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 $\mathrm{\ensuremath{\Phi}}$ and $\ensuremath{\chi}$. We show that the coupling between ladder legs provides a way to effectively change the ground-state fermion-number parity, by varying $\ensuremath{\chi}$. Specifically, we demonstrate that varying $\ensuremath{\chi}$ by $2\ensuremath{\pi}$ (one flux quantum) leads to an apparent fermion-number parity switch. We find that persistent currents exhibit a robust $4\ensuremath{\pi}$ periodicity as a function of $\ensuremath{\chi}$, despite the fact that $\ensuremath{\chi}\ensuremath{\rightarrow}\ensuremath{\chi}+2\ensuremath{\pi}$ 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 $4\ensuremath{\pi}$ periodicity effects are robust with respect to temperature and disorder, and outline potential physical realizations using cold atomic gases and photonic lattices, for bosonic analogs of the effects.
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