  The combined effect of disorder and interactions is central to the richness
of condensed matter physics and can lead to novel quantum states such as the
Bose glass phase in disordered bosonic systems. Here, we report on the
experimental realisation of the two-dimensional Bose glass using ultra-cold
atoms in an eight-fold symmetric quasicrystalline optical lattice. By probing
the coherence properties of the system, we observe a Bose glass to superfluid
transition and map out the phase diagram in the weakly interacting regime.
Moreover, we reveal the non-ergodic nature of the Bose glass by probing the
capability to restore coherence. Our observations are in good agreement with
recent quantum Monte Carlo predictions and pave the way for experimentally
testing the connection between the Bose glass, many-body localisation, and
glassy dynamics more generally.
