Fig. 3: Non-adiabaticity of the Bose glass.

a, Condensate fraction in the 2D quasicrystal (normalized within each plot) as a function of lattice depth for different loading durations and scattering lengths. Although 15-ms ramps result in consistently lower condensate fractions, there is no consistent difference between 30 ms and longer ramps. b, FWHM of the central peak (w_r) after a linear ramp of duration τ from the 2D quasicrystal into a regular 3D cubic lattice, where the ground state is a superfluid. The coloured circles correspond to different depths of the quasicrystalline potential V₀ for a fixed scattering length of a = 10a₀. For \({V}_{0} < {V}_{{\rm{loc}}}^{(10)}\) (blue circles), the initial state in the quasicrystal is superfluid and the final states show strong superfluid order for all explored ramp times. For a deep Bose glass at \({V}_{0} > {V}_{{\rm{loc}}}^{(10)}\) (red circles), in contrast, there is no initial coherence and only a very limited degree of phase coherence can be restored, demonstrating the absence of adiabatic evolution into and out of the Bose glass. c, An equivalent measurement for a Mott insulator in a regular 3D cubic lattice (V_x,y,z = 16 E_rec, a = 150a₀). Although the initial state also lacks coherence, it can be rapidly restored by ramping down the lattice depth in τ ≳ 2 ms. Insets in b and c show TOF images and OD denotes the optical density. d, Phase diagram showing w_r for a slow ramp with τ = 15 ms highlighting three different regimes: a pure superfluid (light blue), an intermediate regime where superfluid and Bose glass coexist in the trap, and finally the pure Bose glass (darker blues). The transition into the pure Bose glass is consistent with the phase boundary extracted in Fig. 2b (dashed line). e, Comparing condensate fraction f_c in the quasicrystal with w_r for a = 23a₀, demonstrating the consistency of all observations. The dashed line denotes the critical lattice depth \({V}_{{\rm{loc}}}^{(23)}\) extracted from the main diagram of Fig. 2b and the grey area indicates the intermediate regime where superfluid and Bose glass coexist. The solid lines in b, c and e are guides to the eye.