Abstract
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.
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