Controlled parity switch of persistent currents in quantum ladders

Abstract

We investigate the behavior of persistent currents for a fixed number of noninteracting fermions in a periodic quantum ladder 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 $χ$. Specifically, 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 $χ\to χ+ 2π$ leads to modifications of order $1/N$ of the energy spectrum, where $N$ is the number of sites in each ladder leg. We show that these parity-switch and $4π$ periodicity effects are robust with respect to temperature and disorder, and outline potential physical realizations using cold atomic gases and, for bosonic analogs of the effects, photonic lattices.