Microwave electrometry with quantum-limited resolutions in a Rydberg atom array

Abstract

Microwave (MW) field sensing is foundational to modern technology, yet its evolution, reliant on classical antennas, is constrained by fundamental physical limits on field, temporal, and spatial resolutions. Here, we demonstrate an MW electrometry that simultaneously surpasses these constraints by using individual Rydberg atoms in an optical tweezer array as coherent sensors. This approach achieves a field sensitivity within 13% of the standard quantum limit, a response time that exceeds the Chu limit by more than 11 orders of magnitude, and in-situ near-field mapping with λ/3000 spatial resolution. This work establishes Rydberg-atom arrays as a powerful platform that unites quantum-limited sensitivity, nanosecond-scale response time, and sub-micrometer resolution, opening new avenues in quantum metrology and precision electromagnetic field imaging.

Figures (5)

• Figure 1: Microwave electrometry with Rydberg-atom array. (a) Schematic of the experimental setup. The atoms are loaded and imaged in the reservoir zone, while the MW measurement is performed in the target zone. A movable optical tweezer shuttles the atoms between the two zones. The insets show the trajectory of the shuttling tweezer and the relevant atomic levels. (b) Experimental sequence. In the target zone, each atom undergoes optical pumping (OP), Rydberg excitation via STIRAP, MW measurement, and state-selective de-excitation. The local pulse is applied for weak-field measurements. See text and Appendix \ref{['APD:apparatus']} for details. (c) Calibration of field-measurement schemes. The weak-field single-atom homodyne measurement results of the Rabi frequency $\Omega_\mathrm{S}$ of the signal field (purple circles) agree well with the fitting curve obtained from strong-field Rabi-oscillation data (cyan squares). (d) A representative single-atom homodyne measurement in the weak-field regime. (e) A typical Rabi oscillation in the strong-field regime. Error bars represent $1\sigma$ standard errors.
• Figure 2: Sensitivity approaching the standard quantum limit (SQL). Allan deviation of the measured electric-field amplitude $E=260nV\per cm$ is shown as the relative field uncertainty versus the averaging time $t$ (bottom axis) and the number of measurements $N$ (top axis). A solid line fit ($\propto N^{-1/2}$) to the data yields a single-atom, single-shot sensitivity of $\sigma_E = 3.98(3)µV\per cm$. The red dashed line marks the SQL of $\sigma_E^{\mathrm{SQL}} = 3.53(9)µV\per cm$.The small difference between $\sigma_E$ and $\sigma_E^{\mathrm{SQL}}$ is analyzed in Appendixes \ref{['APD:SQL']} and \ref{['APD:cali']}. The measured sensitivity corresponds to 545(4)nV cm^-1 Hz^-1/2 at the current measurement rate of 53Hz. The blue dotted line shows the projected sensitivity of 18.7nV cm^-1 Hz^-1/2 achievable at a 45kHz rate in the continuous operation mode. Error bars represent $1\sigma$ standard errors.
• Figure 3: Frequency response to an ultrafast pulse. (a) Single-atom homodyne measurements at signal frequency offset $\updelta f=0$ (cyan squares) and -100MHz (purple circles), with sinusoidal fits. (b) The normalized response plotted as a function of $\updelta f$. The measured spectral profile (red solid curve) exhibits a bandwidth exceeding the fundamental Chu limit for a classical antenna of comparable size (blue dashed curve) by 11 orders of magnitude. Inset: Full scan of the frequency response. Each data point represents the fitted amplitude $\updelta P$ obtained from sinusoidal fits as in (a). A sinc-type fit (solid curve) to the data yields a pulse duration of 9.4(2)ns, corresponding to a mainlobe width of 213(4)MHz. Error bars represent $1\sigma$ standard errors.
• Figure 4: In-situ measurement of sub-wavelength field distribution. (a) Rabi oscillations recorded via the population in $\ket{\uparrow}$. Sinusoidal fits yield Rabi frequencies of $\Omega_\mathrm{A} = 2\pi \times 3.187(1)MHz$ and $\Omega_\mathrm{B} = 2\pi \times 3.160(1)MHz$ for atom A ($x = 0µm$) and atom B ($x = 224µm$), respectively. The oscillations accumulate a measurable phase shift of approximately 0.4 periods over 47 Rabi cycles. (b) Spatial map of the relative field strength. The local Rabi frequency at each position $(x, y)$ is determined from a sinusoidal fit to the continuous Rabi oscillation. The color scale represents the normalized field variation $\zeta(x, y)$.
• Figure 5: Ultrafast pulse spectra reconstructed by receivers with different bandwidths. The 10-ns signal pulse exhibits a sinc-type spectrum with mainlobe width 200MHz (purple solid curve), which is filtered by sensors with comparable (blue dashed curve) or significantly lower bandwidth (cyan dotted curve). The measured data fall close to the spectrum of the original signal, indicating a bandwidth of $\gg200MHz$.