Hybrid-spin decoupling for noise-resilient DC quantum sensing

Abstract

The excellent sensitivities of quantum sensors are a double-edged sword: minuscule quantities can be observed, but any undesired signal acts as noise. This is challenging when detecting quantities that are obscured by such noise. Decoupling sequences improve coherence times and hence sensitivities, though only AC signals in narrow frequency bands are distinguishable. Alternatively, comagnetometers operate gaseous spin mixtures at high temperatures in the self-compensating regime to counteract slowly varying noise. These are applied with great success in various exotic spin-interaction searches. Here, we propose a method that decouples specific DC fields from DC and AC magnetic noise. It requires any spin cluster where the effect on each individual spin is different for the target field and local magnetic fields, which allows for a different approach compared to comagnetometers. The presented method has several key advantages, including an orders-of-magnitude increase in noise frequencies to which we are resistant. We explore electron-spin nuclear-spin pairs in nitrogen-vacancy centres in diamond, with a focus on their merit for light dark-matter searches. Other applications include gradient sensing, quantum memory, and gyroscopes.

Figures (5)

• Figure 1: Protocol. a In a diamond lattice, a substitutional nitrogen atom and a neighbouring missing carbon atom form a nitrogen-vacancy (NV) centre. The negatively charged NV centre has an electron spin, while the nitrogen atom has a nuclear spin. b Energy level diagram for the electron spin of the NV centre only for simplicity (not to scale). Spin-1 systems have a splitting at zero field, while a magnetic field $B$ splits its $\ket{\pm1}$ states, and hyperfine coupling splits these further depending on the state of the nuclear spin. c Graph of the proposed protocol. Swap gates allow both spins to contribute to the sensing result. d Example pulse sequence to implement the graph from c. A green laser initialises the electron spin, and a microwave (MW) creates a superposition. After an initial interaction delay, the state is swapped to the nuclear spin, and later it is swapped back. Swaps are possible by using three controlled-not gates using the hyperfine splitting, an example is indicated with the cyan arrow for a transition in b. Finally, the final state of the electron spin is read with a MW and laser pulse. Not to scale, notably generally $\tilde{\tau}_e \ll \tilde{\tau}_N$.
• Figure 2: Coherence. a Normalised $h_n$ versus different correlation times $\tau_c$ of the noise, for various $n$. The gyromagnetic ratio of the electron spin and the $^{14}$N nuclear spin are used, and the fine-tuning condition of \ref{['eq:fine-tuning']} is applied. Dashed lines represent the asymptotic behaviours in the three regimes of $\tau_c$. b Simulated decays for $4$ different $n$s with pink noise. The magnitude of the noise is chosen to limit the coherence time within the simulation time window. c Dependence of the coherence time on $n$. Given \ref{['eq:sigma_exp']}, for noise following $\tau_c \gg \tilde{\tau}_N$, the coherence time is proportional to $n^{0.68}$ (red line). For white noise, which is most similar to $\tau_c \ll \tilde{\tau}_e$, the coherence time is nearly independent of $n$ (red dashed-dotted line). For pink noise, a mixture of regimes applies, which results in a more complex dependency (red dashed line).
• Figure 3: Noise. a. The noise contribution [calculated via \ref{['eq:G']}] in the hybrid-spin decoupling protocol as a function of the angular frequency $\omega$ for a white noise profile. The $y$-axis is normalized for demonstration. b. For $n=4$, the effect of several swap-gate lengths is calculated. For realistic lengths (${\tilde{t}_{\mathrm{sw}}^{}}\sim\tau_N/80$), the effect is negligible. c Simulation results for $n=1$ with a fixed difference in magnetic fields between the two spins, thus like a DC gradient field. The projection of the phase is plotted for each time during the sequence of Fig. \ref{['fig:protocol']}d between the two $\pi/2$-pulses. For clarity, $\gamma_N=-0.5\gamma_e$ is used, so $\tau_N=2\tau_e$. The different lines are for different mutual DC magnetic fields at each spin, which could be DC noise. The DC gradient in magnetic field is detected. d Five example simulation results for four different repetitions $n$, with pink noise added. The noise is randomly set before a simulation, thus each simulation has different noise. e For each $n$, a simulation is run $500$ times, and the uncertainty in the readout signal (e.g. final data points in d) is plotted; the inset gives an example for finding this uncertainty for $n=1$. The fit shows a decrease in uncertainty with an increase in $n$.
• Figure 4: Prospected dark matter constraints. a. Constraints on the axion decay constant vs axion mass as set by various experiments on earth Adelberger:2006dhBloch:2021vnnBloch:2022kjmXu:2023vfnWei:2023rzsGavilan-Martin:2024nlo (coloured dashed lines OHare:2020), including recent work with comagnetometers (green dashed line) which includes over two months of collected data Gavilan:2025. Our potential constraints with a current state-of-the-art ensemble sample ($10^{12}$ NVs) for a one-month long measurement is plotted in black. The dotted line indicates the Ramsey result from previous work Chigusa:2024psk, which is affected by noise. The solid line is for the presented work, which negates this magnetic noise. Finally, the dashed line is when utilising the potential increase in coherence time for large $n$ at low temperature. b The current best constraint based on neutron stars, K-$^3$He comagnetometers, ChangE and SN1987A Lella:2023bfb (grey dashed-dotted line) is compared with potential future experiments JacksonKimball:2017elrWu:2019exdGarcon:2019inhBloch:2019lcyGao:2022nuqBrandenstein:2022eif (coloured dashed lines OHare:2020). For our prospects, we look at a large sample ($10^{20}$ NVs) for a year-long measurement. This illuminates that the resilience to noise becomes more important when the sensitivity becomes better.
• Figure 5: Comparison of sensitivities to the axion-electron coupling between the Ramsey (dashed) and hybrid-spin decoupling (solid) protocols under external magnetic noises. Also shown by dash-dotted lines are the projection noise-limit sensitivities in Chigusa:2023roq. The orange and blue dashed lines represent the existing constraints from red giant stars Capozzi:2020cbu and solar axion searches at XENONnT XENON:2022ltv.