Quantum sensing leverages quantum properties like coherence and entanglement to surpass classical sensing limitations. Its applications span various physical quantities, including electric and magnetic fields, temperature, and acceleration. Spins are ideal for magnetic field sensing, with Nitrogen-Vacancy (NV) centers in diamonds demonstrating high sensitivity. However, increasing spin concentration reduces memory time, limiting sensitivity unless specialized decoupling schemes are employed. While NV centers achieve sensitivities on the order of µT Hz⁻¹/² (single centers) and nT Hz⁻¹/² (ensembles), achieving pT Hz⁻¹/² requires specific protocols. Molecular spins offer an alternative with long coherence times even at room temperature and high spin concentrations, showing promise for quantum gates and algorithms. Their tailored ligands allow selective attachment to targets, making them useful for probing biological systems and functional surfaces. This research investigates the feasibility of using molecular spins in quantum sensing schemes, which has not been previously explored experimentally despite theoretical proposals.

The literature extensively covers the use of Nitrogen-Vacancy (NV) centers in diamond for quantum sensing of magnetic fields, reporting sensitivities ranging from µT Hz⁻¹/² for single NV centers to tens of nT Hz⁻¹/² for single spins using ODMR and dynamical decoupling. Ensemble NV centers offer advantages in signal strength but face memory time limitations with increasing spin concentration. Advanced decoupling schemes are necessary to overcome this. Record sensitivities of pT Hz⁻¹/² have been reported using auxiliary frequency tones without dynamical decoupling. Molecular spins, with their long coherence times and potential for tailored ligand attachment, have been studied for quantum computing applications, but their use in quantum sensing has been largely theoretical. This study addresses this gap.

Two molecular spin systems were investigated: oxovanadium (IV) tetraphenyl porphyrin (VO(TPP)) and the organic radical a, γ-bisdiphenylene-β-phenylallyl (BDPA). Samples were placed on a superconducting coplanar resonator (ν₀ ≈ 6.91 GHz) at 3K. A radiofrequency (RF) copper coil applied additional RF modulation synchronized with microwave (MW) pulse sequences (Hahn echo and Dynamical Decoupling). The sensing principle relies on phase accumulation induced by the RF field during the free spin precession time. The echo signal's phase variation correlates with the RF field's amplitude and phase. Experiments assessed the echo signal's dependence on RF field amplitude, phase, and the integral of the modulation. The symmetry of the RF modulation (even/odd n in νRF = n/(2τ)) was also investigated, along with its additivity over the free precession time (2τ). The protocol was extended to Dynamical Decoupling sequences (Periodic Dynamical Decoupling (PDD) and Carr-Purcell-Meiboom-Gill (CP)) to enhance sensitivity and explore the effect of the number of pulses. The sensitivity was estimated by determining the minimum detectable field for a unitary signal-to-noise ratio and bandwidth, considering the linear dependence of the echo phase on the RF field amplitude. Concentration sensitivity (Svol) was calculated by normalizing the sensitivity over the square root of the spin density.

The Hahn echo-based protocol demonstrated a linear relationship between echo phase and RF field amplitude for VO(TPP), allowing the estimation of a transduction coefficient (dϕecho/dBRF = 9.8 × 10⁻⁶ T⁻¹). A minimum detectable field of ≈10⁻⁵ T was estimated, consistent with Allan deviation analysis. The sensitivity was ≈6 × 10⁻⁶ T Hz⁻¹/², with an active sensing volume of ≈1.75 × 10⁻⁶ mm³ and concentration sensitivity (Svol) of ≈1.2 × 10⁻⁹ THz⁻¹/² µm³/². Dynamical Decoupling protocols (PDD and CP) improved sensitivity, reaching ≈10⁻⁶ T Hz⁻¹/². The sensitivity increased with the number of pulses up to a point where the inhomogeneity introduced by the RF coil caused a decrease in signal-to-noise ratio. These results compare favorably to those reported for NV centers and even slightly outperform those reported for defects in hexagonal Boron Nitride (hBN) or nanodiamonds. The achieved sensitivity was obtained using short sequences (4–5 pulses) without optical detection, and using samples with higher spin concentration than typically used in literature for solid-state defects. The analysis of the echo phase modulation with respect to RF phase confirmed the expected dependence based on the integration of the RF field during free precession and highlighted the effects of RF modulation symmetry.

The study successfully demonstrates quantum sensing using molecular spin ensembles. The achieved sensitivities are comparable to or better than those reported for NV centers, particularly considering the absence of optical readout and use of shorter pulse sequences. The higher spin concentrations used in this study potentially offer advantages. The linear dependence of echo phase on RF field amplitude, verified experimentally and theoretically, allows for accurate field estimations. The observed limitation of sensitivity at high pulse numbers in dynamical decoupling protocols highlights the trade-off between increased sensing time and dephasing effects caused by field inhomogeneities. This warrants further investigation into optimization of the RF field application and decoupling sequences. The success with both VO(TPP) and BDPA suggests broader applicability of the approach.

This work demonstrates the feasibility of quantum sensing using molecular spins, achieving sensitivities comparable to, and in some aspects exceeding, those of established NV-center-based sensors. The simplicity of the microwave-based detection, the short pulse sequences employed, and the potential for tailoring molecular interactions open exciting avenues for developing molecular-spin-based sensors. Future research should focus on optimizing the RF field application and exploring the potential for nanoscale sensing with single molecular sensors, investigating noise spectroscopy and multi-frequency field sensing.

The sensitivity enhancement using dynamical decoupling plateaus at higher pulse numbers due to increasing magnetic field inhomogeneities introduced by the RF coil. The study focuses on sensing monochromatic RF fields; extending to more complex signals will require further investigation. The current experimental setup may be further optimized to improve sensitivity and potentially reduce the number of pulses required.