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A generic scheme to trap atoms at the magic wavelengths($\lambda_{\rm{magic}}$s) that are independent of vector and tensor componentsof 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 Csatoms are demonstrated and their corresponding polarizability values withoutvector and tensor contributions are given. Consequently, these$\lambda_{\rm{magic}}$s are independent of magnetic sublevels and hyperfinelevels of the atomic states involved in the transition, thus, can offer uniqueapproaches to carry out many high precision measurements with minimalsystematics. Inevitably, the proposed technique can also be used for electronicor hyperfine transitions in other atomic systems.

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