Collective effects of organic molecules based on the Holstein–Tavis–Cummings model

We study the collective effects of an ensemble of organic molecules confined in an optical cavity based on the Holstein–Tavis–Cummings model. By using the quantum Langevin approach and adiabatically eliminating the degree of freedom of the vibrational motion, we analytically obtain the expression of the cavity transmission spectrum to analyze the features of polaritonic states. As an application, we show that the dependence of the frequency shift of the lower polaritonic state on the number of molecules can be used in the detection of the ultra-cold molecules. We also numerically analyze the fluorescence spectrum. The variation of the spectral profile with various numbers of molecules provides signatures for the modification of molecular conformation.