Landau Zener Interaction Enhanced Quantum Sensing in Spin Defects of Hexagonal Boron Nitride

Abstract

Negatively charged boron vacancies (V$_{\text{B}}^{-}$) in hexagonal boron nitride (hBN) comprise a promising quantum sensing platform, optically addressable at room temperature and transferrable onto samples. However, broad hyperfine-split spin transitions of the ensemble pose challenges for quantum sensing with conventional resonant excitation due to limited spectral coverage. While isotopically enriched hBN using $^{10}$B and $^{15}$N isotopes (h$^{10}$B$^{15}$N) exhibits sharper spectral features, significant inhomogeneous broadening persists. We demonstrate that, implemented via frequency modulation on an FPGA, a frequency-ramped microwave pulse achieves around 4-fold greater $|0\rangle\rightarrow|-1\rangle$ spin-state population transfer and thus contrast than resonant microwave excitation and thus 16-fold shorter measurement time for spin relaxation based quantum sensing. Quantum dynamics simulations reveal that an effective two-state Landau-Zener model captures the complex relationship between population inversion and pulse length with relaxations incorporated. Our approach is robust and valuable for quantum relaxometry with spin defects in hBN in noisy environments.

Figures (5)

• Figure 1: Experimental configuration, energy levels and mechanism of generating frequency ramp to be applied to V$_\text{B}^-$ defects in isotopically enriched hexagonal boron nitride (h$^{10}$B$^{15}$N). (a) Gold on sapphire device generating linearly polarized microwaves. Center: multilayer h$^{10}$B$^{15}$N containing spin defects. (b) Lattice structure of h$^{10}$B$^{15}$N with V$_\text{B}^-$. (c) Electronic energy level diagram of V$_\text{B}^-$ showing S=1 triplet states with four hyperfine levels arising from total 3/2 spin of the three $^{15}$N surrounding the defect, for non-zero m$_\text{s}$ spin states, and S=0 metastable state mediating ODMR (green: optical excitation, red: radiative decay, dashed black: intersystem crossing decay). $|e\rangle$, $|s\rangle$ and $|g\rangle$ represent excited, metastable, and ground states. (d) I and Q values fed into FPGA is convoluted with the carrier frequency to generate the frequency ramp (e) of $\Delta f = 200$ MHz centered at $f_0 = 3.2$ GHz.
• Figure 2: ODMR, Rabi oscillation, and frequency-ramped microwave pulses for enhanced spin inversion (population transfer) across broad hyperfine-split transitions in h$^{10}$B$^{15}$N. (a) Continuous wave ODMR spectrum showing the $|0\rangle$ to $|-1\rangle$ transition isolated by applied magnetic field, with solid line being composite of dashed hyperfine Lorentzian peaks (inset: optical image of the hBN flake). (b) Rabi oscillation at resonant frequency of 3191 MHz at the third hyperfine peak, showing maximum contrast of approximately 1.2% for $\pi$-pulse. (c) Pulse sequence diagram illustrating the ramped frequency microwave pulse application scheme, with contrast measured by comparison to the pulse sequence without microwave. (d) Frequency ramp demonstrating contrast enhancement beyond 1.2%, robust to variation in ramp center frequency, with optimal performance at $\Delta f \approx 200$ MHz. Rabi oscillation and frequency ramp measurements (b, d) performed at MW gain = 25000 and collection time = 1 $\mu$s, and ODMR spectrum in (a) also obtained at the same MW gain. The microwave ramp duration used in (c, d) is T=1.67 $\mu$s.
• Figure 3: Microwave gain and ramp time dependence of frequency-ramped spin inversion in V$_\text{B}^-$ h$^{10}$B$^{15}$N. Experimental contrast (measured at various MW power; left axis) demonstrates optimal ramp time for maximum contrast enhancement using frequency ramp of $\Delta f = 200$ MHz centered at 3160 MHz. Simulations via QuTiP Lindblad master equation (dashed lines, right axis) with optimized parameters (coupling $\Omega/2\pi$ and decoherence times T$_1$, T$_2$ for each gain level) fitted to experimental peak-normalized transition probabilities. Left inset: Schematic illustration of Landau-Zener transitions showing adiabatic versus diabatic pathways at an avoided crossing. Right inset: Comparison of full quantum simulation (dashed cyan) versus analytical Landau-Zener prediction (solid orange) for MW gain 30000. All measurements performed at collection time = 1 $\mu$s; simulations share T$_1$ = 12.63 $\mu$s across power levels.
• Figure 4: Comparison of single frequency-ramped microwave pulse versus resonant-frequency microwave pulse spin manipulation for spin-lattice relaxation measurements in V$_\text{B}^-$ h$^{10}$B$^{15}$N. Contrast decay measurements (circles: single frequency-ramped pulse with $\Delta f = 200$ MHz centered at 3160 MHz; triangles: resonant-frequency $\pi$-pulse at 3191 MHz) are fitted with exponentials (solid lines) to extract longitudinal relaxation time T$_1$. The frequency-ramped approach demonstrates four-fold contrast enhancement intially and overall superior signal-to-noise ratio. Data acquired at MW gain 25000 and collection time = 1 $\mu$s, with the inset showing the pulsing sequence for microwave on and off respectively, for obtaining the contrast.
• Figure 5: Multi-sweep frequency-ramp induced $|0\rangle \rightarrow |-1\rangle$ spin inversion in V$_\text{B}^-$ defects in h$^{10}$B$^{15}$N. Contrast measurements (experimental data: circles for single sweep, squares for double consecutive sweeps, triangles for triple consecutive sweeps; left axis) showing leftward shift in optimal ramp time and reduced peak contrast with increasing number of sweeps. QuTiP Lindblad simulations of transition probability (solid lines, right axis) for consecutive forward frequency ramps with $\Delta f = 200$ MHz centered at 3160 MHz, coupling $\Omega/2\pi = 4.52$ MHz, T$_1$ = 12.6 $\mu$s, and T$_2$ = 0.139 $\mu$s, corroborating the experimental trends. Data acquired at MW gain 30000 and collection time 20 ns.