Energy spectrum and the thermal Mandel Q-parameter of a quadratically coupled phonon–photon polariton

A model polariton system with a linear and a quadratic coupling is investigated. The energy spectrum is obtained by using a squeezing transformation followed by the second-order Rayleigh–Schrodinger perturbation theory and subsequently the thermal counterpart of the Mandel Q -parameter ( Q t h ) is calculated for the phonons. It is shown that the phonons in a quadratically coupled polariton is super-Poissonian at all temperatures and at all values of the coupling parameters. The dependence of the average phonon number on the coupling parameters, phonon frequency and temperature is also investigated.