We report theoretical calculations and experimental observations of Pancharatnam's phase originating from arbitrary SU (2) transformations applied to polarization states of light. We have implemented polarimetric and interferometric methods which allow us to cover the full Poincaré sphere. As a distinctive feature, our interferometric array is robust against mechanical and thermal disturbances, showing that the polarimetric method is not inherently superior to the interferometric one, as previously assumed. Our strategy effectively amounts to feed an interferometer with two copropagating beams that are orthogonally polarized with respect to each other. It can be applied to different types of standard arrays, like a Michelson, a Sagnac, or a Mach-Zehnder interferometer. We exhibit the versatility of our arrangement by performing measurements of Pancharatnam's phases and fringe visibilities that closely fit the theoretical predictions. Our approach can be easily extended to deal with mixed states and to study decoherence effects.

The coherent manipulation of acoustic waves on the nanoscale usually requires multilayers with thicknesses and interface roughness defined down to the atomic monolayer. This results in expensive devices with predetermined functionality. Nanoscale mesoporous materials present high surface-to-volume ratio and tailorable mesopores, which allow the incorporation of chemical functionalization to nanoacoustics. However, the presence of pores with sizes comparable to the acoustic wavelength is intuitively perceived as a major roadblock in nanoacoustics. Here we present multilayered nanoacoustic resonators based on mesoporous SiO 2 thin-films showing acoustic resonances in the 5-100 GHz range. We characterize the acoustic response of the system using coherent phonon generation experiments. Despite resonance wavelengths comparable to the pore size, we observe for the first time well-defined acoustic resonances. Our results open the path to a promising platform for nanoacoustic sensing and reconfigurable acoustic nanodevices based on soft, inexpensive fabrication methods.

Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems [1]. The possibility of engineering systems with unidirectional wave propagation and protected against disorder is at the heart of this growing interest [2]. Topogical acoustic effects have been observed in a variety of systems [3][4][5][6][7][8], most of them based on kHz-MHz sound waves, with typical wavelength of the order of the centimeter. Recently, some of these concepts have been successfully transferred to acoustic phonons in nanoscaled multilayered systems [9,10]. The reported demonstration of confined topological phononic modes was based on Raman scattering spectroscopy [9], yet the resolution did not suffice to determine lifetimes and to identify other acoustic modes in the system. Here, we use time-resolved pump-probe measurements [11][12][13] using an asynchronous optical sampling (ASOPS) technique [14] to overcome these resolution limitations. By means of one-dimensional GaAs/AlAs distributed Bragg reflectors (DBRs) as building blocks [15][16][17][18][19], we engineer high frequency (∼ 200 GHz) topological acoustic interface states [9,20]. We are able to clearly distinguish confined topological states from stationary band edge modes. The detection scheme reflects the symmetry of the modes directly through the selection rules [21,22], evidencing the topological nature of the measured confined state. These experiments enable a new tool in the study of the more complex topology-driven phonon dynamics such as phonon nonlinearities and optomechanical systems with simultaneous confinement of light and sound [23,24].