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Register a new userSu-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States
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If a full band gap closes and then reopens when we continuously deform a periodic system while keeping its symmetry, a topological phase transition usually occurs. A common model demonstrating such a topological phase transition in condensed matter physics is the Su-Schrieffer-Heeger (SSH) model. As well known, two distinct topological phases emerge when the intracell hopping is tuned from smaller to larger with respect to the intercell hopping in the model. The former case is topologically trivial, while the latter case is topologically non-trivial. Here, we design a 1D periodic acoustic system in exact analogy to the SSH model. The unit cell of the acoustic system is composed of two resonators and two junction tubes connecting them. We show that the topological phase transition happens in our acoustic analog when we tune the radii of the junction tubes which control the intercell and intracell hoppings. The topological phase transition is characterized by the abrupt change of the geometric Zak phase. The topological interface states between non-trivial and trivial phases of our acoustic analog are experimentally measured, and the results agree very well with the numerical values. Further, we show that topologically non-trivial phases of our acoustic analog of the SSH model can support edge states, on which the discussion is absent in previous works about topological acoustics. The edge states are robust against localized defects and perturbations.
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In this work, we experimentally report the acoustic realization the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of air channels. We analytically study the steady state dynamics of the system using a set of discrete equations for the acoustic pressure, leading to the 2D SSH Hamiltonian matrix without using tight binding approximation. By building an acoustic network operating in audible regime, we experimentally demonstrate the existence of topological band gap. More supremely, within this band gap we observe the associated edge waves even though the system is open to free space. Our results not only experimentally demonstrate topological edge waves in a zero Berry curvature system but also provide a flexible platform for the study of topological properties of sound waves.
Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by the geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.
We demonstrate a platform for synthetic dimensions based on coupled Rydberg levels in ultracold atoms, and we implement the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian. Rydberg levels are interpreted as synthetic lattice sites, with tunneling introduced through resonant millimeter-wave couplings. Tunneling amplitudes are controlled through the millimeter-wave amplitudes, and on-site potentials are controlled through detunings of the millimeter waves from resonance. Using alternating weak and strong tunneling with weak tunneling to edge lattice sites, we attain a configuration with symmetry-protected topological edge states. The band structure is probed through optical excitation to the Rydberg levels from the ground state, which reveals topological edge states at zero energy. We verify that edge-state energies are robust to perturbation of tunneling-rates, which preserves chiral symmetry, but can be shifted by the introduction of on-site potentials.
We propose a realization of topological quantum interference in a pumped non-Hermitian Su-Schrieffer-Heeger lattice that can be implemented by creation and coherent control of excitonic states of trapped neutral atoms. Our approach is based on realizing sudden delocalization of two localized topological edge states by switching the value of the laser phase controlling the lattice potential to quench the system from the topological to the gapless or trivial non-topological quantum phases of the system. We find interference patterns in the occupation probabilities of excitations on lattice sites, with a transition from a two-excitation interference seen in the absence of pumping to many-excitation interferences in the presence of pumping. Investigation of the excitation dynamics in both the topological and trivial non-topological phases shows that such interference patterns which originate in topology are drastically distinct from interference between non-topological states of the lattice. Our results also reveal that unlike well-known situations where topological states are protected against local perturbations, in these non-Hermitian SSH systems a local dissipation at each lattice site can suppress both the total population of the lattice in the topological phase and the interference of the topological states.
We investigate the Su-Schrieffer-Heeger model in presence of an injection and removal of particles, introduced via a master equation in Lindblad form. It is shown that the dynamics of the density matrix follows the predictions of calculations in which the gain and loss are modeled by complex $mathcal{PT}$-symmetric potentials. In particular it is found that there is a clear distinction in the dynamics between the topologically different cases known from the stationary eigenstates.
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