Quantum sensing of time-dependent magnetic signals with molecular spins

Abstract

Molecular spins offer a promising platform for quantum sensing, particularly in organic, supramolecular or biological environments.. Recognition of the signals by these systems is of particular interest, given their possible integration into more complex structures and their possible use as sensors in close proximity to analytes. In this work, we develop two quantum sensing protocols that enable discrimination between different time-dependent magnetic field, without requiring its periodicity or specific matching conditions with the microwave manipulating sequence. These are based on the Hahn echo sequence and have been tested on VO(TPP) and VOPt(SOCPh$)_{4}$ molecular spins embedded in a superconducting YBCO microwave resonator. We report a magnetic field sensitivity up to a few $10^{-7}$ T Hz$^{-\frac{1}{2}}$ (with lower bounds approaching $10^{-8}$ T Hz$^{-\frac{1}{2}}$) for signals with duration of a few microseconds. Under the given conditions, the minimum signal area that can be measured is in the $10^{-10}$ T s range, suggesting a potential trade-off between minimum measurable field and the required signal duration and memory time.

Figures (5)

• Figure 1: (a) YBCO superconducting coplanar resonator used to deliver the MW pulses, $B$1,MW. The sample is placed in the middle of the resonator and it is surrounded by a RF copper coil used to deliver the external magnetic field to be measured, $B$1($t$). The static field, $B_0$, is applied along the longitudinal axis of the resonator. Figure reproduced from bonizzoniQuantumSensingMagnetic2024 under CC license. (b) Molecular structures of VO(TPP) (left) and VOPt(SOCPh)4 (right). The picture of the VO(TPP) molecule is adapted from bonizzoniNPJQUANT2020 under CC license. (c) Sequence 1: the two MW pulses (blue) are used to generate an echo, and the interpulse delay $\tau$ is changed step-by-step while the position of the magnetic field signal, s, is held fixed. (d) Sequence 2: the interpulse delay is kept fixed while the position of the magnetic field signal is swept across the whole sequence by increasing $s$ step-by-step. In both (c) and (d), the phase accumulation is proportional to the difference between the signal areas remaining before and after the $\pi$ pulse (opposite phase precession sign is represented with red and green shaded areas).
• Figure 2: Sequences 1 and 2 performed on VO(TPP) at 2-3.5 K and at a fixed value of the static field $B$0. The protocols are tested with a Gaussian signal (a,b) or with a rectangular signal (c). (d,g) Phase accumulation measured for different amplitudes, $B$1,max, of the Gaussian signal for Sequence 1 (d) and 2 (g). (e,h) Phase accumulation measured when the central position, $t$0, of the Gaussian signal is changed in both sequence 1 (e) and 2 (h). (f, i) The amplitude, $B$1,max, of the rectangular signal is changed in both Sequence 1 (f) and 2 (i). In all panels experimental data are shown with dots, while solid lines represent calculated curves obtained with Eq. \ref{['eq:phase2']}.
• Figure 3: Tests performed with Sequence 2 on VOPt(SOCPh)4 at $3-3.5K$ and at a fixed static field ($B_0$). A gaussian (a,b,c) and a rectangular (d) signal are used. Phase accumulation (e,f,g) measured when the amplitude $B$1,max (e), the central position $t$0 (f) and the width $\sigma$ of the Gaussian signal (g) are progressively increased. (h) Phase of the echo measured for different amplitudes $B$1,max of a rectangular pulse signal. In all panels, the dotted traces represent experimental points, while the solid lines represent calculated curves obtained according to Eq. \ref{['eq:phase2']}).
• Figure 4: Phase accumulation of the echo obtained with sequence 2 on VOPt(SOCPh)4 for differently shaped external signals (sketched in inset): (a) Sawtooth, (b) Square Wave + Gaussian, (c) Double Gaussian, (d) Asymmetric Double Gaussian. The experimental data are shown as red dots. The solid blue lines represent calculated curves obtained with the corresponding external signal parameters in Eq. \ref{['eq:phase2']}.
• Figure 5: Detectable areas (blue shaded) that can be measured using Sequence 1 and Sequence 2 depending on the duration of the time-domain signal and on its field strength. The solid curves represent the the minimum measurable area with the VOPt(SOCPh)4 sample and using a Gaussian signal for Sequence 1 (red line) and for Sequence 2 (blue line). The signal duration is taken as $3\sigma$ (with $\sigma$ being the Gaussian width in Eq. \ref{['eq:Gaussian']}). The limit in signal duration ($T$lim) imposed by the memory time of the sample is shown by vertical lines for Sequence 1 (dashed line) and Sequence 2 (dashed-dotted line). The markers correspond to the Gaussian signal generated by the dipolar field of a $S$ = 1/2 spin located at a distance $d$ from the sensor and undergoing a full rotation (triangle: $\sigma$ = 130 ns, $d$ = 1.8 nm; square: $\sigma$ = 1.6 $\mu$s, $d$ = 4.4 nm).