Recent experimental advances in creating dissipative couplings provide a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spin waves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically induced-transparency spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings.
Recent experimental advances in creating dissipative couplings provide a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spin waves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically induced-transparency spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings.
Robust quantum state transfer (QST) is the foundation for information exchange among nodes in quantum networks. In this paper, we propose a robust QST protocol that utilizes topological edge modes in the qubit chains to encode (decode) quantum states (flying qubits). By employing qubits with tunable couplings, we construct Su-Schrieffer-Heeger (SSH) chains as the nodes of a quantum network. The end qubit of each SSH chain is dissipatively coupled to a chiral waveguide, and the dissipative strength is a constant. We refer to the SSH chain with a dissipation channel at the end qubit as the non-Hermitian SSH chain. Comparing the symmetry and energy spectra of the non-Hermitian SSH chain with those of the SSH chain, our analysis reveals that the dissipative dynamics of the topological edge state in the non-Hermitian SSH chain are governed by its imaginary spectra. The edge mode with the imaginary spectrum can be used to encode (decode) quantum states (flying qubits), thereby enabling robust QST between two remote mirrored non-Hermitian SSH chains. Our numerical simulations demonstrate that high-fidelity QST can be achieved even in the presence of coupling errors. Furthermore, we extend our analysis to consider QST in imperfect chiral waveguides, providing insights into the robustness of our protocol under realistic conditions. Our discussion is applicable to various quantum platforms and holds significant implications for constructing large-scale quantum networks.
Fock-state lattice (FSL) offers a powerful quantum simulator for topological phenomena due to the unbounded scalability and ease of implementation. Nevertheless, the unique topological properties induced by its site-dependent coupling have remained elusive, mainly due to the challenge of handling an infinite state space without translational symmetry. Here, we rigorously analyze the topological features of a semi-infinite FSL-based Su-Schrieffer-Heeger (SSH) model, in both Hermitian and non-Hermitian realms, by mapping it to the solvable Jaynes-Cummings model via a unitary displacement transformation. We find a topological zero mode persisting across all parameter regimes, which is more stable than the conventional SSH model. It originates from the bound state at the inherent domain wall under anisotropic conditions. With gain and loss introduced, we predict a non-Hermitian bound effect, i.e., any state overlapping with the bound state will quickly stabilize to the domain wall, with the minimal stabilization time occurring in the vicinity of exceptional point. The parity-time phase transition can be observed by the oscillating-to-steady crossover of dynamics in the subspace orthogonal to the bound state. Furthermore, a concrete experimental proposal based on the trapped-ion setup is provided.
Abstract The Su–Schrieffer–Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer trans -polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically protected, dispersionless boundary states. Here, using 87 Rb atoms in a momentum-space lattice, we realize fully tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.
We investigate the dynamics of entanglement in dissipative fermionic and bosonic Su-Schrieffer-Heeger (SSH) models and discover that they exhibit a revival dynamics of entanglement when the decoherence channel preserves the chiral symmetry. This behavior is only observable in the topological phase, and the visibility of the revival diminishes to zero at the phase boundary. Furthermore, the revival acquires a universal character, meaning that the entire time-evolution profile remains independent of system size, provided that the size exceeds the localization length of the edge modes associated with the topological phase. Our findings suggest that the universal entanglement revival originates from the topological properties of the SSH model. These dynamical properties may be experimentally accessible, for instance, by utilizing photonic quantum computers.
Topological insulators are unique materials possessing forbidden topological gap and behaving similar to usual insulators in their bulk, but at the same time supporting localized in-gap states at their edges that demonstrate exceptional robustness, because they are protected by topology of the system and cannot be destroyed by local disorder or edge perturbations. Topological insulators discovered in different areas of physics, including optics, acoustics, and physics of Bose-Einstein and polariton condensates, usually employ potential landscapes (or lattices), designed such as to feature specific degeneracies in their linear modal spectra, that can be lifted by various physical effects or controllable deformations of the potential, leading to opening of the topological gap, where edge states appear. In this work, using binary Bose-Einstein condensate we propose a type of topological insulator that does not explicitly use specially designed potential landscape, but instead utilizes spatially inhomogeneous Rabi coupling between two components, in the form of a one- or two-dimensional Su-Schrieffer-Heeger structure, combined with Zeeman splitting. Such Rabi lattices reveal the appearance of topologically nontrivial phases (including higher-order ones) controlled by spatial shift of the domains with enhanced coupling between condensates within unit cells of the structure, where localized topological states appear at the edges or in the corners of truncated Rabi lattice. We also show that the properties of edge states, their spatial localization, and location of their chemical potential within topological gap can be controlled by interatomic interactions that lead to formation of gap topological edge solitons bifurcating from linear edge states. Such solitons in condensates with inhomogeneous Rabi coupling appear as very robust nonlinear topological objects that do not require any threshold norm for their formation even in two-dimensional geometries, and that can exist in stable form for both attractive and repulsive interactions. Our results demonstrate considerable enhancement of stability of solitons in topological Rabi lattices in comparison with trivial Rabi lattices. They open additional prospects for realization of topologically nontrivial phases by spatial engineering of coupling in multicomponent systems.
Abstract The Su–Schrieffer–Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higher-dimensional extension of the mean chiral displacement measurement, however, this has not yet been verified in experiment. Here, we report the realization of this model with ultracold atoms in a momentum lattice. We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary.