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 $\Phi$ 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.

5 pages, 4 figures + Supplemental Material

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• Tunable gauge potential for neutral and spinless particles in driven lattices
• Time-reversal symmetry breaking in circuit-QED based photon lattices
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• Spin-orbit coupled fermions in an optical lattice clock
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• Drude weight increase by orbital and repulsive interactions in fermionic ladders
• Static properties of two linearly coupled discrete circuits