Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes

In this work, we present a stochastic variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. The light-matter coupled system is described by the Pauli-Fierz Hamiltonian. The spatial wave function and the photon spaces are optimized by a random selection process. Examples for a two-dimensional trion and confined electrons as well as for the He atom and the Hydrogen molecule are presented showing that the light-matter coupling drastically changes the electronic states.