Controlled parity switch of persistent currents in quantum ladders

TL;DR

This paper studies how coupling in quantum ladders can effectively switch fermion parity and induce a robust 4π periodicity in persistent currents, with potential realizations in cold atoms and photonic systems.

Contribution

It demonstrates a controllable fermion-number parity switch and 4π periodicity in persistent currents through magnetic flux variation in quantum ladders, highlighting robustness against temperature and disorder.

Findings

Varying transverse flux $oldsymbol{oldsymbol{ ext{ extchi}}}$ by $2oldsymbol{ ext{ extpi}}$ switches fermion parity.

Persistent currents show a robust 4π periodicity in $oldsymbol{ ext{ extchi}}$.

Effects are stable against temperature and disorder.

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.