Effect of non-Hermiticity on adiabatic elimination in coupled waveguides

Abstract

We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides. We show that adiabatic elimination is not affected when the system is in parity-time symmetric phase. However, in the broken phase the eliminated waveguide loses its darkness namely its amplitude starts increasing, which means adiabatic elimination does not hold in the broken phase. Our results can advance the control of the dynamics in coupled laser cavities, and help the design of controllable absorbers. [14][15][16]. Among the non-Hermitian systems, Parity and Time reversal (PT) symmetric systems are specifically important because of showing phase transition from the exact phase with real spectrum to the broken phase with complex spectrum [17]. The transition point is known as exceptional point or PT symmetry breaking point. At the exceptional point two or more eigenvectors of the system in a pairwise manner coalesce and their associated eigenvalues become degenerate. In each phase, many interesting features have been discovered and experimentally demonstrated. Among them are unidirectional invisibility [18,19], parity anomaly [20], loss induced lasing [21], protected bound state [22,23], and non-Hermiticity induced flat band [8].

Eigenstates Transition without Undergoing an Adiabatic Process

“…If the on-site potentials of middle levels become larger and larger the adiabatic process needs to get slower and slower [48]. Interestingly enough for the same cases with large on-site potentials of the middle levels, one can show that the same gain and loss parameters that we provided for DASA in the two-level system will result in DASA in higher dimensions without any extra effort [41,48]. Note that although in higher di-mensions we lose the special form of the eigenvalues for a two-level system (one real the other complex), the complex form of the eigenvalues come to our benefit [48].…”

Optical lattices with higher-order exceptional points by non-Hermitian coupling

“…For multiple waveguides systems, the interesting physics arising from non-Hermiticity is not limited to those EPs that are induced by a twowaveguide system. Recently, the dark state 14,21 and the PT symmetry recovery behaviors 22,23 have been found in three-waveguide and four-waveguide system, respectively. Furthermore, a PT-symmetric topological interface state has been experimentally demonstrated in a non-Hermitian waveguide arrays system 24 .…”