Universal Optima of EIT-based quantum sensors for Rydberg RF-field detection

Electric field sensors based on thermal Rydberg atoms hold great potential as wideband RF field sensors, with Standard Quantum Limit (SQL) sensitivities at the pV/cm/√Hz level. Despite significant progress, experiments are still orders of magnitude away from achieving the SQL. We present an analytical and numerical study of one aspect of this shortfall: to find the universal optimum performance, under minimal assumptions, of electromagnetically induced transparency (EIT) based spectroscopy. We determine under what conditions EIT probing approaches the standard quantum limit, deduce the numerical inefficiency of EIT relative to Ramsey spectroscopy, and derive the optimal probing strengths for realistic experimental parameters. Our generalized model is not specific to Rydberg sensors, and is generally applicable to any quantum sensor that relies on EIT spectroscopy readout. As such, these results set a bound to how close such an EIT-probed quantum sensor can get to the SQL and what experimental resources are required to achieve it.