Quantum kinetic theory of light-matter interactions: From quantum plasmas to photon condensates

This thesis presents a quantum kinetic description of light–matter systems in which electrons and photons are treated as fully quantum-degenerate fields. Starting from a minimal-coupling Hamiltonian, we derive coupled Wigner equations for their phase space distributions, showing how quantum light–matter interactions enter directly at the kinetic level. Taking the semiclassical limit yields modified Vlasov and fluid equations that include explicit Hartree and Fock contributions to single-particle energies, phase space velocities, and forces, together with absorption, emission, and collision terms linking the two sectors.

First, we apply the coupled kinetic equations to degenerate electron systems. In the context of quantum plasmas, the theory uncovers hybrid plasmon–photon modes and nonlinear instabilities driven by strong light–matter coupling. Extending the analysis to bilayer solid-state systems, we show that a dynamical Fock potential reshapes the phase space flow through additional shifts in plasmon dispersion and enhancement of localization effects.

Numerical solutions reveal screening and momentum transfer, yielding quantitative corrections to Coulomb drag and influencing the stability of low dimensional electron gases. The kinetic formulation is then applied to the description of quantum states of light. In plasma environments, the theory predicts that repeated nonlinear Compton processes can drive photons toward condensation under experimentally accessible conditions.

A driven dissipative version of the kinetic equations that incorporates pumping and loss is constructed, thereby enabling a microscopic description of thermalisation and coherence dynamics in semiconductor photon condensates. Numerical simulations reveal transitions from thermal Bose–Einstein distributions to single-mode condensates and, at higher pump powers, to multimode states resembling laser operation. An effective Gross Pitaevskii equation is derived in which photon–photon interactions emerge from the electronic response of the medium. The resulting nonlocal interaction gives rise to modulational instabilities supporting supersolid light, pointing toward a rich landscape of strongly correlated photonic phases.