Towards a Bose glass transition in an optical Penrose quasicrystal

We study numerically a 2D Bose-Einstein condensate in a quasiperiodic array of potential peaks, assumed to be generated by superimposing five blue detuned laser beams. By using a Bogoliubov ansatz for the excitations we show that the system approaches a gapless, insulating phase upon increasing the potential, consistent with a Bose glass phase. The characteristics of the transition in terms of phase correlations, oscillatory modes, and superfluid fraction are discussed.