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 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 (third-order) EP with coalesced eigenvalues and eigenvectors emerges only when the amplitude of 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 EP, 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 EPs that may find unique applications in for example enhancing sensitivity.

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Cited by in corpus (7)

• Resolving the topology of encircling multiple exceptional points
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Non-Hermitian Bloch-Zener phase transition
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Imaginary coupling induced Dirac points and group velocity control in non-reciprocal Hermitian Lattice
• Landau-Zener transitions through a pair of higher order exceptional points