Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

Abstract

Open, non-equilibrium systems with balanced gain and loss, known as parity-time ()-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the -symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the -symmetric phase is protected in the presence of a periodic disorder which leads to a positive -symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the -symmetry breaking transition. We elucidate the interplay between such localization and the -symmetry breaking phenomena in disordered -symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.

Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

“…As the number of dimers increases, the tight-binding results approach the analytical results. The open diamonds are results obtained from beam propagation method 30 , 31 for an array of N = 21 dimers (see refs 26 , 32 , 33 for details of waveguide parameters and calculations). We would like to note that the number of dimers we can simulate, N = 21, is constrained by the discretization-size in the direction transverse to the waveguide that is necessary to obtain stable numerical results.…”

Emergent PT symmetry in a double-quantum-dot circuit QED setup

“…(see recent reviews [35][36][37][38][39] for further details and references). A wide variety of physically motivated one-dimensional (for example, [40][41][42][43][44][45][46][47][48][49]), and twodimensional (for example, [50][51][52][53][54]) condensed-matter lattice models have also been studied. From a fundamental perspective, exploration of topological aspects of non-Hermitian systems has been gaining ground both theoretically (for example, [25,40,45,[53][54][55][56][57]) and experimentally [13,27,[58][59][60].…”

Passive parity-time-symmetry-breaking transitions without exceptional points in dissipative photonic systems [Invited]

“…(For more details regarding these calculations, see Refs. [42][43][44].) Figure 6 a,b show the resultant intensity plots I(x, z) = |ψ(x, z = ct/n 0 )| 2 dx for a dissipative trimer with an exceptional point, δ = 0.…”