Do quantum effects influence the energy of polariton states?

If an ensemble of molecules is placed inside a nano-scaled Fabry-Pérot cavity capable of trapping a photon resonant with a transition level of the molecule, the photonic and molecular (excitonic) states will exchange energy. If the exchange of energy between the two states is faster than the decay rate of either state, a pair of hybridized light-matter states known as polaritons may form. Polaritons involving a single photon and one type of molecular excitation can be modeled using a two-level Hamiltonian, with the eigenvalues of the matrix serving as the energies of the polariton states. At resonance, the separation between the two polariton states is referred to as the Rabi splitting, and is proportional to the square root of the concentration of the molecules involved in the coupling. In this manuscript data from previously reported cavity polariton measurements is analyzed, and it is found that while the relationship between the square root of the concentration and Rabi splitting holds for the overall energy difference between the polariton states, it is observed that this relationship does not hold for individual polariton energy levels. The basic particle in a box model and harmonic oscillator models of quantum mechanics are invoked in an attempt to qualitatively account for this discrepancy.