  Light emission from solid-state quantum emitters is inherently prone to
environmental decoherence, which results in an inhomogeneous line broadening
and in the deterioration of photon indistinguishability. Here we employ photon
correlation Fourier spectroscopy (PCFS) to study the temporal evolution of such
a broadening for the biexciton and exciton emission in resonantly driven GaAs
quantum dots. Differently from previous experiments, the time scales we probe
range from a few nanoseconds to milliseconds and, simultaneously, the spectral
resolution we achieve can be as small as 2 $\mu$eV. We find pronounced
differences in the temporal evolution of the two lines, which we attribute to
differences in their homogeneous linewidth and sensitivity to charge noise. We
then analyze the effect of irradiation with additional white light, which
reduces blinking at the cost of enhanced charge noise. Due to its robustness
against experimental imperfections and its high temporal resolution and
bandwidth, PCFS outperforms established spectroscopy techniques, such as
Michelson interferometry. We discuss its practical implementation, its
limitations, and the possibility to use it to estimate the indistinguishability
of consecutively emitted single photons for applications in quantum
communication and photonic-based quantum information processing.
