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Electromagnetically-induced-transparency (EIT) spectroscopy has been used asa sensitive sensor in quantum metrology applications. The sensitivity of asensor strongly depends on the measurement precision of EIT spectrum. In thiswork, we present a theoretical study of the spectral lineshape measurement on athree-level $\Lambda$-type EIT media based on Fisher information (FI) analysis.Using two kinds of probing source: the single-photon Fock state and thecoherent state, we calculate the FI in an EIT medium and quantify the quantumadvantage and limitations of the single-photon probe. The analysis of FIstructure also provides a clear picture to classify the spectral lineshape intotwo different regimes, the EIT and Aulter-Townes splitting (ATS). This workprovides a systematic analysis of the single-photon EIT spectrum, whichprovides essential knowledge of quantum sensing based on EIT and deepens ourunderstanding of spectral characteristics of $\Lambda$-type media.

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