  The excited state population of single solid-state emitters is subjected to
energy fluctuations around the equilibrium driven by the bath and relaxation
through the emission of phonons or photons. Simultaneous measurement of the
associated spectral dynamics requires a technique with a high spectral and
temporal resolution with an additionally high temporal dynamic range. We
propose a pulsed excitation-laser analog of Photon-Correlation Fourier
Spectroscopy (PCFS), which extracts the lineshape and spectral diffusion
dynamics along the emission lifetime trajectory of the emitter, effectively
discriminating spectral dynamics from relaxation and bath fluctuations. This
lifetime-resolved PCFS correlates photon-pairs at the output arm of a Michelson
interferometer in both their time-delay between laser-excitation and
photon-detection and the time-delay between two photons. We propose the utility
of the technique for systems with changing relative contributions to the
emission from multiple states, for example, quantum emitters exhibiting
phonon-mediated exchange between different fine-structure states.
