  The homogeneous photoluminescence spectral linewidth in semiconductors
carries a wealth of information on the coupling of primary photoexcitations
with their dynamic environment as well as between multi-particles. In the limit
in which inhomogeneous broadening dominates the total optical linewidths, the
inhomogeneous and homogeneous contributions can be rigorously separated by
temperature-dependent %linear spectral measurements such as steady-state
photoluminescence spectroscopy. This is possible because the only
temperature-dependent phenomenon is optical dephasing, which defines the
homogeneous linewidth, since this process is mediated by scattering with
phonons. However, if the homogeneous and inhomogeneous linewidths are
comparable, as is the case in hybrid Ruddlesden-Popper metal halides, the
temperature dependence of linear spectral measurement \emph{cannot} separate
rigorously the homogeneous and inhomogeneous contributions to the total
linewidth because the lineshape does \emph{not} contain purely Lorentzian
components that can be isolated by varying the temperature. Furthermore, the
inhomogeneous contribution to the steady-state photoluminescence lineshape is
not necessarily temperature independent if driven by diffusion-limited
processes, particularly if measured by photoluminescence. Nonlinear coherent
optical spectroscopies, on the other hand, do permit separation of homogeneous
and inhomogeneous line broadening contributions in all regimes of
inhomogeneity. Consequently, these offer insights into the nature of many-body
interactions that are entirely inaccessible to temperature-dependent linear
spectroscopies. When applied to Ruddlesden-Popper metal halides, these
techniques have indeed enabled us to quantitatively assess the exciton-phonon
and exciton-exciton scattering mechanisms.
