We experimentally demonstrate the existence and control of coherent superpositions of elastic states in the direction of propagation of an ultrasonic pseudospin i.e., a φ-bit. The experimental realization of this mechanical pseudospin consists of an elastic aluminum rod serving as a waveguide sandwiched between two heavy steel plates. The Hertzian contact between the rod and the plates leads to restoring forces which couple the directions of propagation (forward and backward). This coupling generates the coherence of the superposition of elastic states. We also demonstrate φ-bit gate operations on the coherent superposition analogous to those used in quantum computing. In the case of a φ-bit, the coherent superposition of states in the direction of propagation are immune to wave function collapse upon measurement as they result from classical waves.

We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu’s equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave.

The crystal structure of the mineral junitoite, ideally CaZn2Si2O7·H2O (calcium dizinc disilicate monohydrate), was first determined by Hamilton & Finney [Mineral. Mag. (1985), 49, 91–95] based on the space group Ama2, yielding a reliability factor R of 0.10, with isotropic displacement parameters for all non-H atoms. The present study reports a structure redetermination of junitoite using single-crystal X-ray diffraction data from a natural sample, demonstrating that the space group of this mineral is actually Aea2, which can be attained simply by shifting the origin. Topologically, the structure models in the space groups Aea2 and Ama2 are analogous, consisting of chains of corner-sharing ZnO4 tetra­hedra parallel to the b axis, cross-linked by Si2O7 tetra­hedral dimers (the site symmetry of the bridging O atom is ..2) along a and c, forming a three-dimensional framework. The Ca2+ cations (site symmetry ..2) are situated in cavities of the framework and are bonded to five O atoms and one H2O mol­ecule (site symmetry ..2) in a distorted octa­hedral coordination environment. However, some bond lengths, especially for the SiO4 tetra­hedron, are noticeably different between the two structure models. Hydrogen bonding in junitoite is found between the water mol­ecule and a framework O atom.