Atom-based radio-frequency field calibration and polarization measurement using cesium $nD_J$ Floquet states

We investigate atom-based electric-field calibration and polarization measurement of a 100-MHz linearly polarized radio-frequency (RF) field using cesium Rydberg-atom electromagnetically induced transparency (EIT) in a room-temperature vapor cell. The calibration method is based on matching experimental data with the results of a theoretical Floquet model. The utilized 60$D_J$ fine structure Floquet levels exhibit $J$- and $m_j$-dependent AC Stark shifts and splittings, and develop even-order RF-modulation sidebands. The Floquet map of cesium 60$D_J$ fine structure states exhibits a series of exact crossings between states of different $m_j$, which are not RF-coupled. These exact level crossings are employed to perform a rapid and precise ($\pm 0.5\%$) calibration of the RF electric field. We also map out three series of narrow avoided crossings between fine structure Floquet levels of equal $m_j$ and different $J$, which are weakly coupled by the RF field via a Raman process. The coupling leads to narrow avoided crossings that can also be applied as spectroscopic markers for RF field calibration. We further find that the line-strength ratio of intersecting Floquet levels with different $m_j$ provides a fast and robust measurement of the RF field's polarization.