  The precise determination of the excitation energies in condensed-phase
molecular systems is important for understanding system-environment
interactions as well as for the prerequisite input data of theoretical models
used to study the dynamics of the system. The excitation energies are usually
determined by fitting of the measured optical spectra that contain broad and
unresolved peaks as a result of the thermally random dynamics of the
environment. Herein, we propose a method for precise energy determination by
strongly coupling the molecular system to an optical cavity and measuring the
energy of the resulting polariton. The effect of thermal fluctuations induced
by the environment on the polariton is also investigated, from which a power
scaling law relating the polariton's linewidth to the number of molecules is
obtained. The power exponent gives important information about the
environmental dynamics.
