Optimal single-photon quantum light spectroscopy

Pulsed quantum light with few photons offers a promising avenue for high-precision spectroscopy. However, an appreciation of the essential nonclassicality of the light that underpins spectroscopic advantages remains unknown. Our work leverages quantum estimation theory to establish fundamental limits on the precision of single-molecule spectroscopy using quantum light. Specifically, we calculate the quantum Fisher information (QFI), which quantifies the maximum precision attainable by a quantum probe to estimate an unknown parameter. In a scheme probing single two-level emitters with propagating single-photon pulses, we analytically maximize the quantum Fisher information (QFI) in the scattered pulse. In a coherent scenario, where the pulse is fully absorbed, emitted, and measured, we establish an equivalence with an arbitrary Hamiltonian parameter estimation problem. This allows us to derive and maximize the QFI for any molecular parameter. Furthermore, we derive analytical expressions for the single-photon emission state, absorption probabilities, and the excited emitter state, in the presence of a phononic and an electromagnetic environment. Using this we calculate quantities of the emitted light field such as the two-point field correlation function and the QFI.