Fundamental Limits on Estimation of Molecular Parameters Using Entangled Photon Spectroscopy

Nonlinear spectroscopy using entangled photons has been shown to offer a number of apparent advantages over classical light, including increased selectivity in exciting transitions, enhanced signal-to-noise ratio of detected signal, as well as a larger set of control parameters (such as entanglement time). We recast the basic spectroscopic question of how much information about the matter system one can extract from the detected state of quantized light as that of a quantum estimation problem. By evaluating the quantum and classical Fisher informations (with respect to the parameters of interest of the matter system) of the output states of light, we can estimate the optimal input field states as well as the detection schemes for the inference problem. We illustrate this in the context of the linear biphoton spectroscopic probe of a coupled dimer system, where one of the members of an entangled photon pair (resulting from a type-II parametric down-conversion (PDC) process) couples with the matter system, and is detected in coincidence with the other photon. Under the influence of various models of the bath that coupled to the matter system, we show that the entanglement of the input probe state of light plays a role in setting these fundamental bounds. We also examine the analogous problem with other quantum states of light, as well as classical fields, to demonstrate the relative usefulness of the various probes in our estimation paradigm.