Cooperative molecular structure in polaritonic and dark states

An ensemble of identical, intrinsically non-interacting molecules exposed to quantum light is discussed. Their interaction with the quantum light induces interactions between the molecules. The resulting hybrid light-matter states exhibit a complex structure even if only a single vibrational coordinate per molecule is considered. Since all molecules are identical, it is appealing to start from the uniform situation where all molecules possess the same value of this vibrational coordinate. Then, polaritons and dark states follow like in atoms but are functions of this coordinate, and this vibrational degree of freedom makes the physics different from that of atoms. However, despite all molecules being identical, each molecule does have its own vibrational coordinate. It is thus a vital issue to understand the meaning of the uniform situation and how to depart from it and enable one to realistically investigate the ensemble. A rigorous and physically relevant meaning of the polariton energy curves in the uniform situation has been found. It is proven that any point on a polariton energy curve is a (local) minimum or maximum for departing from the uniform situation. It is shown how to explicitly compute the energetic impact of departing from the uniform situation using solely properties of a single free molecule in the absence of the quantum light. The structure of the dark states and their behavior upon departing from the uniform situation are analyzed as well. Useful techniques not used in this topical domain are introduced, and general results on, for example, minimum energy path and symmetry breaking and restoration are obtained. It is shown how to transfer the findings to include several or even many nuclear degrees of freedom per molecule and thus to address the problem of quantum light interacting with many complex molecules. It is demonstrated that the interplay of several vibrational degrees of freedom in a single molecule of the ensemble is expected to lead to additional and, in part, qualitatively different physics. General consequences are discussed.