Coupling mechanism between microscopic two-level system and superconducting qubits

We propose a scheme to clarify the coupling nature between superconducting Josephson qubits andmicroscopic two-level systems. Although dominant interest in studying two-level systems was in phase qubits previously, we find that the sensitivity of the generally used spectral method in phase qubits is not sufficient to evaluate the exact form of the coupling. On the contrary, our numerical calculation shows that the coupling strength changes remarkably with the flux bias for a flux qubit, providing a useful tool to investigate the coupling mechanism between the two-level systems and qubits.Comment: 5 pages, 4 figure

Detecting fractional Josephson effect through 4π4\pi phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe fractional DC Josephson effect of semiconductor nanowire-based topological Josephson junction through 4{\pi} phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting the resonant tunneling with 4{\pi} phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4{\pi} phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.Comment: 5 pages, 3 figure

Detecting fractional Josephson effect through 4π4\pi phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe fractional DC Josephson effect of semiconductor nanowire-based topological Josephson junction through 4{\pi} phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting the resonant tunneling with 4{\pi} phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4{\pi} phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.Comment: 5 pages, 3 figure

A Symmetric Rank-one Quasi Newton Method for Non-negative Matrix Factorization

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix approximation is proposed. This method mainly bases on the active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. Our method improves the recent results of those methods in [Pattern Recognition, 45(2012)3557-3565; SIAM J. Sci. Comput., 33(6)(2011)3261-3281; Neural Computation, 19(10)(2007)2756-2779, etc.]. Moreover, the object function decreases faster than many other NMF methods. In addition, some numerical experiments are presented in the synthetic data, imaging processing and text clustering. By comparing with the other six nonnegative matrix approximation methods, our experiments confirm to our analysis.Comment: 19 pages, 13 figures, Submitted to PP on Feb. 5, 201

Laboratory photo-chemistry of covalently bonded fluorene clusters: observation of an interesting PAH bowl-forming mechanism

The fullerene C$_{60}$, one of the largest molecules identified in the interstellar medium (ISM), has been proposed to form top-down through the photo-chemical processing of large (more than 60 C-atoms) polycyclic aromatic hydrocarbon (PAH) molecules. In this article, we focus on the opposite process, investigating the possibility that fullerenes form from small PAHs, in which bowl-forming plays a central role. We combine laboratory experiments and quantum chemical calculations to study the formation of larger PAHs from charged fluorene clusters. The experiments show that with visible laser irradiation, the fluorene dimer cation - [C$_{13}$H$_{9}$$-$C$_{13}$H$_{9}$]$^+$ - and the fluorene trimer cation - [C$_{13}$H$_{9}$$-$C$_{13}$H$_{8}$$-$C$_{13}$H$_{9}$]$^+$ - undergo photo-dehydrogenation and photo-isomerization resulting in bowl structured aromatic cluster-ions, C$_{26}$H$_{12}$$^+$ and C$_{39}$H$_{20}$$^+$, respectively. To study the details of this chemical process, we employ quantum chemistry that allows us to determine the structures of the newly formed cluster-ions, to calculate the hydrogen loss dissociation energies, and to derive the underlying reaction pathways. These results demonstrate that smaller PAH clusters (with less than 60 C-atoms) can convert to larger bowled geometries that might act as building blocks for fullerenes, as the bowl-forming mechanism greatly facilitates the conversion from dehydrogenated PAHs to cages. Moreover, the bowl-forming induces a permanent dipole moment that - in principle - allows to search for such species using radio astronomy.Comment: 8 pages, 7 figures, accepte