Nonlinear topological edge states in a non-Hermitian array of optical waveguides embedded in an atomic gas

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 intercell 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 a 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.