The acoustic analogue of a topological insulator is shown: a metamaterial exhibiting one-way sound transport along its edge. The system — a graphene-like array of stainless-steel rods — is a promising new platform for exploring topological phenomena.

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Acoustic topological insulator and robust one-way sound transport

The study of classical wave physics has been reinvigorated by incorporating the concept of the geometric phase, which has its roots in optics, and topological notions that were previously explored in condensed matter physics. Recently, sound waves and a variety of mechanical systems have emerged as excellent platforms that exemplify the universality and diversity of topological phases. In this Review, we introduce the essential physical concepts that underpin various classes of topological phenomena realized in acoustic and mechanical systems: Dirac points, the quantum Hall, quantum spin Hall and valley Hall effects, Floquet topological phases, 3D gapless states and Weyl crystals. This Review describes topological phenomena that can be realized in acoustic and mechanical systems. Methods of symmetry breaking are described, along with the consequences and rich phenomena that emerge.

Topological phases in acoustic and mechanical systems

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Topological Phononic Crystals with One-Way Elastic Edge Waves

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system Finally, we prove the robustness of the measure by introducing dynamical disorder in the system This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems The detection of topological invariants in the bulk remains challenging even in state-of-the-art experiments Here, Cardanoet al propose a method to read-out the Zak phases and topological invariants in one-dimensional chiral systems and detect those in a photonic quantum walk of twisted photons

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Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Recently, we witnessed a tremendous effort to conquer the realm of acoustics as a possible playground to test with sound waves topologically protected wave propagation. Acoustics differ substantially from photonic and electronic systems since longitudinal sound waves lack intrinsic spin polarization and breaking the time-reversal symmetry requires additional complexities that both are essential in mimicking the quantum effects leading to topologically robust sound propagation. In this article, we review the latest efforts to explore with sound waves topological states of quantum matter in two- and three-dimensional systems where we discuss how spin and valley degrees of freedom appear as highly novel ingredients to tailor the flow of sound in the form of one-way edge modes and defect-immune protected acoustic waves. Both from a theoretical stand point and based on contemporary experimental verifications, we summarize the latest advancements of the flourishing research frontier on topological sound.

Topological Sound

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics and mechanics as well, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here we report experimental demonstration of anomalous Floquet topological insulator for sound: a strongly coupled metamaterial ring lattice that supports one-way propagation of pseudo-spin-dependent edge states under T-symmetry. We also demonstrate the formation of pseudo-spin-dependent interface states due to lattice dislocations and investigate the properties of pass band and band gap states.

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Experimental demonstration of anomalous Floquet topological insulator for sound.

The problem of direction-of-arrival (DOA) estimation for sparse array is addressed. The perspective that DOA estimation in virtual array response model can be cast as the problem of sparse recovery is introduced. Two methods are proposed, based on different optimization problems, which are solvable using second-order cone (SOC) programming. Without the knowledge of the number of sources, the proposed methods yield superior performances, which are verified by numerical simulations.

DOA Estimation for Sparse Array via Sparse Signal Reconstruction

A one-bit joint sparse representation direction of arrival (OBJSR-DOA) estimation approach is proposed in this letter. By exploiting the joint spatial and spectral correlations inherent in acoustic sensor array data, the proposed OBJSR-DOA approach provides reliable DOA estimation from only the sign bit of randomly subsampled acoustic sensor data. The random subsampling and single-bit quantization allow significant reduction of data to be transmitted to the fusion center without additional energy consumption requirement in the source coding/compression operation. Compared with existing compressive sensing-based DOA estimation methods, the superiority of the proposed approach in providing data volume reduction and performance improvement is verified by both simulations and field experiments using a prototype wireless sensor array network platform.

DOA Estimation From One-Bit Compressed Array Data via Joint Sparse Representation

In this paper, we present a generalized iterated Kalman filter (GIKF) algorithm for state estimation of a nonlinear stochastic discrete-time system with state-dependent multiplicative observation noise. The GIKF algorithm adopts the Newton–Raphson iterative optimization steps to yield an approximate maximum a posteriori estimate of the states. The mean-square estimation error (MSE) and the Cramer–Rao lower bound (CRLB) of the state estimates are also derived. In particular, the local convergence of MSE of GIKF is rigorously established. It is also proved that the GIKF yields a smaller MSE than those of the generalized extended Kalman filter and the traditional extended Kalman filter. The performance advantages and convergence of GIKF are demonstrated using Monte Carlo simulations on a target tracking application in a range measuring sensor network.

Generalized Iterated Kalman Filter and its Performance Evaluation

Understanding unidirectional and topological wave phenomena requires the unveiling of intrinsic geometry and symmetry for wave dynamics. This is essential yet challenging for the flexible control of near-field evanescent waves, highly desirable in broad practical scenarios ranging from information communication to energy radiation. However, exploitations of near-field waves are limited by a lack of fundamental understanding about inherent near-field symmetry and directional coupling at sub-wavelengths, especially for longitudinal waves. Here, based on the acoustic wave platform, we show the efficient selective couplings enabled by near-field symmetry properties. Based on the inherent symmetry properties of three geometrically orthogonal vectors in near-field acoustics, we successfully realize acoustic Janus, Huygens, spin sources and quadrupole hybrid sources, respectively. Moreover, we experimentally demonstrate fertile symmetry selective directionality of those evanescent modes, supported by two opposite meta-surfaces. The symmetry properties of the near-field acoustic spin angular momenta are revealed by directly measuring local vectorial fields. Our findings advance the understanding of symmetries in near-field physics, supply feasible approaches for directional couplings, and pave the way for promising acoustic devices in the future.

Ming Bao

Papers

Experimental demonstration of anomalous Floquet topological insulator for sound.

DOA Estimation for Sparse Array via Sparse Signal Reconstruction

DOA Estimation From One-Bit Compressed Array Data via Joint Sparse Representation

Generalized Iterated Kalman Filter and its Performance Evaluation

Symmetry selective directionality in near-field acoustics.