Broadband Heterodyne Microwave Detection using Rydberg Atoms with High Sensitivity

TL;DR

The paper addresses precise microwave electric-field sensing with broad bandwidth using Rydberg atoms in a vapor cell. It introduces a dual-tone heterodyne scheme that combines resonant Autler-Townes splitting with far-off-resonant AC Stark shifts to achieve continuous frequency coverage up to $3~\mathrm{GHz}$ while preserving high sensitivity. The method delivers a minimum detectable field of $2.4~\mu\mathrm{V/cm}$ and a sensitivity of $760~\mathrm{nV/cm/\sqrt{Hz}}$, with a dynamic range up to about $90~\mathrm{dB}$ when exploiting AT splitting with a single strong MW field. This approach provides a practical platform for high-precision electric-field metrology, spectrum monitoring, and EMC testing, leveraging beat-note spectroscopy and self-calibrating AT measurements.

Abstract

We present a Rydberg atom-based microwave electric field sensor that achieves extended dynamic range and enhanced sensitivity across a broad bandwidth. By characterizing the Autler-Townes (AT) splitting induced by a single-tone microwave field, we demonstrate a spectroscopic method that simultaneously extracts both the microwave frequency and electric field strength directly from the splitting pattern. We implement dual-tone heterodyne detection, achieving a minimum detectable field strength on the order of uV/cm and a sensitivity in the sub-uV/cm/Hz^1/2 regime, while extending the operational bandwidth up to 3 GHz. Through systematic characterization of frequency and power dependencies, we identify optimal operating conditions to minimize power broadening in the resonant AT regime and maximize sensitivity in the far-off-resonance AC Stark regime. The resulting platform combines high sensitivity, broad bandwidth, and a dynamic range of approximately 90 dB, establishing Rydberg atoms as practical sensors for precision electric field metrology.

Figures (5)

• Figure 1: (a) Energy level diagram for $^{87}\rm{Rb}$. Atoms are excited to the $|53D\rangle$ Rydberg states from the ground state $|5S_{1/2}\rangle$ via the intermediate state $|5P_{3/2}\rangle$. Two MW fields with different powers and frequencies are applied, which drive the transition to the target states $|54P_{3/2}\rangle$ (14.23 GHz) and $|52F\rangle$ (15.59 GHz). The stronger microwave field is designated as the LO field, while the weaker one serves as the signal field for measuring the minimum detectable electric field. The LO frequency is tuned to the transition between the $|53D_{5/2}\rangle$ state and either the $|54P_{3/2}\rangle$ or $|52F\rangle$ state, with a detuning of $\Delta_{LO}$. The signal field frequency is then offset from the LO frequency by a beat frequency difference of $\Delta_{beat}$. (b) Schematic of the experimental setup. The probe field is frequency-locked using saturation absorption spectroscopy, while the coupling field scans across the $|53D\rangle$ states. The MW fields are generated by two separate signal generators, combined using a power combiner, and emitted from a horn antenna. A separate reference cell, denoted as the Ref. Cell, is used for laser frequency calibration.
• Figure 2: Autler-Townes splitting of Rydberg-EIT spectra. (a) EIT transmission as a function of coupling laser detuning and MW frequency for the $|53D\rangle$$\rightarrow$$|54P_{3/2}\rangle$ transition. The panel also displays the spectral lines corresponding to the resonant MW frequencies of 14.231 GHz and 14.153 GHz. (b) EIT and AT splitting spectra with a fixed MW frequency of 14.231 GHz. The splitting of 54 MHz is observed, corresponding to an electric field strength of 12 mV/cm. The red solid line represents a field strength of 1.8 mV/cm ($\Omega_{MW}/2\pi=8.5$ MHz), where the splitting is unresolvable. (c) Spectra obtained with the probe laser intensity reduced by a factor of 5. This adjustment reduces power broadening of the EIT linewidth, allowing the 1.8 mV/cm field to be resolved.
• Figure 3: Rydberg EIT spectra with beat signals measured under different field strengths. (a) Beat signal spectra as a function of LO field strength, with a fixed signal field strength of 1.9 mV/cm. (b) Beat signal spectra versus signal field strength, with a fixed LO field strength of 9.7 mV/cm. In these measurements, the beat frequency was set to $\Delta_{beat} = 7$ kHz to ensure clear resolution of the beat signals. The legend in (a) represents the LO field strength and that in (b) indicates the relative strength of the signal field, where 0 dB corresponds to the 1.9 mV/cm, determined from the AT splitting. (c) FFT of the probe transmission for different signal field strengths. These beat-note measurements were performed with fixed probe and coupling laser frequencies. The beat frequency was fixed at $\Delta_{beat}=50$ kHz. In the rightmost panel, the estimated signal field strength of 6.1 $\mu$V/cm yields a beat signal with an SNR of 16 dB.
• Figure 4: (a) Beat-note SNR with varied beat frequency, $\Delta_{beat}$. The signal decay at higher $\Delta_{beat}$ indicates a maximum detectable frequency difference of approximately 6 MHz. (b) The detectable range of varying the LO field frequency with $\Delta_{beat}=50$ kHz. Detuning 0 MHz was defined as the frequency of the transition from $|53D_{5/2}\rangle$ to $|54P_{3/2}\rangle$. Results show a detectable tuning range of 3 GHz (SNR $\geq 10$ dB) and a nearly constant high-sensitivity range of 2.2 GHz (SNR $\geq 40$ dB). (c) Beat-note SNR as a function of LO field strength. The optimal LO field strength varies between the resonant AT transitions ($54P$ and $52F$) and the AC Stark transition (detuned by 500 MHz and 800 MHz from the $54P$ state).
• Figure 5: Beat-note SNR as a function of signal electric field strength. Black circles correspond to the resonant AT transition ($54P$), while gray squares represent the AC Stark transition (detuned by 500 MHz from the $54P$ state). The electric field strength is derived from the measured AT splitting (right axis), indicated by the red solid circles.