Atomic electrometry based on heterodyne detection of microwave-induced optical phase shift in a Rydberg medium

The coherence established in a Rydberg medium through the electromagnetically induced transparency (EIT) process is significantly modified with the inclusion of a microwave (MW) field, leading to a dramatic change in the susceptibility. However, the majority of existing studies focus on the impact of the MW electric field (E-field) on the absorptive properties, while little experimental progress has been made in studying the MW-induced optical phase shift (MIOPS), a feature derived from the MW-dressed refractive index. Here we investigate this coherent effect by measuring the MIOPS of the probe laser in a Rydberg-EIT system in a ${}^{87}\mathrm{Rb}$ vapor cell. We illustrate the optical phase shift as a function of the MW E-field strength under various conditions and achieve a shift of 0.18 rad in the optical phase (corresponding to a variation of $4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ in the refractive index) with a MW E-field strength of 8 mV/cm. Moreover, we develop a MW sensor based on MIOPS and achieve a sensitivity of $92.4\phantom{\rule{0.2em}{0ex}}\mathrm{nV}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$ or $279.5\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{V}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}\phantom{\rule{0.2em}{0ex}}{n}^{2}$ when scaling the quantum number $n$ of the Rydberg states. Our experiment demonstrates a promising platform for studying nonlinear quantum optics in a MW-dressed Rydberg medium and opens the avenue for developing next-generation MW electrometry.