Number Fluctuations and Phase Diffusion in a Bose-Einstein Condensate of Light

Bose-Einstein condensates of quasiparticles such as exciton-polaritons, magnons and massive photons allow for new experimental possibilities as compared to the atomic Bose-Einstein condensates. In this Thesis we focus on a condensate of photons, first created at Bonn University in 2010. One of the recent achievements is the measurement of number fluctuations in such a condensate of photons. We present a general theory to calculate these number fluctuations in a harmonically trapped interacting Bose gas and apply this to the available experimental results on the condensate of photons, finding good quantitative agreement. Additionally, we investigate the fundamental phenomenon of phase diffusion, which is based on the fact that a Bose-Einstein condensate can be described as a symmetry-broken phase. However, the symmetry-broken phase is only well defined in the thermodynamic limit, such that in a finite system the phase of the Bose-Einstein condensate can have nontrivial dynamics. We propose a new type of interference experiment involving a condensate of photons to measure this dynamical behavior of the phase. By calculating the effects of quantum and thermal fluctuations we find different time scales on which the interference pattern vanishes. Based on these time scales, we conclude that phase diffusion is experimentally observable within the precision of current devices.