$\mathcal{PT}$-symmetric currents of a Bose-Einstein condensate in a triple well

TL;DR

This paper investigates how $ ext{PT}$-symmetric perturbations affect currents in a degenerate triple-well Bose-Einstein condensate, revealing conditions for stability and the role of interactions.

Contribution

It demonstrates that stable currents depend on perturbation coupling and shows that on-site interactions can restore current stability in degenerate systems.

Findings

Stable currents occur only when perturbations do not couple to degenerate states.

On-site interactions can restore the ability to support stable currents.

Degeneracy complicates the establishment of stationary currents.

Abstract

We study the case of $\mathcal{PT}$-symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question, whether or not a stationary current through such a system can be established, i.e.\ whether or not the $\mathcal{PT}$-symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.