Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice

Abstract

This article aims to study the existence of stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian system when exposed to external fields. We investigate a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric diamond chain network and its transport dynamics in two different situations, namely in a flat band case and a non-flat band case. The considered system does not support unbroken-$\mathcal{P}\mathcal{T}$ phase or completely real eigenspectra in any of the parametric regions in both the flat and non-flat band cases. In the flat band case, up to a critical value of the gain-loss parameter, the bands are found to be gapless or inseparable, and for other values the bands are isolated. Considering the non-flat band case, all the bands are found to be complex dispersive and are also isolated. In the case of completely broken $\mathcal{P}\mathcal{T}$ phase, we look upon the possibility to have stable dynamics or Bloch oscillations upon the application of external fields like synthetic electric field. In particular, when the complex bands are isolated, we point out that the Landau-Zener tunneling induced by the synthetic electric field can enable Bloch oscillations. The amplitude of these Bloch oscillations is large and persists for a long propagation distance which reveals that super Bloch oscillations can be observed in the broken $\mathcal{P}\mathcal{T}$ phase of the system. We also report the amplified Bloch oscillations which pave the way towards controlling transport phenomena in non-Hermitian systems.

arXiv commentAccepted for publication in Phys. Rev. A

References in corpus (47)

• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Topological Band Theory for Non-Hermitian Hamiltonians
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices
• Superfluid-insulator transition in a periodically driven optical lattice
• Aharonov-Bohm cages in two-dimensional structures
• Observation of dynamic localization in periodically-curved waveguide arrays
• Coherent control of dressed matter waves
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Photonic Bloch oscillations and Zener tunneling in two-dimensional optical lattices
• Invisibility in PT-symmetric complex crystals
• Experimental observation of Aharonov-Bohm cages in photonic lattices
• Experimental properties of Bose-Einstein condensates in 1D optical lattices: Bloch oscillations, Landau-Zener tunneling and mean-field effects
• Interaction induced delocalisation for two particles in a periodic potential
• Fractional Bloch oscillations in photonic lattices
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Flat band states: disorder and nonlinearity
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Acoustic Analogue of Bloch Oscillations and Resonant Zener Tunneling in Ultrasonic Superlattices
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Bloch-Zener oscillations
• Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields
• Landau-Zener Bloch oscillations with perturbed flat bands
• Measuring topological invariants in photonic systems
• Flat bands in lattices with non-Hermitian coupling
• Physics counterpart of the PT non-hermitian tight-binding chain
• Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling
• Non-Hermiticity Induced Flat Band
• Effective magnetic fields for photons in waveguide and coupled resonator lattices
• Impact of loss on the wave dynamics in photonic waveguide lattices
• Non-Hermitian scattering on a tight-binding lattice
• Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice
• Nonlinear symmetry breaking of Aharonov-Bohm cages
• Observation of valley Landau-Zener-Bloch oscillations and pseudospin imbalance in photonic graphene
• Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Conservative and PT-symmetric compactons in waveguide networks
• Nonlinear Landau-Zener Tunnelling in Coupled Waveguide Arrays
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Frustration and time reversal symmetry breaking for Fermi and Bose-Fermi systems
• Single and double linear and nonlinear flatband chains: spectra and modes
• Super Bloch Oscillation in a PT symmetric system
• Non-adiabatic transitions in a non-symmetric optical lattice
• Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field I: Tunneling rates

Cited by in corpus (6)

• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials
• Correlations at higher-order exceptional points in non-Hermitian models
• Landau-Zener transitions through a pair of higher order exceptional points