Thermodynamic properties of systems with strong light-matter coupling

Abstract

We consider an lattice of isotropic simple harmonic oscillators, with charge, immersed in a dielectric background, which will couple strongly with the light traveling in the medium. Neglecting quadrupoles, the oscillators have an electric dipole moment and interact with each other through an instantaneous Coulombian interaction. Starting from a quantum formalism, we obtain the dispersion relation, leading to the quantization of the Hamiltonian of the coupled system, in terms of the bosonic operators of creation and annihilation. From the eigenstates and energy eigenvalues of the polaritons, we obtained the canonical partition function, through which the connection with thermodynamics is established, allowing us to determine physical quantities of interest, such as the Helmholtz free energy, internal energy, specific heat, and pressure. In this work, we analyze and discuss the effect of light-matter interaction on such physical properties.