Localization and multifractality in driven cold-atom quasicrystal and its relation to the driven integer quantum Hall matter

By independently controlling dipolar and phasonic modulations applied to atoms in an 1D incommensurate bichromatic lattice, we have experimentally demonstrated coherent tuning of the localization transition [1] and observed the competition between dynamic and Anderson localization. Here we elucidate the mapping between this system and a two-dimensional driven integer quantum Hall system, in which our combined modulation protocol maps to illumination by light with fully tunable polarization. As an application of the mapping, we discuss how to Floquet engineer an extended critical phase hosting multifractal wave functions, embedded in an interleaved localization phase diagram, simply by tuning the polarization of the driving light from linear to circular.