Investigating electromagnetically induced transparency spectral lineshape distortion due to non-uniform fields in Rydberg-atom electrometry

We investigate the effects of spatially non-uniform radio-frequency electric (E) field amplitudes on the spectral line shapes of electromagnetically induced transparency (EIT) signals in Rydberg atomic systems used in electrometry (i.e., the metrology of E-field strengths). Spatially non-uniform fields distort the EIT spectra from that of an ideal case, and understanding this distortion is important in the development of Rydberg atom-based sensors, as these distortions can limit accuracy and sensitivity. To characterize this distortion, we present a model that approximates the atom vapor as multi-layered media and then uses Beer's law to combine the absorption through its many discrete thin segments. We present a set of expected line distortions caused by various RF electric-field distributions found in practice. This provides an intuitive diagnostic tool for experiments. We compare this model to measured experimental atomic spectra in both two-photon and three-photon excitation schemes in the presence of non-uniform radio-frequency fields. We show that we can accurately model and reproduce the EIT lineshape distortion observed in these experimental data.