Beyond Photon Shot Noise: Chemical Limits in Spectrophotometric Precision

Abstract: In this work, we investigate precision limitations in spectrophotometry (i.e., spectroscopic concentration measurements) imposed by chemical processes of molecules. Using the recently developed Photon-resolved Floquet theory, which generalizes Maxwell-Bloch theory for higher-order measurement statistics, we analyze a molecular model system subject to chemical reactions whose electronic and optical properties depend on the chemical state. Analysis of sensitivity bounds reveals: (i) Phase measurements are more sensitive than intensity measurements; (ii) Sensitivity exhibits three regimes: photon-shot-noise limited, chemically limited, and intermediate; (iii) Sensitivity shows a turnover as a function of reaction rate due to the interplay between coherent electronic dynamics and incoherent chemical dynamics. Our findings demonstrate that chemical properties must be considered to estimate ultimate precision limits in optical spectrophotometry.