Untying links through anti-parity-time-symmetric coupling

Abstract

We reveal how the vector field links are untied under the influence of anti-parity-time-symmetric couplings in a dissipative sublattice-symmetric topological photonic crystal lattice. The topology of the quasi-one-dimensional two-band system is encoded in the geometric topology of the vector fields associated with the Bloch Hamiltonian. The linked vector fields reflect the topology of the nontrivial phase. The topological phase transition occurs concomitantly with the untying of the vector field link at the exceptional points. Counterintuitively, more dissipation constructively creates a nontrivial topology. The linking number predicts the number of topological photonic zero modes.

Coupling-induced nonunitary and unitary scattering in anti- PT -symmetric non-Hermitian systems

“…In this section, we study the properties of an anti-PT -symmetric non-Hermitian scattering center, which is a four-site scattering center with imaginary coupling. The imaginary coupling can be realized through dissipation in the non-Hermitian systems [56]. The schematic of the anti-PT -symmetric non-Hermitian system is shown in Fig.…”

“…Notably, each dot in the schematics represents a primary resonator and each line between the two neighbor primary resonators represents the effective coupling induced by the linking resonator after adiabatically eliminating the linking resonator. The effective coupling induced by the off-resonance passive linking resonator without dissipation/gain is real and Hermitian [67]; in contrast, the effective coupling induced by the on-resonance dissipative/active linking resonator with dissipative/gain is imaginary and non-Hermitian [56,60]. In the two situations, the effective coupling strength is approximately equal to the product of the two couplings between the linking resonator and its two adjacent primary resonators divided by the off-resonant frequency or the dissipation/gain rate of the linking resonator.…”

“…Anti-PT symmetry ensures the real part of the energy spectrum either being zero or opposite in pairs; in contrast, PT symmetry ensures the imaginary part of the energy spectrum either being zero or opposite in pairs. The dissipation induces nontrivial topology in anti-PT -symmetric systems [56,57], which greatly differs from the unaffected topology in PTsymmetric systems [61].…”

“…Recently, imaginary coupling has been demonstrated in atomic vapors [48], electrical circuits [58], and optical waveguides [59]. In the coupled resonator array, the linking resonator with dissipation can be adiabatically eliminated to realize the imaginary coupling between two adjacent resonators [56,60]. Anti-PT symmetry ensures the real part of the energy spectrum either being zero or opposite in pairs; in contrast, PT symmetry ensures the imaginary part of the energy spectrum either being zero or opposite in pairs.…”

Unitary Scattering Protected by Pseudo-Hermiticity

“…The resonator detuning ∆ j is real. The coupling iγ j is non-Hermitian and can be realized through the gain [64,109]. The scattering center H c is pseudo-Hermitian for the unitary matrix q = I 3 ⊗ σ z .…”