Multimode Effects on a Bose-Einstein Condensate of photons in a Dye-Filled Microcavity

Abstract

In this bachelor’s thesis we study multi-mode effects on the Bose-Einstein condensation (BEC) of photons in a dye-filled microcavity. The repulsive effective interaction of the photons should increase the conden- sate size. We show how the condensate radius of the ground state and an excited state depend on this effective interaction of the photons. We show that the spatial form of the excited state can also decrease the radius of the ground state. For this effect to occur, we expect a sufficiently large effective interaction. Comparing our model with experimental data gives us an effective interaction of g ̃ = (5.2 ± 2.3) × 10−5. However, one should interpret this result with care, because better measurements of the photon occupa- tion numbers are needed before we can reach solid conclusions. We further investigate rate equations for the BEC of photons to understand the stationary photon occupation numbers. We find approximated solutions to these rate equations to find the dependence of the photon occupation numbers on the pump rate which excites the dye molecules in the condensate. Despite those approximations we estimate critical parameters for which either lasing or saturation of the photon numbers is expected. We conclude that the rate of decay from the cavity and emission rates of the dye is very important. From comparing the model with experiment we can conclude that the approximations are well enough to capture the right trend of real data. However, in the limit of large photon numbers, the approximations aren’t good enough anymore and a more accurate approach will be necessary.