Quasiperiodic potentials in condensed matter systems have garnered much interest, due to their peculiar geometrical and physical properties. Particles subjected to such potentials organize themselves into long-range ordered structures, but their localized states display properties akin to those of disordered systems. In recent years, technological advancements in the field of optically trapped ultracold atoms have led to investigate the properties of trapped bosons in a 2D quasiperiodic potential; there, particles are expected to manifest a localized, but compressible, Bose Glass phase, in addition to the superfluid and insulating phases typical of periodic systems.
In this talk, we will present numerical results obtained through Path Integral Monte Carlo techniques, through which we have probed the behavior of trapped bosons across different phases and temperatures. In particular, the introduction of a new class of mesoscopic estimators has allowed us to identify the Bose Glass phase in finite-size systems, and to predict its robustness to thermal fluctuations. We will discuss how these results connect to current and future experiments, as well as further developments aimed at the low-density regime.