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

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) field. In addition to the two zero-crossing points, the dispersion signal has two positive maxima with an interval defined as the shoulder interval of the dispersion signal $\Delta f_{\text{sho}}$. The relationship of MW field strength $E_{\text{MW}}$ and $\Delta f_{\text{sho}}$ are studied at the MW frequencies of 31.6 GHz, 22.1 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 the interval of two zero-crossing points $\Delta f_{\text{zeros}}$ 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 $E_{\text{MW}}$.