Long-Lived Mechanically-Detected Molecular Spins for Quantum Sensing

Abstract

Quantum sensors based on individual spins provide unprecedented access to local magnetic fields in condensed matter, chemistry, and biology, with solid-state defect spins emerging as the leading platform. However, their molecular-sensing capabilities are limited by confinement to a host lattice, which prevents placement in close proximity to a target molecule. Molecular spins offer an alternative, enabling chemical tunability and flexible positioning relative to the target system. Here we present a nanoscale sensing platform that combines molecular electron spins, ultrasensitive mechanical readout, and Hamiltonian engineering. Using a modified XYXY dipolar decoupling sequence, we suppress electron-electron dipolar interactions across a broad distribution of control fields, extending coherence times to $\sim 400~μ$s in an attoliter-scale droplet containing $\sim$100 trityl-OX063 radicals. Leveraging this sequence, we demonstrate frequency-selective detection of nanotesla-scale AC fields and perform sensing and spectroscopy of small, local nuclear-spin ensembles. Collectively, these results establish SQUINT (Spin-based QUantum Integrated Nanomechanical Transduction) as a framework for quantum sensing that affords molecular-level control over sensor properties and enables direct integration into complex molecular targets.

Figures (5)

• Figure 1: SQUINT sensing platform. (a) Optical image of the SiNW chip, showing an array of SiNW mechanical sensors fabricated along the chip edge. (b) Schematic of the sensing platform, including the SiNW oscillator, sample, polystyrene spacer, and current-focusing field gradient source (CFFGS). The bright red region indicates the spatial profile of the readout gradient. The molecules depicted inside the sample droplet are trehalose and trityl-OX063. Inset: Zoomed-in optical image of the tip of a SiNW, showing the polystyrene spacer and attached sugar droplet. (c) Molecular structure of the trityl-OX063 radical, with the central unpaired electron (red arrow) serving as the sensor spin. (d) Schematic of the correlation-based spin measurement protocol. The signal is obtained by correlating the readout-gradient-weighted longitudinal magnetization measured before and after a control sequence of duration $\tau_c$, with repeated measurement windows of duration $\tau_0$. Each measure block is comprised of the MAGGIC spin detection sequence Tabatabaei2024Haas2022Rose2018. (e) Distribution of electron Rabi frequencies for the sample used in this work, measured using the Fourier encoding scheme described in Rose2018Haas2022. The Rabi frequencies were generated by passing a peak current of $5$ mA through the CFFGS at the electron Larmor frequency.
• Figure 2: XYXYd sequence design and simulation. (a) Numerical evaluation of the dipolar rescaling factors $\Phi_{\parallel}(H_D)$ (red) and $\Phi_{\perp}(H_D)$ (blue) for a single $\hat{\mathbf{n}}$-primitive with $\tau_d = 800$ ns, showing a rescaling of $\Phi_* = -0.42$ at the center of the Rabi distribution ($u = 55$ MHz). Pulses labeled as $\hat{\mathbf{n}}_1\rightarrow\hat{\mathbf{n}}_2$ denote adiabatic half passages (AHPs) that map $\hat{\mathbf{n}}_1$ to $\hat{\mathbf{n}}_2$ on the Bloch sphere. The AHPs were 67 ns long, and designed using the optimal control protocol given in Ref. Tabatabaei2021. (b) Dipolar $|\Phi(H_D)|$ and resonance offset $|\Phi(H_\Delta)|$ suppression metrics for a single XYXYd block. (c) Measured XYXYd decay curves and associated exponential fits (solid lines) as a function of the total XYXYd time $NT$. (d) Pulse sequence used in (c), consisting of $N$ repetitions of an XYXYd block of duration $T$. (e) Phase-accumulation test used to rule out spin-locking. An effective $z$-field is introduced by applying a phase shift of $+\varphi/(8N)$ to each $\hat{\mathbf{x}}$-primitive and $-\varphi/(8N)$ to each $\hat{\mathbf{y}}$-primitive. The observed modulation in the signal as a function of $\varphi$ rules out spin-locking during the XYXYd sequence.
• Figure 3: Quantum sensing of external fields. (a) XYXYd-$N$ filter function magnitude as a function of normalized drive frequency $T\nu_m$, showing the first four filter function lobes. (b) Measured in-phase signal $C_I$ as a function of the drive frequency $\nu_m$ for $N=24$ repetitions of the XYXYd block ($T=1.780~\mu$s). The modulation was applied by passing a peak current of $I_\mathrm{pk} = 14.5~\mu$A through the CFFGS during the XYXYd sequence (inset). The corresponding ensemble-averaged RMS field, inferred from the distribution in (e), was 740(68) nT. (c) Measured in-phase signal for the $k=1$ lobe at different XYXYd repetitions. The $N\times I_\mathrm{pk}$ product was kept constant to keep the phase accrued by the electron the same at the center of the lobe. (d) In-phase and quadrature signals measured at the center of the first lobe as a function of the