Simple broadband signal detection at the fundamental limit

Abstract

Broadband detection of a weak oscillatory field with unknown carrier frequency underlies magnetometry, axion searches and gravitational-wave sensing. We show that the Grover-like integration-time lower bound for this task is a geometric corollary an upper bound on the integrated quantum Fisher information, a metrological constraint. We further give an all-analog multi-resonant protocol based on a randomized Su-Schrieffer-Heeger control Hamiltonian and an m-register GHZ probe and verify near-optimal scaling through simulation.

Figures (2)

• Figure 1: Simple broadband sensing by internal band engineering. a) An incoming AC magnetic field field excites a transition from the ground state ($\ket{g}$) to an excited state ($\ket{e}$). b) Broadband sensing. Vertical dashed lines indicate engineered transition frequencies $\{\omega_i\}$ spanning $\Delta\omega$, approximating a grid of spacing $\sim mB_{\min}$ (solid lines). Each resonance contributes a broadened Rabi response of width $\sim mB$ (inset). A randomized construction may require a mild $\log r$ oversampling to avoid rare large gaps (see End Matter).
• Figure 2: Simulated stopping time $T$ for the all-analog broadband protocol versus the predicted scale $X=\sqrt{|\Delta\omega|}/(mB_{\min})^{3/2}$ [Eq. \ref{['eq:time']}]. For each $(m,B_{\min},\Delta\omega)$ we draw $\omega\sim\mathop{\mathrm{Unif}}\nolimits(\Delta\omega)$ and report the mean and standard deviation of the smallest $T$ for which a fixed GHZ-diagonal population statistic exceeds a preset $L_1$ threshold (see End matter for more details). Time evolution uses a three-harmonic Floquet truncation; filled markers use a fast GHZ evaluation, while open markers show brute-force tensor-state validation at small $m$. We take $\omega_{\min}=100\,\mathrm{MHz}$ and $|\Delta\omega|\gg mB_{\min}$. The black line is unit slope to guide the eye. Inset: minimum normalized witness density $\min_{\omega}s_\omega/\bar{s}$ versus $\Delta\omega/B$ (equivalently, a flatness certificate against deep spectral holes, see the main text).