Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas

Abstract

We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-PT -- symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra -- and inter-cell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-PT -symmetric configurations, broken and unbroken PT -symmetric phases, topologically trivial and nontrivial phases, as well as transitions between linear and nonlinear regimes. The introduced scheme generalizes the Rice-Mele Hamiltonian for a nonlinear non-Hermitian quadrimer array featuring odd-PT symmetry and makes accessible unique phenomena and functionalities that emerge from the interplay of non-Hermiticity, topology, and nonlinearity. We also show that in the presence of nonlinearity the system sustains nonlinear topological edge states bifurcating from the linear topological edge states and the modes without linear limit. Each nonlinear mode represents a doublet of odd-PT -conjugate states. In the broken PT phase, the nonlinear edge states may be effectively stabilized when an additional absorption is introduced into the system.

arXiv comment7 pages, 3 figures

References in corpus (42)

• Topological Insulators
• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Berry Phase Effects on Electronic Properties
• Topological Photonics
• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Analogs of quantum Hall effect edge states in photonic crystals
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Non-Hermitian Chern bands
• Nonlinear topological photonics
• The Zak phase and the existence of edge states in graphene
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• PT-symmetry with a system of three-level atoms
• Waveguide-coupled single collective excitation of atomic arrays
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• Low-Light-Level Optical Interactions with Rubidium Vapor in a Photonic Bandgap Fiber
• Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions
• Nonlinear modes in finite-dimensional PT-symmetric systems
• Observation and control of nonlinear electromagnetic topological edge states
• Nonlinear modes in the harmonic PT-symmetric potential
• PT-symmetric optical potentials in a coherent atomic medium
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry
• Odd-time reversal $PT$ symmetry induced by anti-$PT$-symmetric medium
• Discrete solitons in PT-symmetric lattices
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Parity-time symmetric optical coupler with birefringent arms
• Tunable nonlinear PT-symmetric defect modes with an atomic cell
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• PT-Symmetric Representations of Fermionic Algebras
• Surface modes and breathers in finite arrays of nonlinear waveguides
• Spectral singularities of odd-$PT$-symmetric potential
• Surface Solitons in Three Dimensions

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• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• Topological edge solitons in \{chi}(2) waveguide arrays
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux