Magnetic sublevel independent magic wavelengths: Application in the Rb and Cs atoms

A generic scheme to trap atoms at the magic wavelengths ($\lambda_{\rm{magic}}$s) that are independent of vector and tensor components of the interactions of the atoms with the external electric field is presented. The $\lambda_{\rm{magic}}$s for the laser cooling D2 lines in the Rb and Cs atoms are demonstrated and their corresponding polarizability values without vector and tensor contributions are given. Consequently, these $\lambda_{\rm{magic}}$s are independent of magnetic sublevels and hyperfine levels of the atomic states involved in the transition, thus, can offer unique approaches to carry out many high precision measurements with minimal systematics. Inevitably, the proposed technique can also be used for electronic or hyperfine transitions in other atomic systems.Comment: Accepted for publication in Phys. Rev.

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use