peak CFFGS current $I_\mathrm{pk}$. The quadrature signal was measured by changing the phase of the last AHP by $\pi/2$. (e) Longitudinal-field distribution $p(B_\mathrm{ext})$ of the ensemble for $1~\mu$A peak current, extracted from the Fourier transform of the data in (d). All solid lines in (a-d) are calculations using Eq. (\ref{['eq:CICQ']}) and the measured $B_\mathrm{ext}$ distribution (e). (f) Time-domain correlation-spectroscopy signal, (bottom) with and (top) without undersampling. The shaded curve represents the expected modulation $\propto \sum_{n=1}^4 \cos[2\pi \nu^{(n)} t]$. (g) The correlation spectroscopy pulse sequence. For the measurements in (f), we used $N=24$. (h) Power spectral density (PSD) of the undersampled data in (f), showing four peaks at the expected frequencies $\nu^{(n)}$ of the applied field. Zero-padding was used for visualization of the PSD. All measurements are taken with a $T = 1.780~\mu$s XYXYd duration. The shaded areas correspond to 68% confidence regions. All reported RMS fields have a common relative uncertainty of $9\%$.
• Figure 4: Nuclear spin sensing and spectroscopy using the XYXYd sequence. (a) Magnitude of the XYXYd filter function $\zeta_N(T\nu_{\mathrm{nuc}})$ as a function of $T$, with $\nu_{\mathrm{nuc}}$ evaluated at the ${}^1$H and ${}^{13}$C Larmor frequencies. The two lobes at $T = 1.563~\mu$s and $T = 1.847~\mu$s correspond to the $k=6,7$ harmonics of the ${}^{1}$H filter function, while the lobe at $T = 1.693~\mu$s corresponds to the $k=2$ harmonic for ${}^{13}$C. The separate vertical axes correspond to the ${}^1$H (red) and ${}^{13}$C (blue) nuclei. (b) Nuclear spin sensing measurements obtained by sweeping the XYXYd duration $T$ for different numbers of repetitions $N$. Echo suppression is observed when a filter-function harmonic is tuned to the ${}^1$H or ${}^{13}$C Larmor frequency. Solid lines in all panels denote simulations based on intramolecular ${}^1$H and ${}^{13}$C nuclei, unless stated otherwise. (c,d) Correlation signal measured with the XYXYd filter function placed at the ${}^1$H and ${}^{13}$C resonances, respectively, as a function of the number of XYXYd repetitions $N$. (e) Correlation spectroscopy pulse sequence, consisting of two XYXYd-$N$ blocks separated by a variable free-evolution time $t$. (f) Time-domain correlation signal measured at the ${}^1$H resonance. Similar to the external field sensing experiments, the data was intentionally undersampled to reduce the number of measurements. (g) Frequency spectrum of the ${}^1$H correlation signal reveals a hyperfine-broadened local lineshape relative to the independently measured bulk proton NMR spectrum (left inset). The solid curve in the inset depicts a Gaussian fit to the bulk proton lineshape. (h) Time-domain correlation signal for the ${}^{13}$C resonance, along with the corresponding frequency spectrum (lower inset). Right insets of (g) and (h): Spatial maps of the fractional contribution of each ${}^1$H and ${}^{13}$C nucleus on the OX063 molecule to the $t=0$ correlation signal, respectively. The total signal is normalized to 100%. All quoted spectral widths correspond to full widths at half maximum.
• Figure 5: Magnetic field and nuclear spin sensitivity. (a) Calculated minimum detectable longitudinal field amplitude $B_{\min}$ as a function of readout efficiency $\Lambda$ and acquisition time $\tau_{\mathrm{acq}}$, in order to achieve unit SNR. (b) Maximum sensor-nucleus separation $r_{\max}$ for unit SNR detection of a single proton spin using the $(t=0)$ XYXYd correlation spectroscopy sequence. The calculation assumes optimal orientation of the sensor-nucleus separation vector $\mathbf{r}$ relative to the static field. The hatched region in (a,b) indicates parameter regimes for which the single-shot SNR of the bare electron signal satisfies $\mathrm{SNR}_0 < 1$, making sensing with unit SNR unfeasible. In both panels, the black dashed line indicates the experimental readout efficiency for the $\mathop{\mathrm{\sim}}\nolimits 140$ sensor spin ensemble in this work ($\Lambda = 3.4$), and the solid line indicates the projected readout efficiency achievable with a single sensor spin using near-term improvements to the mechanical readout ($\Lambda = 12.4$). (c) An envisioned use case for nuclear-spin sensing: two sensor radicals placed near a molecular target interrogate nuclei in the target through hyperfine couplings. The red and blue surfaces depict the $\abs{\sin(2\theta)}$ orientation dependence of the pseudo-secular hyperfine coupling for the red and blue sensors, respectively, where $\theta$ is the angle between the sensor--nucleus separation vector $\mathbf{r}$ and the static field. The color intensity within the example target molecule (Lysozyme protein) illustrates the spatial dependence $\abs{A_1} \propto \abs{\sin(2\theta)}/r^3$ and is color-coded for each sensor. Dots denote the locations of $^{13}$C nuclei inside the target molecule.