Simultaneous SI-traceable measurement of the amplitude and the ellipticity of microwave fields with cold Rydberg atoms

We present a method for the simultaneous measurement of the amplitude and the ellipticity of microwave fields using trap-loss spectroscopy based on Rydberg excitation of a cold ensemble of 87Rb atoms. The measurement consists of probing the energy spectrum of the $61S_{1/2}$ to $61P_{1/2}$ transition in the presence of microwave, which depends on the electric field amplitude $|E|$ and the third Stokes parameter $|S_3|$. We use a millimeter-size magneto-optical trap to perform strongly-localized measurements, which mitigates the effect of microwave field inhomogeneities. This allows us to work with large Rabi frequencies and thus resolve small deviations from linear or circular states of polarization. Taking into account the effect of non-resonant couplings to neighboring Rydberg states, we measure $|E|$ and $|S_3|$ with an accuracy on the order of 1 percent in the Autler-Townes regime where the measurements can be traced to the international system of units. By studying the visibility of the spectral features as a function of the polarization of the excitation laser beams, we extract some information on the angle of arrival of the microwave field onto the atoms, with good agreement between theory and experiment.