Fisher-Based Sensitivity Framework for Rydberg Atom Microwave Electrometry

Abstract

Fisher information provides a rigorous theoretical benchmark for evaluating quantum sensor sensitivity; however, a comprehensive framework for quantifying the fundamental limits of Rydberg-atom microwave electrometers remains lacking. In this work, we establish such a framework by deriving the Fisher information for slope detection and establishing its connection to sensitivity through signal-to-noise ratio, leading to an analytical expression jointly determined by photon shot noise and atomic response. Numerical implementation with real parameters in cesium vapor systems reveals a Fisher-optimized sensitivity below $\mathrm{nV\,cm^{-1}\,Hz^{-1/2}}$, highlighting a substantial potential for sensitivity enhancement in practical experiments through the suppression of technical noise. Importantly, the theory predicts that sub-nanovolt sensitivity is robust against moderate variations in system parameters, thereby delineating both the ultimate sensitivity and optimal operational regime of Rydberg-atom microwave electrometers.

Figures (3)

• Figure 1: (Color online) A schematic of RAME. Probe laser (input power $P_{\mathrm{in}}$) propagates through a vapor cell (length $L$), with transmitted power $P_{\mathrm{tr}}$. Microwave field (Rabi frequency $\Omega_s$) introduced via horn antenna sedlacek2012. Corresponding four-level atomic system configuration is detailed in Table \ref{['tab:table1']}.
• Figure 2: (Color online) Sub-nV Sensitivity in a Robust Operational Window. (a) Heatmap of Fisher information $F(\Omega_s)$ [Eq. (\ref{['eq:Ferr']})] versus reference microwave Rabi frequency $\Omega_0$ and coupling detuning $\Delta_c$, under $\Delta_p = \Delta_s = 0$. (b) comparison of two characteristic operation points at $\Delta_c = 0$ with vertical lines marking: Fisher information maximum at $\Omega_0^{\mathrm{F}}/2\pi = 11.860\,\mathrm{MHz}$ (dashed orange), and local microwave Rabi frequency $\Omega_0^{\mathrm{S}}/2\pi = 7.896\,\mathrm{MHz}$ (dashed black) in Ref. Jing2020. (c) Microwave field measurement sensitivity $\mathcal{E}_s$ [Eq. (\ref{['eq:sens']})] versus $\Omega_0$ at $\Delta_c = 0$ demonstrates a continuous operational regime (shaded region in (b,c) with a wide range of reference microwave Rabi frequency $\Omega_0/2\pi \sim [5,30]\,\mathrm{MHz}$) maintaining shot-noise-limited sub-nV sensitivity ($\mathcal{E}_s \leq 1.0\,\mathrm{nV\,cm^{-1}\,{Hz}^{-1/2}}$), with optimal performance $\mathcal{E}_s^{\mathrm{opt}} = 0.227\,\mathrm{nV\,cm^{-1}\,{Hz}^{-1/2}}$ (dashed orange vertical line). The legend for vertical lines in subplot (c) and its inset (identical to those in panels (b)) is positioned on the right side of (c). All parameters listed in Table \ref{['tab:table1']} replicate the experimental parameters from Ref. Jing2020.
• Figure 3: (Color online) Universal Optimization of Microwave Sensing Parameters. (a) 3D surface of Fisher information $\mathrm{max}_{\Omega_0}\{F(\Omega_s)\}$ maximized over reference microwave $\Omega_0$, mapped as functions of probe-to-coupling ratio $\Omega_p/\Omega_c$ and normalized coupling strength $\Omega_c/\Omega_c^{\mathrm{S}}$ under three-photon resonance ($\Delta_p=\Delta_s=\Delta_c = 0$). Gold circle marks local maxima along the ridge suggests optimal $(\Omega_p,\Omega_c,\Omega_0)$ configurations. (b,c) Parameter-optimized characteristics along decline the ridge in (a): optimal reference microwave Rabi frequency $\Omega_{0}^{\mathrm{opt}}$ and corresponding sensitivity $\mathcal{E}_s^{\mathrm{opt}}$, respectively. Shading band indicates robust operational window sustaining sub-nV sensitivity $\mathcal{E}_s^{\mathrm{opt}} \leq \mathcal{E}_s \leq 1.0\,\mathrm{nV\,cm^{-1}\,{Hz}^{-1/2}}$ as in Fig. \ref{['fig2']}(b,c). All configurations along the ridge in (a) achieve $\mathcal{E}_s^{\mathrm{opt}} <1.0\,\mathrm{nV\,cm^{-1}\,Hz^{-1/2}}$.