Optimal atomic quantum sensing using electromagnetically-induced-transparency readout

Quantum sensors offer the capability to reach unprecedented precision by operating at the standard quantum limit (SQL) or beyond by using quantum entanglement. But an emerging class of quantum sensors that use Rydberg electromagnetically-induced transparency (EIT) to detect rf electric fields have yet to reach the SQL. In this work we prove that this discrepancy is due to fundamental limitations in the EIT probing mechanism. We derive the optimum sensitivity of a three-level quantum sensor based on EIT, or more generally coherent spectroscopy, and compare this to the SQL. We apply a minimal set of assumptions, while allowing strong probing fields, thermal broadening, and large optical depth. We derive the optimal laser intensities and optical depth, providing specific guidelines for sensitive operation under common experimental conditions. Clear boundaries of performance are established, revealing that ladder-EIT can not achieve the SQL due to unavoidable absorption loss. The results may be applied to any EIT-based quantum sensor, but we particularly emphasize our results' importance to the growing field of Rydberg quantum sensing.