Dynamical evolutions in non-Hermitian triple-well system with complex potential

TL;DR

This paper studies the dynamical behavior of a non-Hermitian triple-well system with complex potential, revealing how loss, nonlinear interactions, and system size influence dark states and system damping.

Contribution

It provides new insights into the effects of nonlinear interactions and system size on the dynamics of non-Hermitian triple-well systems with complex potentials.

Findings

Existence of a zero-energy dark state unaffected by loss factor without nonlinear interactions.

Nonlinear interactions diminish the projection of dark states and increase loss.

Loss reduction scales with system size in extended (2n+1)-well systems without nonlinear interactions.

Abstract

We investigate the dynamical properties for non-Hermitian triple-well system with a loss in the middle well. When chemical potentials in two end wells are uniform and nonlinear interactions are neglected, there always exists a dark state, whose eigenenergy becomes zero, and the projections onto which do not change over time and the loss factor. The increasing of loss factor only makes the damping form from the oscillating decay to over-damping decay. However, when the nonlinear interaction is introduced, even interactions in the two end wells are also uniform, the projection of the dark state will be obviously diminished. Simultaneously the increasing of loss factor will also aggravate the loss. In this process the interaction in the middle well plays no role. When two chemical potentials or interactions in two end wells are not uniform all disappear with time. In addition, when we extend the triple-well system to a general (2n + 1)-well, the loss is reduced greatly by the factor 1=2n in the absence of the nonlinear interaction.