Topological Transitions for Lattice Bosons in a Magnetic Field

We study the Hall response of the Bose-Hubbard model subjected to a magnetic field. We show that the Hall conductivity is proportional to the particle density plus an integer. The phase diagram is intersected by topological transitions between different integer values. These transitions originate from points in the phase diagram with effective charge conjugation symmetry, and are attributed to degeneracies in the many body spectrum which serve as sources for the Berry curvature. We find that extensive regions in the phase diagram exhibit a negative Hall conductivity, implying that flux flow is reversed in these regions - vortices there flow upstream. We discuss experimental implications of our findings.Comment: 11 pages, 7 figure

Driving induced many-body localization

Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hardcore bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent suppression of tunneling for engineering long-lived Floquet phases.Comment: 9 pages, 9 figure

Disorder induced transitions in resonantly driven Floquet Topological Insulators

We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasi-energy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.Comment: 18 pages, 13 figure

Elliptic Rydberg states as direction indicators

The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of a hydrogen atom that mimic classical elliptic orbits are the coherent states of the SO(4) rotation group.It is known how to produce these states experimentally. They have minimal dispersions of the two conserved vectors and can be used as direction indicators. We compare the fidelity of this transmission method with that of the idealized optimal method

Quantized large-bias current in the anomalous Floquet-Anderson insulator

We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasing the bias, the chiral Floquet edge mode connecting source to drain becomes fully occupied and the current rapidly approaches its quantized value.Comment: 5+ pages; to appear in PRB(R