2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130205We report the observation of high order resonances of the quantum $δ$-kicked accelerator using a BEC kicked by a standing wave of light. The signature of these resonances is the existence of quantum accelerator modes. For the first time quantum accelerator modes were seen near 1/4 and 1/3 of the Talbot time. Using a BEC enabled us to study the detailed structure of the modes and resonances which are related to the fractional Talbot effect. We present a general theory for this system and apply it to predict the behavior of the accelerator modes.4 pages, 4 figuresAtomic Physicstext