Laser cooling of a magnetically guided ultra cold atom beam

We report on the transverse laser cooling of a magnetically guided beam of ultra cold chromium atoms. Radial compression by a tapering of the guide is employed to adiabatically heat the beam. Inside the tapered section heat is extracted from the atom beam by a two-dimensional optical molasses perpendicular to it, resulting in a significant increase of atomic phase space density. A magnetic offset field is applied to prevent optical pumping to untrapped states. Our results demonstrate that by a suitable choice of the magnetic offset field, the cooling beam intensity and detuning, atom losses and longitudinal heating can be avoided. Final temperatures below 65 microkelvin have been achieved, corresponding to an increase of phase space density in the guided beam by more than a factor of 30.Comment: 9 pages, 4 figure

Oscillation of solutions of second-order nonlinear differential equations of Euler type

AbstractWe consider the nonlinear Euler differential equation t2x″+g(x)=0. Here g(x) satisfies xg(x)>0 for x≠0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t2x″+a(t)g(x)=0

Fixed point theorems for multivalued generalized nonlinear contractive maps in partial metric spaces

We prove some fixed-point results for multivalued generalized nonlinear contractive mappings in partial metric spaces, which generalize and improve the corresponding recent fixed-point results due to Ćirić [L. B. Ćirić, “Multivalued nonlinear contraction mappings,” Nonlin. Anal., 71, 2716–2723 (2009)] and Klim and Wardowski [D. Klim and D. Wardowski, “Fixed-point theorems for set-valued contractions in complete metric spaces,” J. Math. Anal. Appl., 334, 132–139 (2007)].Доведено ДЄЯКІ теореми про нерухому точку в частково метричних просторах, що узагальнюють та покращують відповідні нові результати про нерухому точку, отримані Чірічем (CiriC L. B. Multivalued nonlinear contraction mappings // Nonlinear Anal. - 2009. - 71. - P. 2716-2723) та Клімом i Вардовським (Klim D., Wardowski D. Fixed point theorems for set-valued contractions in complete metric spaces // J. Math. Anal. and Appl. - 2007. - 334. - P. 132-139)

Ytterbium-doped tantalum pentoxide waveguides: spectroscopy for compact waveguide lasers

Ytterbium-doped materials are common gain media in high-performance laser systems. In this work, the first spectroscopic investigation of ytterbium-doped tantalum pentoxide (Yb:Ta2O5) for compact waveguide laser applications is presented