Laser locking to the Hg-199 S-1(0)-P-3(0) clock transition with 5.4x10(-15)/root tau fractional frequency instability

With Hg-199 atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is similar to 15 Hz. Here we lock an ultrastable laser to this ultranarrow S-1(0) - P-3(0) clock transition and achieve a fractional frequency instability of 5.4 x 10(-15) / root tau for tau <= 400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0 x 10(-17) s-(1) (-16.9 mHzs(-1) at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4 x 10(-16) per cavity. (c) 2012 Optical Society of America

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.