Coherent nonlinear spectroscopy offers us a window into the system-bath interactions in materials. Specifically, the spectral lineshapes can reveal the nature and dynamics of the environmental fluctuations surrounding the system of interest. Here we will discuss how stochastic non-equilibrium exciton dynamics manifest in the peculiar lineshapes and how they provide mechanistic insights into the nature of exciton-phonon and exciton-exciton interactions in nanostructured derivatives of metal halide perovskites. Despite the success of such classical optical probes in unveiling the many-body physics in materials, we will elaborate on the ambiguities still present in the resultant photophysical models that stem primarily due to the high excitation intensities used in the measurements. We will also discuss alternative experimental methodologies based on quantum entangled photons, which may offer superior signal to noise ratio and thus enabling the measurement of many-body interactions at close to single photon excitation densities.
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