Fundamental Limits of Spectroscopy of Single Complex Quantum Systems using Pulsed Quantum Light

Pulsed optical states exhibiting nonclassical correlations and composed of a few photons are a novel spectroscopic tool. In a setup that probes single molecules in free space, we will calculate fundamental bounds on precision of estimators constructed from continuous field measurements, using an explicit light-matter coupling model. For arbitrary configuration of matter Hamiltonian and incoming state of light, we will show that QFI of detected light can be calculated as the trace variation of a generalised density matrix (GDM) whose dynamics admits hierarchical equations of motion. For the particular example of one-photon Fock pulses, we will demonstrate the complementary nature of optimal detection for phase-like matter Hamiltonian parameters versus that of loss-like parameters of the interaction Hamiltonian. For phase-like matter parameters (such as transition frequency) we will show that optimal measurements can be implemented in a two-element POVM. Finally, we employ in the one-photon interaction biphoton setup, entangled two-photon states where one of the photons functions as a noiseless ancila. In this setup, we will show that correlated LOCC detection schemes have an assured advantage over uncorrelated/single-photon measurements. We will also show that for the restricted but experimenally relevant class of parametrically downconverted (PDC) states, more entangled photon states yield both yield both ultimate precision bounds, as well as more efficient LOCC estimation strategies.