Fig. 3: PDTC-based a.c. magnetic field sensing.
a, Narrow-linewidth a.c. sensing: fidelity F (blue data points) is measured by sweeping the frequency fa.c. with Ba.c. = 8.24 μT and N = 4, keeping other parameters consistent with those in Fig. 1c. A sharp increase in the PDTC lifetime (and hence, fidelity) occurs at the resonance condition \({f}_{AC}={f}_{res}\). By contrast, the spin-lock sensing scheme introduced in ref. 54 (grey data points) lacks frequency selectivity. (i) Zoomed-in view into the resonance feature, showing a narrow linewidth Δℓ ≈ 70 mHz, determined by \({({T}_{2}^{{\prime} })}^{-1}\). Points (b)–(d) are marked on the spectral wing. (ii) Time-domain PDTC profiles of \(\langle {I}^{x}\rangle\) at points (a)–(d) in a and (i) at various offset frequencies from resonance. (a) Far off-resonance: fast signal decay, similar to bare PDTC case. (b) On resonance: substantially extended PDTC lifetime. (c) and (d) Slightly off-resonance, showing long lifetimes with beat pattern at frequency \(\delta f={f}_{AC}-{f}_{res}\), resulting in \({T}_{2}^{{\prime} }\)-limited a.c. sensing. Supplementary Section 4E discusses exploiting this for noise-rejected sensing: (π/2)y and θx pulses (~51.5 μs); γy pulse (~103 μs); τ (~36 μs). b, Robustness of the resonance feature to deviations in γy kick angle, γy = π − ϵ (colour bar). The fidelity baselines for different γy kick angles were offset by 2 × 10−2 to prevent overlap. Data show that the spectral width Δℓ remains independent of ϵ. Similar experimental mapping of the PDTC phase diagram with respect to γy is shown in Supplementary Fig. 2. (π/2)y and θx pulses (~52.25 μs); τ (~36 μs); γy pulse length scales linearly with its angle, with a π pulse (~104.5 μs). c, Tunable sensor profile for two-frequency sensing. Inset: sequence with two interspersed γy pulse blocks, leading to two resonance conditions: \({f}_{res}^{(1)}\) and \({f}_{res}^{(2)}\). Ba.c. = 32.96 μT. Main panel: measured frequency response (similar to a), showing a two-tone response centred at 208 Hz and 250 Hz, with a narrow linewidth Δℓ ≈ 5.5 Hz. (π/2)y and θx pulses (~50.25 μs); γy pulse (~100.5 μs). tacq ≈ 13.6 μs for c.
