The modern theory of charge polarization in solids is based on a generalization of Berry's phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.

Condensed-matter and other engineered systems, such as cold atoms, photonic, or phononic metamaterials, have proven to be versatile platforms for the observation of low-energy counterparts of elementary particles from relativistic field theories. These include the celebrated Majorana modes, as well as Dirac and Weyl fermions. An intriguing feature of the Weyl equation is the chiral symmetry, where the two chiral sectors have an independent gauge freedom. While this freedom leads to a quantum anomaly, there is no corresponding axial background field coupling differently to opposite chiralities in quantum electrodynamics. Here, we provide the experimental characterization of the effect of such an axial field in an acoustic metamaterial. We implement the axial field through an inhomogeneous potential and observe the induced chiral Landau levels. From the metamaterials perspective these chiral channels open the possibility for the observation of non-local Weyl orbits and might enable unidirectional bulk transport in a time-reversal invariant system. arXiv:1806.09628v1 [cond-mat.other]

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: Although answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.

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Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we construct a two-dimensional topological acoustic crystal induced by the synthetic spin-orbit coupling, a crucial ingredient of topological insulators, with spin non-conservation. Our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a nonvanishing "spin" Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. More importantly, we observe the spin flipping transport in an H-shaped device, demonstrating evidently the spin non-conservation of the boundary states.

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We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable sensitivity and address the question of whether quantumness of the probe state may provide a precision enhancement. The ultimate bounds to precision are quantified in terms of the corresponding Quantum Fisher Information. Our results show that states with no classical limit perform better than semiclassical ones and that a non-trivial interplay exists between the external field and the statistical model. More intense fields generally lead to a better precision, with the exception of position measurements in the case of freely-falling systems.