Controlled Parity Switch of Persistent Currents in Quantum Ladders

We investigate persistent currents for a fixed number of fermions in periodic quantum ladders threaded by Aharonov-Bohm and transverse magnetic fluxes Φ and χ. We show that the coupling between ladder legs provides a way to effectively change the ground-state fermion-number parity, by varying χ. We demonstrate that varying χ by 2π (one flux quantum) leads to an apparent fermion-number parity switch. We find that persistent currents exhibit a robust 4π periodicity as a function of χ, despite the fact that χ→χ+2π leads to modifications of order 1/N of the energy spectrum, where N is the number of sites in each ladder leg. We connect the parity switching effect to the quantum Hall regime in two-dimensional systems. We show that the parity switching effect is related to the parity of the number of filled Landau levels and that it inherits strong robustness against disorder in the Harper-Hofstadter quantum Hall regime. The parity-switching and the 4π periodicity effects are robust with respect to temperature and disorder and we outline potential physical realizations using Corbino disk geometries in solid state systems, quantum ladders with cold atomic gases and, for bosonic analogs of the effects, photonic lattices.
arXiv:1710.02152