Quantum coherence of Hard Core Bosons and Fermions in one dimensional quasi-periodic potentials: superfluid, Mott and glassy phases

We use Hanbury- Brown-Twiss interferometry (HBTI) to characterize and contrast the different quantum phases exhibited by hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic potential. In addition to the Bose-glass, superfluid and Mott insulator phases characteristic of interacting disordered bosons, we show the quasi-periodic potential induces a cascade of Mott-like band insulator transitions triggered by the fermion-type statistics of HCBs~. A comparative study of the fermion model shows that except for a sign difference, HCB and fermion interferometric patterns~coincide~in the localized phases. In the extended phase,~~however, fermions~behave quite differently~; ~their correlation functions reflect some of the multi-fractal properties characteristic of the metal-insulator transition. When plotted as a function of the filling factor, their quasi-momentum distribution displays an Arnold tongue-like structure and the HBTI peak intensity follows a step-like pattern which resembles a devil's staircase at the onset of the localization transition.