2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172070We study a composite photon-Bose condensed atoms (BEC) system in an optical lattice confined in a cavity. We show that the system is able to produce an effective photon-photon repulsion in the presence of an external pump. We predict for the first time zero-temperature quantum phases of light coupled to BEC in the photon blockade regime in the presence of an external pump.4 pages, 4 figuresStatistical Mechanicstext