximum angle between the NV axis and the magnetic field direction. b, Optical signal as a function of time. c, Left panel, sketch depicting the angular motion of the diamond on magnetization of one class of NV spins using only two angles θx and θy for simplicity. B is the orientation of the magnetic field. Right panel, angular trajectory represented in (θx, θy) space. We note O is the particle orientation without NV magnetization (Mz = 0). The red (green) line is the trajectory in the isotropic (anisotropic) case (see Methods). θd is the detected angle. d, Power spectra of the librational Brownian motion for two different speckle alignments taken with a resolution bandwidth of 1 Hz. The red curve shows all three librational modes. For the blue curve, the detection is tuned to be mainly sensitive to the mode with the highest confinement frequency. The latter detection setting is used for the data shown in a and b.

### Extended Data Fig. 5 Measurement of spin polarization rates.

a, Sequences employed to measure the laser induced polarization rate to the ground state (i) and to measure the microwave induced polarization rate to the magnetic state $${m{\prime} }_{{\rm{s}}}=-1$$ (ii). The laser is kept on at all times for both sequences. b, Trace i shows the photoluminescence (PL) rate at a time τ after having turned off the microwave signal. An exponential fit to the data gives a laser polarization time of 300 μs. Trace ii shows the photoluminescence rate at a time τ after having turned on the microwave signal. The polarization time to the magnetic state is here 124 μs.

### Extended Data Fig. 6 Particle angle dynamics for different microwave detunings in the bistable regime.

af, Left panel, experimental observation of the reflected signal amplitude as a function of time for microwave frequencies (in GHz) of 2.8000 (a), 2.8010 (b), 2.8020 (c), 2.8030 (d), 2.8035 (e), 2.8040 (f), tuned to the red of the spin transition. Right panel, histogram showing the number of counts within each bin.

## Supplementary information

### Supplementary Information

This supplementary file details the theory behind the observations, both on the spin-cooling and phonon lasing effects.

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Delord, T., Huillery, P., Nicolas, L. et al. Spin-cooling of the motion of a trapped diamond. Nature 580, 56–59 (2020). https://doi.org/10.1038/s41586-020-2133-z

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