Microwave polarimetry using multi-level Rydberg Spectroscopy in Ultracold Atoms

Rydberg atoms, with their valence electrons excited to high principal quantum numbers n, have emerged as versatile tools for quantum science. Their special properties—strong dipole–dipole and van der Waals interactions, large dc polarizability, long lifetimes and a dense ladder of microwave transitions—enable applications ranging from quantum simulation to precision electrometry and rf-polarimetry. 

Conventional Rydberg-EIT–based microwave electrometry provides a method to measure microwave fields across a broad frequency range, typically from MHz to THz. These are usually done in all-optical methods where the MW field is directly inferred from the Autler Townes splitting of the EIT resonance, or using interferometric methods where the MW antenna is heterodyned with a calibrated local oscillator - giving us the projection of the microwave field onto the LO’s polarization axis with a much higher sensitivity.  However, these are sensitive only to the projection of the field along the quantization axis. 3d polarimetry usually requires multiple LOs, precise calibration of their relative phases and amplitudes, or magnetic-field tuning to separate individual polarization components. These approaches become impractical in environments where microwave polarization varies significantly with frequency, as often occurs in cold-atom setups containing metallic structures near atoms. To address this, we introduce a self-calibrated scheme that extracts the full three-dimensional microwave polarization—including relative phases between the polarization components—using a single spectroscopic measurement that invloves all possible Zeeman sublevels of a Rydberg-Rydberg transition. By exploiting interference pathways between all allowed transitions, this method provides complete polarimetric information at a fixed microwave frequency, eliminating the need for frequency scans or multi-antenna arrangements. This capability is crucial for accurate electrometry in experimental platforms where microwave propagation is distorted by the surrounding hardware.