Symmetry breaking in a one-dimensional atom-cavity system with harmonic trap
We investigate the effects of harmonic trapping in the self-organisation phase transition in a transversely pumped atom-cavity system. We study a one-dimensional model that captures the dynamics along the cavity axis using the same pump intensity for all harmonic trap strengths. In the absence of harmonic confinement, there are two equiprobable density wave states in the self-organised phase. Employing a semiclassical phase space method, the harmonic confinement strength is varied and the statistics for the symmetry broken states is obtained. We find that for weak confinement the two states remain nearly equiprobable. However, for sufficiently strong confinement, the system starts to favour one of the two possible density wave state.