Fig. 1. Concept of the proposed quantum spectroscopy and model system.

(A) Schematic of the optical setup. A pulsed laser pumps a nonlinear crystal to generate entangled photon pairs. The signal photon excites the sample, and the resulting fluorescence is analyzed with a spectrometer and a single-photon camera [e.g., DLD (48)]. The idler photon is routed to a reference arm for joint spectral and temporal measurements. Coincidences between the idler and fluorescence channels are recorded. BS, beam splitter. (B) Joint temporal intensity in Eq. 1. By virtue of the Fourier transform relation, the quantum state of light in Eq. 1 exhibits negative time correlation, and its joint temporal amplitude approximately satisfies the condition $t_{\mathrm{S}}=-t_{\mathrm{I}}$. (C) Schematic showing the temporal relationships of the arrival times of the signal, idler, and fluorescence photons in the measurement of (A). Because of the correlation $t_{\mathrm{S}}=-t_{\mathrm{I}}$ from (B), the excitation-fluorescence delay $\mathrm{\Delta }{t}_{\text{FS}}=t_{\mathrm{F}}-t_{\mathrm{S}}$ can be reconstructed from the measured detection times, $\mathrm{\Delta }{t}_{\text{FS}}=t_{\mathrm{F}}+t_{\mathrm{I}}$. Thus, scanning $t_{\mathrm{F}}+t_{\mathrm{I}}$ enables the direct probe of the excited-state dynamics. (D) Monomer subunit of the FMO pigment-protein complex from C. tepidum with seven BChl molecules; BChls 3, 6, and 7 are highlighted in green. The pigments are numbered as in PDB file 3ENI (64).