Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Abstract

Abstract.We study theoretical models of three coupled wave guides with a PT -symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

High-order exceptional points in supersymmetric arrays

“…Different types of energy level coalescence exist in non-Hermitian systems. The most common types of EPs are the two-state coalescence (EP2) that exhibits a squareroot dependence on the system parameters [6][7][8]30] and * jinliang@nankai.edu.cn the three-state coalescence (EP3) that exhibits a cubicroot dependence on the system parameters [31,[45][46][47][48]. Even four-state coalescence (EP4) are accessible in the coupled resonators [49,50].…”

Complex symmetric Hamiltonians and exceptional points of order four and five

“…The details may be found in Figure Nr. 3 of Ref. [29]. What the latter studies revealed was, first of all, the phenomenon of the characteristic permutation of the components of |ψ .…”

“…Such a change of perspective was inspired by the recent growth of interest in sophisticated experiments localizing the exceptional points of higher order in classical systems. We felt mostly inspired by the recent conference report [29] in which the exceptional points of the third order (EP3) were studied in a system of coupled waveguides. We also noticed that in Ref.…”

Realization of PT -symmetric and PT -symmetry-broken states in static optical-lattice potentials

“…It was shown that the use of a strong loss term leads to the creation of a stationary state in the corresponding lattice site due to the quantum Zeno effect [39,40]. However these stationary states do not have the characteristics of the solutions in the PT -symmetric TMS in equation (6). In the following, it is shown that the setting of appropriate initial phases and particle numbers of the condensates leads to stationary and exponentially decaying states with the PTsymmetric and PT -symmetry broken characteristics of the TMS, respectively.…”

“…see [2]). They can, for example, be used to describe delocalization transitions in condensed matter [3], or for the investigation of population biology [4] and exceptional points [5][6][7][8]. Furthermore, the concept of PT symmetry can be applied to the fields of laser modes [9][10][11], electronic circuits [12][13][14], microwave cavities [15], or for the realization of unidirectional invisibility [16][17][18].…”