Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum

Nat. Commun. 15, 5063 (2024) · DOI: 10.1038/s41467-024-49175-3

License: CC BY 4.0.

Abstract

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate at pressures below $10^{-5}$ Torr. We have driven a nanodiamond to rotate up to 20 MHz ($1.2 imes 10^{9}$ rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena.

Figures

16 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (d): Power spectral densities of the levitated nanodiamond's centre-of-mass motion, PSD (V$^2$/Hz) against frequency (kHz), at $1.0 \times 10^{-1}$ Torr (blue) and $9.8 \times 10^{-6}$ Torr (orange). The print labels the $x$, $y$ and $z$ motional peaks; the labels are not drawn here. data.csv
• panel (e): ODMR spectra of the levitated nanodiamond, contrast (%) against MW frequency (GHz), at $1.0 \times 10^{1}$ Torr (blue circles) and $6.9 \times 10^{-6}$ Torr (orange squares), each with its fit curve. The dashed vertical lines mark the zero-field splittings of the two spectra. data.csv
• panel (f): Internal temperature of the levitated nanodiamond, temperature (K) against pressure (Torr, log scale), with error bars giving the standard deviation over three measurements, and the orange curve the print draws through the points. data.csv

Fig. 2

• panel (c): Power spectral densities of the rotational motion of the levitated nanodiamond, PSD (V$^2$/Hz) against frequency (MHz), at eleven rotation frequencies $-\omega_r/2\pi$ from 0.1 to 20 MHz, one colour each. Each trace is thinned to the minimum and maximum of every 32 samples. data.csv

Fig. 3

• panel (b): ODMR spectra of the levitated nanodiamond, contrast (%) against MW frequency (GHz), at rotation frequencies $-\omega_r/2\pi$ = 0.1 MHz (blue circles) and 14 MHz (orange squares), each with its fit curve, and the grey dashed vertical line of the print. data.csv
• panel (c): FWHM of the ODMR spectrum (MHz) against rotation frequency $-\omega_r/2\pi$ (MHz): experiment (blue circles, error bars the standard deviation over three measurements) and theory at $\theta = 0$ (solid orange) and $\theta = 20^{\circ}$ (dashed yellow). data.csv
• panel (e-1): Upper panel of (e): ODMR spectrum of the levitated nanodiamond rotating at $-\omega_r/2\pi$ = 0.1 MHz at $1.0 \times 10^{-4}$ Torr, contrast (%) against MW frequency (GHz), red squares with the fit of eight Lorentzian dips (solid curve). data.csv
• panel (e-2): Lower panel of (e): ODMR spectrum of a nanodiamond without a stable rotation ($-\omega_r/2\pi$ = 0) at 10 Torr, contrast (%) against MW frequency (GHz), grey circles with the fit of eight Lorentzian dips (solid curve). data.csv
• panel (f): Frequency of the right-most ODMR dip (GHz) against rotation frequency $-\omega_r/2\pi$ (MHz): experiment (blue circles, error bars the standard deviation over three measurements), theory at $\theta = 20.7^{\circ}$ (green solid) and $\theta = 24.0^{\circ}$ (violet dashed), and a linear fit (magenta dash-dot). data.csv

Fig. 4

• panel (c): ODMR spectrum of the levitated nanodiamond rotating at 100 kHz, contrast (%) against MW frequency (GHz): data (blue points) and a fit curve (orange). Dashed vertical lines 1, 2 and 3 mark the dips whose Rabi oscillations are shown in (d). data.csv
• panel (d): Rabi oscillations of the NV centres at three orientations, contrast (%) against time ($\mu$s), at $f_{MW}$ = 2.935 GHz (1, purple), 3.009 GHz (2, orange) and 3.129 GHz (3, blue), each with its fit curve. Curves 2 and 1 are shifted up by 2 % and 4 %, as printed. data.csv
• panel (e): Rabi oscillation of the NV centres with $\theta = 22^{\circ}$ (dip 3), contrast (%) against time ($\mu$s), at rotation phase $\phi = \pi/2$ (blue circles) and $\phi = \pi$ (black squares, shifted up by 2 % as printed), each with its fit curve. data.csv
• panel (f): Rabi frequency (MHz) at $\theta = 22^{\circ}$ against rotation phase $\phi - \pi/2$ (rad), measured (blue circles, error bars the standard deviation over three measurements) with the theoretical prediction (red curve). The print labels the $x$ axis in multiples of $\pi/2$. data.csv

Fig. 5

• panel (b): Power spectral densities of the levitated nanodiamond's centre-of-mass motion along $x$, PSD (V$^2$/Hz) against frequency (Hz): 0.02 Torr without feedback cooling (noFB, blue), $2 \times 10^{-5}$ Torr with feedback cooling (FB, red) and the noise floor (yellow), with the fit curves to the blue and red spectra (dark lines). data.csv
• panel (c): Power spectral densities of the levitated nanodiamond's centre-of-mass motion along $y$, PSD (V$^2$/Hz) against frequency (Hz): 0.02 Torr without feedback cooling (noFB, blue), $2 \times 10^{-5}$ Torr with feedback cooling (FB, red) and the noise floor (yellow), with the fit curves to the blue and red spectra (dark lines). data.csv
• panel (d): Power spectral densities of the levitated nanodiamond's centre-of-mass motion along $z$, PSD (V$^2$/Hz) against frequency (Hz): 0.02 Torr without feedback cooling (noFB, blue), $2 \times 10^{-5}$ Torr with feedback cooling (FB, red) and the noise floor (yellow), with the fit curves to the blue and red spectra (dark lines). data.csv

Cite

Yuanbin Jin, Kunhong Shen, Peng Ju, Xingyu Gao, Chong Zu, Alejandro J. Grine, Tongcang Li. Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum. Nat. Commun. 15, 5063 (2024). https://doi.org/10.1038/s41467-024-49175-3

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