Experimental investigation of the radiation of sound from an unflanged duct and a bellmouth, including the flow effect

The radiation of sound from an inlet as a function of flow velocity, frequency, duct mode structure, and inlet geometry was examined by using a spinning mode synthesizer to insure a given space-time structure inside the duct. Measurements of the radiation pattern (amplitude and phase) and of the pressure reflection coefficient were obtained over an azimuthal wave number range of 0 to 6 and a frequency range up to 5000 Hz for an unflanged duct and a bellmouth. The measured radiated field and pressure reflection coefficient without flow for the unflanged duct agree reasonably well with theory. The influence of the inlet contour appears to be very drastic near the cut-on frequency of a mode and reasonable agreement is found between the bellmouth pressure reflection coefficient and a infinite hyperboloidal inlet theory. It is also shown that the flow has a weak effect on the amplitude of the directivity factor but significantly shifts the directivity factor phase. The influence of the flow on the modulus of the pressure reflection coefficient is found to be well described by a theoretical prediction

Quantum Circuits for General Multiqubit Gates

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4^n, and scales more favorably than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT gates.Comment: 4 pages, 3 figure

Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing

The Chern number, nu, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana zero modes. Here we show that such a winding can be faithfully identified for any superconducting system (p-wave or s-wave with spin-orbit coupling) through a set of time-of-flight measurements, making it a diagnostic tool also in actual cold atom experiments. As an application, we specialize the measurement scheme for a chiral topological model of spinless fermions. The proposed model only requires the experimentally accessible s-wave pairing and staggered tunnelling that mimics spin-orbit coupling. By adiabatically connecting this model to Kitaev's honeycomb lattice model, we show that it gives rise to nu = \pm 1 phases, where vortices bind Majorana fermions, and nu=\pm 2 phases that emerge as the unique collective state of such vortices. Hence, the preparation of these phases and the detection of their Chern numbers provide an unambiguous signature for the presence of Majorana modes. Finally, we demonstrate that our detection procedure is resilient against most inaccuracies in experimental control parameters as well as finite temperature.Comment: 9+4 pages, 11 figures, expanded versio

Breakdown of the Born-Oppenheimer approximation in solid hydrogen and hydrogen-rich solids

Hydrogen has been the subject of intense research following the discovery of high-temperature superconductivity in hydrides, and as a result of continuous efforts to produce solid hydrogen. The Born-Oppenheimer approximation is the central piece of the quantum mechanical description of molecules and solids and it is expected to have its weakest validity in hydrogen containing matter as it is the lightest element of all. The Born-Oppenheimer approximation is almost always assumed in the description of solids. Some beyond Born-Oppenheimer effects are likely included in the state-of-art method used to describe hydrogen-rich materials, but the effects on the electronic structure in solids have not been considered before. Here we compute the beyond Born-Oppenheimer corrections to electron density and report a breakdown of the Born-Oppenheimer approximation in experimentally known hydride superconductor YH6 and in Cs-IV structure of solid hydrogen. In both of these materials, we find a significant transfer of electron density from the volumes surrounding the expected positions of the hydrogen nuclei to volumes in between the nuclei. We expect these results to be the starting point of the beyond Born-Oppenheimer studies of electronic structure in solids, which is likely necessary to understand these forms of hydrogen-containing materials, also having significant technological importance.Comment: 11 pages, 4 figure

Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation

We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we derive corresponding exchange-correlation potentials and energies. We compare these with predictions of the local-spin-density approximation and discuss its accuracy. Our data will be useful as reference data in testing, comparing and parametrizing exchange and correlation functionals for two-dimensional electronic systems.Comment: Submitted to Physical Review B on January 3, 2012. Second revised version submitted on April 13, 201