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Register a new userObservation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
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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.
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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.
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.
A network model that can describe light propagation in one-dimensional ring-resonator arrays with a dimer structure is studied as a Su-Schrieffer-Heeger-type Floquet network. The model can be regarded as a Floquet system without periodic driving and exhibits quasienergy band structures of the ring propagation phase. Resulting band gaps support deterministic edge states depending on hopping S-matrices between adjacent rings. The number of edge states is one if the Zak phase is $pi$. If the Zak phase is 0, the number is either zero or two. The criterion of the latter number is given analytically in terms of the reflection matrix of the semi-infinite system. These properties are directly verified by changing S-matrix parameters and boundary condition continuously.
We use Langevin sampling methods within the auxiliary-field quantum Monte Carlo algorithm to investigate the phases of the Su-Schrieffer-Heeger model on the square lattice at the O(4) symmetric point. Based on an explicit determination of the density of zeros of the fermion determinant, we argue that this method is efficient in the adiabatic limit. By analyzing dynamical and static quantities of the model, we demonstrate that a $(pi,pi)$ valence bond solid gives way to an antiferromagnetic phase with increasing phonon frequency.
We propose an implementation of a generalized Su-Schrieffer-Heeger (SSH) model based on optomechanical arrays. The topological properties of the generalized SSH model depend on the effective optomechanical interactions enhanced by strong driving optical fields. Three phases including one trivial and two distinct topological phases are found in the generalized SSH model. The phase transition can be observed by turning the strengths and phases of the effective optomechanical interactions via adjusting the external driving fields. Moreover, four types of edge states can be created in generalized SSH model of an open chain under single-particle excitation, and the dynamical behaviors of the excitation in the open chain are related to the topological properties under the periodic boundary condition. We show that the edge states can be pumped adiabatically along the optomechanical arrays by periodically modulating the amplitude and frequency of the driving fields. The generalized SSH model based on the optomechanical arrays provides us a tunable platform to engineer topological phases for photons and phonons, which may have potential applications in controlling the transport of photons and phonons.
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