Robust AC vector sensing at zero magnetic field with pentacene

TL;DR

The paper presents a room-temperature, zero-field vector AC magnetometer based on photoexcited pentacene triplet spins in a naphthalene crystal. By leveraging two crystallographic orientations, it reconstructs the full 3D microwave field from orientation-specific Rabi frequencies, and it introduces a rotary-echo protocol to protect driven-state coherence and boost sensitivity. The demonstrated sensitivity is around 1 μT/√Hz with sub-micrometer spatial resolution, approaching established solid-state sensors while offering zero-field operation advantages. The work highlights the versatility of molecular spin systems for scalable quantum sensing and lays groundwork for future chemical tunability and dense spin-network implementations.

Abstract

Quantum sensors based on electronic spins have emerged as powerful probes of microwave-frequency fields. Among other solid-state platforms, spins in molecular crystals offer a range of advantages, from high spin density to functionalization via chemical tunability. Here, we demonstrate microwave vector magnetometry using the photoexcited spin triplet of deuterated pentacene molecules, operating at zero external magnetic field and room temperature. We achieve full three-dimensional microwave field reconstruction by detecting the Rabi frequencies of anisotropic spin-triplet transitions associated with two crystallographic orientations of pentacene in naphthalene crystals. We further introduce a phase alternated protocol that extends the rotating-frame coherence time by an order of magnitude and enables sensitivities of $1~μ\mathrm{T}/\sqrt{\mathrm{Hz}}$ with sub-micrometer spatial resolution. These results establish pentacene-based molecular spins as a practical and high-performance platform for microwave quantum sensing, and the control techniques are broadly applicable to other molecular and solid-state spin systems.

Figures (4)

• Figure 1: Experimental setup and pentacene properties. (a) Crystal structure of pentacene-doped naphthalene, where $a$, $b$, and $c$ denote the crystallographic axes. The cleaved surface corresponds to the $ab$-plane. (b) Pentacene molecules substitute into two inequivalent lattice sites of the naphthalene host, giving rise to two crystallographically distinct molecular orientations. Both orientations share a common molecular long axis (defined as the $X$-axis), which lies in the $ac$-plane and is tilted by approximately $10^{\circ}$ from the $c$-axis. The local molecular frames are denoted $X OY_1$ and $X O Y_2$, where $Y_1$ and $Y_2$ lie along the short molecular axis within the molecular plane. The Hamiltonian in Eq. \ref{['eq:hamiltonian_mole']} is expressed in this molecular frame. The $Y_1-$ and $Y_2-$ axes are symmetrically split about the $ac$-plane by $47^{\circ}$. For convenience, we define an orthonormal sensing frame $X Y' Z'$, where $X$ coincides with the molecular long axis, $Z'$ is aligned with the crystal $b$-axis, and $Y'$ bisects the angle between $y_1$ and $y_2$. (c) Schematic of the experimental setup showing the crystal cleavage plane ($ab$-plane). The $a$- and $b$-axes can be identified independently Quan2023. Microwave excitation is delivered using a coplanar-waveguide stripline, and optical excitation (532 nm, 0.1 mW) and readout are performed with a confocal microscope. (d) Energy-level diagram of pentacene and relevant inter-level transitions. Green and orange arrows denote optical excitation and fluorescence, respectively, while gray arrows represent the non-radiative intersystem crossing (ISC) processes. The ISC coupling to the $T_X$ sublevel is stronger than to $T_Y$ or $T_Z$. Microwave fields can drive transitions between the triplet spin-states. (e) Optically detected magnetic resonance (ODMR) spectra of the $T_X \leftrightarrow T_Z$ and $T_Y \leftrightarrow T_Z$ transitions measured at zero magnetic field. The linewidths are obtained from Lorentzian fitting.
• Figure 2: Vector AC sensing using two pentacene orientations. (a) Experimental pulse sequence for ODMR and Rabi sensing. The green and blue blocks denote optical initialization and photon collection, respectively. An optional, short ($\sim100$ ns) flip pulse maps the initial $T_X$ state to $T_Y$ when we target the $T_Y \leftrightarrow T_Z$ transition. After applying the continuous target driving $\Omega_t$, optical readout is performed following a delay time $t_d$, during which the triplet sublevels relax at different rates, generating fluorescence contrast between spin states. A post-detection delay time $T_D$ is needed after each PL measurement to reset the population, yielding the total sequence time $T\approx 500\mu$s. (b–d) Optically detected Rabi oscillations of the $T_X \leftrightarrow T_Z$ (b) and $T_Y \leftrightarrow T_Z$ (c) transitions, and their corresponding Fourier spectra (d). Purple and gray curves show the $T_X \leftrightarrow T_Z$ and $T_Y \leftrightarrow T_Z$ transitions, respectively. The Rabi frequencies are proportional to the projection of the applied AC magnetic field onto the relevant molecular axis (inset), e.g., $\Omega_{Y_1} = \gamma_e B_{Y_1}$. Error bars reflect photon shot noise and are obtained by propagating the standard deviation of the measured photon counts through signal normalization.
• Figure 3: Pentacene coherence under continuous driving. (a) Microwave pulse sequence for spin locking and measured longitudinal relaxation times $T_{1\rho}$ at varying driving amplitudes. Each point results from fitting an exponential decay on the spin-locking signal for varying MW driving duration. The decay rate $1/T_{1\rho}$ reflects the longitudinal noise spectrum $S_Z(\nu)$ evaluated at the driving strength. (b) Rabi relaxation time $T_{2\rho}$ (sequence in Fig. \ref{['fig:2']}.a) as a function of the driving amplitude. The decrease in $T_{2\rho}$ at weak drive arises from magnetic-field fluctuations and hyperfine-induced spectral broadening, while the reduction at strong drive is dominated by microwave-amplitude noise. Error bars represent the 95% confidence intervals of the damped Rabi oscillation fit.
• Figure 4: Rotary-echo sensing protocol. (a) Experimental sequence for sensing. The RE control sequence consists strong microwave driving of amplitude $\Omega_c$ with $\pi$ phase flips after each multiple of $\tau$. The target signal to be sensed is continuously applied $\Omega_t$. The flip pulse is still for $T_Y\leftrightarrow T_Z$ transition only. (b) Rabi oscillations without (purple) and with (gray) the control sequence on the $T_X \leftrightarrow T_Z$ transition performed at a target Rabi frequency of $0.17 ~(2\pi) \mathrm{MHz}$. Here the normalized signals are centered around zero for clear comparison of the coherence and contrast between the two scenarios. (c) Decay time, $T_{2\rho}$, versus target field amplitude, $\Omega_t$, in the case of no-control and RE (with $\Omega_c = 2.625 ~(2\pi)\mathrm{MHz}, \tau = 390 ~\mathrm{ns}$). Note that in the case of weak driving, the RE control vastly lengthens the coherence time--about an order of magnitude longer than the simple Rabi driving.