Decoherence of V B − spin defects in monoisotopic hexagonal boron nitride

Abstract

Spin defects in hexagonal boron nitride (hBN) are promising quantum systems for the design of flexible two-dimensional quantum sensing platforms. Here we rely on hBN crystals isotopically enriched with either ¹⁰B or ¹¹B to investigate the isotope-dependent properties of a spin defect featuring a broadband photoluminescence signal in the near infrared. By analyzing the hyperfine structure of the spin defect while changing the boron isotope, we first confirm that it corresponds to the negatively charged boron-vacancy center (${\mathrm{V}}_{\mathrm{B}}^{-}$). We then show that its spin coherence properties are slightly improved in ¹⁰B-enriched samples. This is supported by numerical simulations employing cluster correlation expansion methods, which reveal the importance of the hyperfine Fermi contact term for calculating the coherence time of point defects in hBN. Using cross-relaxation spectroscopy, we finally identify dark electron spin impurities as an additional source of decoherence. This work provides new insights into the properties of ${\mathrm{V}}_{\mathrm{B}}^{-}$ spin defects, which are valuable for the future development of hBN-based quantum sensing foils.

Fig. 1. Optical properties of neutron-irradiated monoisotopic hBN crystals.

a Raman scattering spectra recorded at room temperature on the h¹¹BN (red dots) and h¹⁰BN crystals (blue dots) after neutron irradiation. The solid lines are data fitting with Lorentzian functions. b Typical lateral PL raster scan of the h¹⁰BN crystals under green laser illumination with a power of 1 mW. c Axial confocal scan showing a high PL signal localized at the crystal surfaces. d PL spectra recorded from the h¹¹BN (red) and h¹⁰BN crystals (blue). The data have been normalized and vertically shifted for the sake of clarity.

Fig. 2. Analysis of the hyperfine structure.

a Optically detected ESR spectra recorded on the h¹⁰BN crystal at zero field (top panel) and for a magnetic field B = 14 mT applied along the c axis, i.e., perpendicular to the sample surface. b, c Hyperfine structure of the ESR line measured in b h¹¹BN and c h¹⁰BN crystals. The solid lines are data fitting with a sum of seven Gaussian functions. d, e Simulated hyperfine spectra of the ${\mathrm{V}}_{\mathrm{B}}^{-}$ defect in hBN obtained via the procedure described in the main text while using Δ_s = 30 MHz. The inset shows the atomic structure of the ${\mathrm{V}}_{\mathrm{B}}^{-}$ center in hBN.

Fig. 3. Spin coherence properties.

a Optically detected Rabi oscillations of an ensemble of ${\mathrm{V}}_{\mathrm{B}}^{-}$ spin defects recorded by applying the experimental sequence shown in the top panel. The spin-dependent PL signal S is integrated at the beginning of the readout laser pulse and normalized by a reference signal S_ref, which corresponds to the steady-state PL signal measured at the end of the initialization laser pulse. b T₁ measurements in the two monoisotopic crystals. Here we plot the difference of the normalized PL signal S/S_ref measured with and without applying the resonant microwave π-pulse (see top panel). Solid lines are data fitting with an exponential decay, leading to T₁ ~ 16 μs in both samples. c Measurement of the spin coherence time T₂ using a spin echo pulse sequence. Solid lines are data fitting with an exponential decay. All experiments are performed with a static magnetic field B ~ 15 mT applied along the c axis. The duration of the laser pulses is 8 μs with a power of 1 mW and the integration time window of S and S_ref is fixed to 300 ns. The duration of the microwave π/2 pulse is set to 15 ns.

Fig. 4. Nuclear spin bath induced decoherence.

a, b Simulated spin echo decay curve and corresponding stretched exponential fit for the ${\mathrm{V}}_{\mathrm{B}}^{-}$ defect in a h¹¹BN and b h¹⁰BN. c Calculated spin coherence time T₂ as a function of the abundance of ¹⁰B isotope. The T₂ time is enhanced by the reduced hyperfine and nuclear spin-nuclear spin interaction strengths in ¹⁰B-enriched samples. The black dashed line is a linear fit.

Fig. 5. Cross-relaxation spectroscopy.

a Energy levels of the ${\mathrm{V}}_{\mathrm{B}}^{-}$ spin triplet ground state (top panel) and of a paramagnetic impurity with S = 1/2 (bottom panel) as a function of a static magnetic field B. The two spin systems are brought in resonance for B = B_c ~ 62 mT. b T₁ time of the ${\mathrm{V}}_{\mathrm{B}}^{-}$ spin defect in the h¹⁰BN crystal as a function of a magnetic field applied along the c-axis. The field amplitude is inferred by recording the Zeeman shift of the ESR frequency of the ${\mathrm{V}}_{\mathrm{B}}^{-}$ defect. The solid line is data fitting with a Gaussian function. The error bars correspond to the uncertainty of fitting the T₁ decay curve with an exponential function.