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Register a new userTopological gap solitons in a 1D non-Hermitian lattice
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Added by
Jacqueline Bloch Pr
Publication date
2021
fields
Physics
and research's language is
English
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Nonlinear topological photonics is an emerging field aiming at extending the fascinating properties of topological states to the realm where interactions between the system constituents cannot be neglected. Interactions can indeed trigger topological phase transitions, induce symmetry protection and robustness properties for the many-body system. Moreover when coupling to the environment via drive and dissipation is also considered, novel collective phenomena are expected to emerge. Here, we report the nonlinear response of a polariton lattice implementing a non-Hermitian version of the Su-Schrieffer-Heeger model. We trigger the formation of solitons in the topological gap of the band structure, and show that these solitons demonstrate robust nonlinear properties with respect to defects, because of the underlying sub-lattice symmetry. Leveraging on the system non-Hermiticity, we engineer the drive phase pattern and unveil bulk solitons that have no counterpart in conservative systems. They are localized on a single sub-lattice with a spatial profile alike a topological edge state. Our results demonstrate a tool to stabilize the nonlinear response of driven dissipative topological systems, which may constitute a powerful resource for nonlinear topological photonics.
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Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers new opportunities for robust trapping of light in nano- and micro-meter scale systems subject to fabrication imperfections and to environmentally induced deformations. Here we show lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear topological photonics.
We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to {it enforced exceptional points} which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end-mode in a realistic model of a microcavity lattice.
The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to/from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: i) with time-reversal symmetry, the biorthogonal $mathbb{Z}_2$ invariant based on non-Hermitian Wilson loops, and ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.
Non-Hermitian systems can host topological states with novel topological invariants and bulk-edge correspondences that are distinct from conventional Hermitian systems. Here we show that two unique classes of non-Hermitian 2D topological phases, a 2$mathbb{Z}$ non-Hermitian Chern insulator and a $mathbb{Z}_{2}$ topological semimetal, can be realized by tuning staggered asymmetric hopping strengths in a 1D superlattice. These non-Hermitian topological phases support real edge modes due to robust $mathcal{PT}$-symmetric-like spectra and can coexist in certain parameter regime. The proposed phases can be experimentally realized in photonic or atomic systems and may open an avenue for exploring novel classes of non-Hermitian topological phases with 1D superlattices.
Phase frustration in periodic lattices is responsible for the formation of dispersionless flat bands. The absence of any kinetic energy scale makes flat band physics critically sensitive to perturbations and interactions. We report here on the experimental investigation of the nonlinear dynamics of cavity polaritons in the gapped flat band of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and very abrupt edges, signature of the frozen propagation of switching fronts. This type of gap solitons belongs to the class of truncated Bloch waves, and had only been observed in closed systems up to now. Here the driven-dissipative character of the system gives rise to a complex multistability of the nonlinear domains generated in the flat band. These results open up interesting perspective regarding more complex 2D lattices and the generation of correlated photon phases.
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