  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 $\Phi$ and $\chi$. We show that the coupling
between ladder legs provides a way to effectively change the ground-state
fermion-number parity, by varying $\chi$. Specifically, we demonstrate that
varying $\chi$ by $2\pi$ (one flux quantum) leads to an apparent fermion-number
parity switch. We find that persistent currents exhibit a robust $4\pi$
periodicity as a function of $\chi$, despite the fact that $\chi \to \chi +
2\pi$ 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
$4\pi$ 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.
