Eigenvalue estimates for submanifolds of warped product spaces

We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type $N^n \times_f Q^q$, where $f \in C^\infty(N)$. We also study the essential spectrum of these minimal submanifolds.Comment: 17 page

Breaking the Rayleigh-Plateau instability limit using thermocavitation within a droplet

We report on the generation of liquid columns that extend far beyond the traditional Rayleigh-Plateau instability onset. The columns are driven by the acoustic pressure wave emitted after bubble collapse. A high-speed video imaging device, which records images at a rate of up to 105 fps, was employed to follow their dynamics. These bubbles, commonly termed thermocavitation bubbles, are generated by focusing a midpower (275 mW) continuous wavelength laser into a highly absorbing liquid droplet. A simple model of the propagation of the pressure wavefront emitted after the bubble collapse shows that focusing the pressure wave at the liquid-air interface drives the evolution of the liquid columns. Control over the aspect ratio of the liquid column is realized by adjusting the cavitation bubble's size, beam focus position, and droplet volume. © 2013 by Begell House, Inc

Controllable direction of liquid jets generated by thermocavitation within a droplet.

A high-velocity fluid stream ejected from an orifice or nozzle is a common mechanism to produce liquid jets in inkjet printers or to produce sprays among other applications. In the present research, we show the generation of liquid jets of controllable direction produced within a sessile water droplet by thermocavitation. The jets are driven by an acoustic shock wave emitted by the collapse of a hemispherical vapor bubble at the liquid-solid/substrate interface. The generated shock wave is reflected at the liquid-air interface due to acoustic impedance mismatch generating multiple reflections inside the droplet. During each reflection, a force is exerted on the interface driving the jets. Depending on the position of the generation of the bubble within the droplet, the mechanical energy of the shock wave is focused on different regions at the liquid-air interface, ejecting cylindrical liquid jets at different angles. The ejected jet angle dependence is explained by a simple ray tracing model of the propagation of the acoustic shock wave inside the droplet

Extended coherence time on the clock transition of optically trapped Rubidium

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a stability of 2.4E-11 x tau^(-1/2), where tau is the integration time in seconds. Based on a set of technical improvements, the presented frequency standard is predicted to rival the stability of microwave fountain clocks in a potentially much more compact setup.Comment: 5 pages, 4 figure

Measurement driven quantum evolution

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting and entanglement generation.Comment: 7 pages, 1 figur

Hydrogen sulfide pathway and skeletal muscle: an introductory review.

The presence of the H2 S pathway in skeletal muscle (SKM) has recently been established. SKM expresses the three constitutive H2 S-generating enzymes in animals and humans, and it actively produces H2 S. The main, recognized molecular targets of H2 S, that is, potassium channels and PDEs, have been evaluated in SKM physiology in order to hypothesize a role for H2 S signalling. SKM dysfunctions, including muscular dystrophy and malignant hyperthermia, have also been evaluated as conditions in which the H2 S and transsulfuration pathways have been suggested to be involved. The intrinsic complexity of the molecular mechanisms involved in excitation-contraction (E-C) coupling together with the scarcity of preclinical models of SKM-related disorders have hampered any advances in the knowledge of SKM function. Here, we have addressed the role of the H2 S pathway in E-C coupling and the relative importance of cystathionine β-synthase, cistathionine γ-lyase and 3-mercaptopyruvate sulfurtransferase in SKM diseases

Quantum and thermal spin relaxation in diluted spin ice: Dy(2-x)MxTi2O7 (M = Lu, Y)

We have studied the low temperature a.c. magnetic susceptibility of the diluted spin ice compound Dy(2-x)MxTi2O7, where the magnetic Dy ions on the frustrated pyrochlore lattice have been replaced with non-magnetic ions, M = Y or Lu. We examine a broad range of dilutions, 0 <= x <= 1.98, and we find that the T ~ 16 K freezing is suppressed for low levels of dilution but re-emerges for x > 0.4 and persists to x = 1.98. This behavior can be understood as a non-monotonic dependence of the quantum spin relaxation time with dilution. The results suggest that the observed spin freezing is fundamentally a single spin process which is affected by the local environment, rather than the development of spin-spin correlations as earlier data suggested.Comment: 26 pages, 9 figure

Pyramidal micromirrors for microsystems and atom chips

Concave pyramids are created in the (100) surface of a silicon wafer by anisotropic etching in potassium hydroxide. High quality micromirrors are then formed by sputtering gold onto the smooth silicon (111) faces of the pyramids. These mirrors show great promise as high quality optical devices suitable for integration into micro-optoelectromechanical systems and atom chips. We have shown that structures of this shape can be used to laser-cool and hold atoms in a magneto-optical trap

Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides

We report on the fabrication and microspectroscopy imaging of femtosecond laser written double-filament based Nd3+ :MgO:LiNbO3 optical waveguides. The waveguiding high refractive-index regions are identified by blueshifts of the Nd3+ ion fluorescence lines with no deterioration in the fluorescence efficiency, whereas filamentary low-index regions are identified by both a Nd3+ line redshift and a fluorescence efficiency reduction. The lattice structural micromodifications at the origin of both waveguide formation and Nd3+ fluorescence changes have been investigated by means of confocal micro-Raman experiments. We have found that the direct laser written filaments are mainly constituted by a large density of defects, together with a marked axial compression perpendicular to the filaments �along the optical c-axis�. Conversely, the high-index waveguiding regions are characterized by a pronounced anisotropic dilatation of the LiNbO3 lattice xy-planes