Fisher information analysis for quantum-enhanced parameter estimation in an electromagnetically-induced-transparency spectrum with single photons

Electromagnetically induced transparency (EIT) spectroscopy has been used for the development of sensitive sensors for quantum metrology applications. The sensitivity of a sensor is strongly dependent on the measurement precision of the EIT spectrum. In this work, we present a theoretical study of spectral lineshape measurement of three-level Λ-type EIT media based on Fisher information (FI) analysis. Using two kinds of probing sources, the single-photon Fock state and the coherent state, we calculate the FI in an EIT medium and quantify the quantum advantage and limitations of the single-photon probe. The analysis of the FI structure also provides a clear picture for classifying the spectral lineshape into two different regimes, EIT and Aulter-Townes splitting (ATS). This work provides a systematic analysis of the single-photon EIT spectrum, which provides essential knowledge of quantum sensing based on EIT and deepens our understanding of the spectral characteristics of the Λ-type media.