Experimental High-Accuracy and Broadband Quantum Frequency Sensing via Geodesic Control

Abstract

Accurate frequency estimation of oscillating signals over a broad bandwidth is a central task in quantum sensing, yet it is often compromised by spurious responses to higher-order harmonics in realistic multi-frequency environments. Here we experimentally demonstrate a high-accuracy and broadband quantum frequency sensing protocol based on geodesic control, implemented using the electron spin of a single nitrogen-vacancy center in diamond. By engineering an intrinsically single-frequency response, geodesic control enables bias-free frequency estimation with strong suppression of harmonic-induced systematic errors across a wide spectral range spanning from the megahertz to the gigahertz regime. Furthermore, by incorporating synchronized readout, we achieve millihertz-level frequency resolution under noisy signal conditions. Our results provide systematic experimental benchmarking of geodesic control for quantum frequency sensing and establish it as a practical approach for high-accuracy metrology in realistic environments.

Figures (6)

• Figure 1: (a) Schematic of frequency sensing using a single NV electron spin. The geodesic control of the electron spin acts as a tunable spectral filter, enabling selective detection of the target frequency $\omega_s$ in the presence of a noisy environment. (b) The pulse sequence exploiting the parallel component $B_\parallel(t)$ to sense the low-frequency signals in the MHz regime. (c) Accumulated phase $\Phi_{\text{GD}_\parallel}(t)$ as a function of the scan frequency, exhibiting strong spectral selectivity with a maximum response at $\omega_\text{scan}=\omega_s$. (d) Heterodyne pulse sequence exploiting the perpendicular component $B_\perp(t)$ to enable frequency sensing in the GHz regime. (e) Accumulated phase $\Phi_{\text{GD}_\perp}(t)$ as a function of the scan frequency, exhibiting strong spectral selectivity with a maximum response at $\omega_\text{scan}=\Delta_s$.
• Figure 2: The Fourier components of the modulation functions under finite-width control pulses for (a) MHz signal measurement and (b) GHz signal measurement. a.u., arbitrary units. The solid lines come from the numerical simulation. The diamonds, squares represent the experimental results of conventional and geodesic schemes, respectively. Robustness of the (c) MHz- and (d) GHz-regime sensing protocols against noise signals at the 3rd, 5th and 7th harmonics with varying amplitudes. The diamonds, dots and squares represent the experimental results obtained by adding a single noise component at the $k=3$, $k=5$ and $k=7$ harmonics, respectively. The solid lines represent the results from numerical simulation. The error bars represent the uncertainties estimated by adding Poisson noise to the experimental data.
• Figure 3: The experimental results of frequency sensing with (a) the GD$_\parallel$ scheme (purple dots) compared with the conventional XY scheme (red dots), and (b) the GD$_\perp$ scheme (purple dots) compared with the CPMG scheme (red dots). Solid lines are fits to a Lorentzian function $P=A/(1 + (\omega_{\text{scan}} - \omega_s(\Delta_s))^2/\gamma^2)$, where 2$\gamma$ is the full width at half maximum, and $A$ is the signal amplitude.
• Figure 4: The Fourier transform spectra of the signal-sensing experiment in the MHz (a) and GHz (b) regime. The insets show the fitting results of experimental spectrum slices in the shaded areas.
• Figure 5: The sequences of the synchronized readout technique.