Coherence protection of spin qubits in hexagonal boron nitride

Nat. Commun. 14, 461 (2023) · DOI: 10.1038/s41467-023-36196-7

License: CC BY 4.0.

Abstract

Spin defects in foils of hexagonal boron nitride are an attractive platform for magnetic field imaging, since the probe can be placed in close proximity to the target. However, as a III-V material the electron spin coherence is limited by the nuclear spin environment, with spin echo coherence times of $\sim$100 ns at room temperature accessible magnetic fields. We use a strong continuous microwave drive with a modulation in order to stabilize a Rabi oscillation, extending the coherence time up to $\sim$4 $\mu$s, which is close to the 10 $\mu$s electron spin lifetime in our sample. We then define a protected qubit basis, and show full control of the protected qubit. The coherence times of a superposition of the protected qubit can be as high as 0.8 $\mu$s. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical nitrogen vacancy centres in small nanodiamonds under ambient conditions.

Figures

22 panels with data across 4 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 (b): Photoluminescence spectrum under 532 nm excitation: PL intensity (arb. units, peak 1) against wavelength (nm), drawn as a filled curve. data.csv
• panel (c): Continuous-wave ODMR spectrum: contrast (%) against microwave frequency (GHz), points joined by a line. data.csv
• panel (d): Rabi oscillation of the $m_S = 0$ to $m_S = +1$ ground-state transition: contrast (%) against microwave pulsewidth $\tau$ (ns). Squares are the measurement and the red curve is the fit of a damped cosine. data.csv
• panel (e): Spin echo: contrast (%) against time delay $\delta$ (ns) at low ($\Omega = 22$ MHz, blue) and high ($\Omega = 80$ MHz, red) Rabi frequency, points joined by lines. data.csv
• panel (f): Coherence time (ns) against Rabi frequency $\Omega$ (MHz) from Rabi oscillation (grey squares) and spin echo (blue circles) measurements, points joined by lines. Error bars are the standard error of the fitted coherence times; the dashed line is the theory value the legend labels "Theory, ref. 6". data.csv

Fig. 2

• panel (a): Contrast (%) against microwave pulsewidth $\tau$ ($\mu$s) for the amplitude-modulated CCD scheme with $\epsilon_m = 12$ MHz (grey) and the unprotected, conventional Rabi oscillation (red), points joined by lines. The three insets of the print are hosted as separate panels. data.csv
• panel (a-inset-1): Inset 1 of panel (a), of three (left to right, around 2, 5 and 8 $\mu$s): contrast (%) against pulsewidth $\tau$ ($\mu$s) for the CCD scheme around 2 $\mu$s, points joined by a line. data.csv
• panel (a-inset-2): Inset 2 of panel (a), of three (left to right, around 2, 5 and 8 $\mu$s): contrast (%) against pulsewidth $\tau$ ($\mu$s) for the CCD scheme around 5 $\mu$s, points joined by a line. data.csv
• panel (a-inset-3): Inset 3 of panel (a), of three (left to right, around 2, 5 and 8 $\mu$s): contrast (%) against pulsewidth $\tau$ ($\mu$s) for the CCD scheme around 8 $\mu$s, points joined by a line. data.csv
• panel (b): Contrast (%) against microwave pulsewidth $\tau$ (ns) over the first 250 ns: conventional Rabi oscillation (red squares) and the amplitude-modulated CCD scheme with $\epsilon_m = 12$ MHz (grey squares), points joined by lines. data.csv
• panel (c-1): Top plot of panel (c): contrast (%) against microwave pulsewidth $\tau$ (ns) for the amplitude-modulated CCD scheme with modulation phase $\theta_m = 0$, points joined by a line. data.csv
• panel (c-2): Bottom plot of panel (c): contrast (%) against microwave pulsewidth $\tau$ (ns) for the amplitude-modulated CCD scheme with modulation phase $\theta_m = \pi/2$, points joined by a line. data.csv
• panel (d): Fourier transform spectra of the two traces of panel (c): normalised spectral amplitude against FFT frequency (MHz) for $\theta_m = 0$ (dark grey) and $\theta_m = \pi/2$ (blue). The values at 0 MHz lie above the printed axis. data.csv
• panel (e): Frequency spectrum of amplitude-modulated CCD: normalized spectral amplitude (colour) against FFT frequency (MHz) and modulation phase $\theta_m$ ($^\circ$), with $\omega_m = \Omega = 80$ MHz and $\epsilon_m = 20$ MHz. The amplitude is 1 at its largest value away from 0 MHz; the 0 MHz row lies above the colour scale, as printed. data.csv
• panel (f): Frequency spectrum of amplitude-modulated CCD: normalized spectral amplitude (colour) against FFT frequency (MHz) and modulation frequency $\omega_m/2\pi$ (MHz), with $\theta_m = \pi/2$ and $\epsilon_m = 20$ MHz. The amplitude is 1 at its largest value away from 0 MHz; the 0 MHz row lies above the colour scale, as printed. data.csv
• panel (g): Coherence time ($\mu$s) against modulation amplitude $2\epsilon_m$ (MHz) for amplitude-modulated CCD, centre band (grey squares) and sidebands (red circles), $\Omega_R = 80$ MHz, and phase-modulated CCD, centre band (blue triangles), $\Omega_R = 100$ MHz. Points joined by lines; error bars are the standard error of the fitted coherence times. data.csv

Fig. 3

• panel (b): Stabilized Rabi oscillations recorded during the readout window: contrast (%) against total pulsewidth $T$ (ns) after a $\pi$ ($t_c = 45$ ns, grey squares) and a $2\pi$ ($t_c = 90$ ns, red circles) control pulse, points joined by lines. data.csv
• panel (c): Measured contrast (%, colour) against total pulsewidth $T$ (ns) and control pulsewidth $t_c$ (ns). The dashed guide lines the print draws from the pulse scheme of panel (a) are not reproduced. data.csv
• panel (d): Real part of the FFT of the readout window of panel (c) (arb. units, colour) against control pulsewidth $t_c$ (ns) and FFT frequency (MHz). The centre band at 80 MHz exceeds the colour scale, as printed. data.csv

Fig. 4

• panel (a): Rabi oscillation of the protected qubit: real part of the FFT (arb. units) of the centre band against control pulsewidth $t_c$ (ns). Squares are the measurement and the red curve is the fit. data.csv
• panel (b): Ramsey interference of the protected qubit: real part of the FFT (arb. units) against Ramsey delay time $t_d$ (ns). Squares are the measurement and the red curve is the fit. data.csv
• panel (c): Rabi coherence time ($\mu$s) of the protected qubit against protected Rabi frequency $F_R$ (MHz) for amplitude modulation at $\Omega = 80$ MHz (grey squares) and phase modulation at $\Omega = 80$ MHz (red circles) and 100 MHz (blue triangles). Points joined by lines; error bars are the standard error of the fitted coherence times. data.csv

Cite

Andrew J. Ramsay, Reza Hekmati, Charlie J. Patrickson, Simon Baber, David R. M. Arvidsson-Shukur, Anthony J. Bennett, Isaac J. Luxmoore. Coherence protection of spin qubits in hexagonal boron nitride. Nat. Commun. 14, 461 (2023). https://doi.org/10.1038/s41467-023-36196-7

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