Exciton-polaritons are quasiparticles that consist partly of a photon, and partly of an exciton, which is a bound state of an excited electron and a hole. Exciton-polaritons can be created in microcavities. These are layered semiconductor structures, consisting of Bragg reflectors at the op and the bottom, and one or multiple quantum wells in between. When light is shone onto the microcavity, the photons can become trapped between the Bragg reflectors and be absorbed by an electron inside the cavity, resulting in the creation of an exciton in the quantum well. When the excited electron recombines with the hole, the exciton is converted into a photon. If the photos are many times absorbed and re-emitted before they leave the cavity, then the exciton and the polariton field can become strongly coupled. In that case, we do not describe the system in terms of the photon and exciton fields, but in terms of polaritons, which form a combination of the two.

In this thesis, we study theoretically the evolution of suddenly created exciton-polariton fluids. This evolution is governed by the loss of particles, due to photons escaping from the cavity, and interactions between the polaritons, which originate from the Coulomb interactions between the excitons. The starting point of our description is a homogeneous polariton fluid where all the particles have zero in-plane momentum and the same phase. These initial conditions could be created by an ultrashort laser pulse that is shone at the microcavity at normal incidence and that is in resonance with the lowest single particle energy state. However, this is not the ground state of the total system, comprising many interacting particles.

For homogeneous systems, we obtain a complete picture of the system by using computing the formal solution of the stochastic differential equation, expressed in Green’s functions, numerically. Based on this solution, we calculated the momentum distribution, the first order coherence in real space, and the second order coherence in both real and momentum space. The results can be explained by the dynamical Casimir effect and by the fact that when the density decrease due to the loss of particles, also the interaction energy becomes smaller. The various quantities show that polaritons with nonzero in-plane momentum are produced and that there is a strong correlation between polaritons with opposite momentum. In real space, we see that correlations spread out in a light-cone-like manner, where the speed of sound in the exciton-polariton fluid plays the role of the speed of light.

In addition we studied inhomogeneous system using Monte Carlo simulations of the stochastic differential equation. For systems with an initial Gaussian density distribution we see that the particles spread out because of the repulsive polariton-polariton interactions. As a consequence, the system’s properties in momentum space are different for the inhomogeneous systems as compared to the homogeneous systems. Nevertheless, the first order coherence in real space can de described by the results obtained for the homogeneous systems.