Microwave electrometry with Rydberg atoms in a vapor cell using microwave amplitude modulation

Abstract

We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagnetically induced transparency (EIT) - Autler-Townes (AT) splitting spectra obtained using amplitude modulation of the microwave (MW) electric field. In addition to the two zero-crossing points interval $\Delta f_{\text{zeros}}$, the dispersion signal has two positive maxima with an interval defined as the shoulder interval $\Delta f_{\text{sho}}$, which is theoretically expected to be used to measure a much weaker MW electric field. The relationship of MW field strength $E_{\text{MW}}$ and $\Delta f_{\text{sho}}$ are experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively. The results show that $\Delta f_{\text{sho}}$ can be used to character the much weaker $E_{\text{MW}}$ than that of $\Delta f_{\text{zeros}}$ and the traditional EIT-AT splitting interval $\Delta f_{\text{m}}$, the minimum $E_{\text{MW}}$ measured by $\Delta f_{\text{sho}}$ is about 30 times smaller than that by $\Delta f_{\text{m}}$. As an example, the minimum $E_{\text{MW}}$ at 9.2 GHz that can be characterized by $\Delta f_{\text{sho}}$ is 0.056 mV/cm, which is the minimum value characterized by frequency interval using vapour cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of $E_{\text{MW}}$ measured by spectral frequency interval, which is important in the direct measurement of weak $E_{\text{MW}}$.