Fig. 2: Bose-glass-to-superfluid transition.
From: Observing the two-dimensional Bose glass in an optical quasicrystal
a, TOF images (9 ms TOF, 5 shots averaged) for different scattering lengths a at a fixed lattice depth of V0 = 2.8 Erec. Although the system is localized in the non-interacting and very weakly interacting cases, the appearance of sharp interference peaks for stronger interactions signals the emergence of long-range phase coherence, characteristic for the superfluid. b, Width of the central peak, distinguishing the coherent superfluid (light blue) from the incoherent Bose glass (dark blue). The dashed line is a guide to the eye indicating the detected phase boundary in the centre of the cloud \({V}_{{\rm{loc}}}^{(a)}\). It is identical to the line shown in the inset and in Fig. 3d. White points and error bars denote the QMC prediction from ref. 6 (Methods). Images in a correspond to the parameters marked by red diamonds. The inset shows the condensate fraction fc extracted from the same set of images, highlighting the coexistence of the two phases. c, Phase transition in an inhomogeneous system. The shaded Gaussian denotes the in-trap atomic density and the parabola represents the external trapping potential. For shallow lattices, the ground state is purely superfluid (left). At the non-interacting critical depth \({V}_{{\rm{loc}}}^{(0)}\), the Bose glass starts to appear at the low-density edge of the cloud where interaction effects are small (middle). With increasing lattice depth, the phase boundary gradually moves inwards until the entire cloud enters the Bose glass phase at \({V}_{{\rm{loc}}}^{(a)}\) (right).
