Higher-order exceptional point and Landau–Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices

Abstract

We propose a scheme to realize parity-time (PT) symmetric photonic Lieb lattices of ribbon shape and complex couplings, thereby demonstrating the higher-order exceptional point (EP) and Landau–Zener Bloch (LZB) oscillations in the presence of a refractive index gradient. Quite different from non-Hermitian flatband lattices with on-site gain/loss, which undergo thresholdless PT symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices has completely real values when the index gradient is applied perpendicular to the ribbon, and a triply degenerated higher-order EP (EP3) with coalesced eigenvalues and eigenvectors emerges only when the amplitude of the gain/loss ratio reaches a certain threshold value. When the index gradient is applied parallel to the ribbon, the LZB oscillations exhibit intriguing characteristics, including asymmetric energy transition and pseudo-Hermitian propagation, as the flatband is excited. Meanwhile, a secondary emission occurs each time when the oscillatory motion passes through the EP3, leading to distinct energy distribution in the flatband when a dispersive band is excited. Such novel phenomena may appear in other non-Hermitian flatband systems. Our work may also bring insight and suggest a photonic platform to study the symmetry and topological characterization of higher-order EP that may find unique applications in, for example, enhancing sensitivity.

Topological Photonic States in Waveguide Arrays

“…For instance, a 2D PT-symmetry graphene lattice demonstrates the relation between the PT-symmetry phase transition and the topological phase transition [112] (Figure 4b,c); a PT-symmetric Lieb lattice with ribbon shape and complex couplings demonstrates the higher-order EP and Landau-Zener Bloch oscillations. [113] As mentioned earlier, breaking the z-reversal symmetry of waveguide arrays is another way to endow physical systems with topologically nontrivial phases. When generalizing the Floquet topological theory to non-Hermitian systems, the interplay of Floquet topological phases and non-Hermiticity leads to more exotic effects that have no counterpart in static or Hermitian systems.…”

“…For instance, a 2D PT‐symmetry graphene lattice demonstrates the relation between the PT‐symmetry phase transition and the topological phase transition [ 112 ] (Figure 4b,c); a PT‐symmetric Lieb lattice with ribbon shape and complex couplings demonstrates the higher‐order EP and Landau–Zener Bloch oscillations. [ 113 ]…”

Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model

“…For PT -symmetric systems, the dynamics of OTOCs signals the Yang-Lee edge singularity [28] of phase transition and shows the quantized response to external driven potential [29]. It is now widely accepted that the non-Hermiticity is a fundamental modification to conventional quantum mechanics [30][31][32][33][34][35][36] since many systems, such as optics propagation in the "gain-or-loss" medium [37][38][39], the electronics transport in the dissipative circuit [40][41][42][43], and cold atoms in the tailored magneto-optical trap [44][45][46][47][48], are described by a non-Hermitian theory. The extension of Floquet systems to non-Hermitian regimes uncovers rich understandings of physics [49][50][51][52][53].…”

Symmetry-protected higher-order exceptional points in staggered flatband rhombic lattices

“…It has shown that the PT -symmetric frustrated lattices with fine-tuned non-Hermitian couplings can also give arise to flatbands as well as EPs [31]. More importantly, recent progress has demonstrated that even the higherorder EPs can exist in the PT -symmetric flatband lat-tices [32][33][34]. Nevertheless, due to the band touching (vanishing bandgap) between flat and dispersive bands, so far, realizations of the non-zero valued higher-order EPs have been limited to flatband systems with non-Hermitian couplings [35][36][37][38][39].…”