  Precision measurements and quantum information processing with cold atoms may
benefit from trapping atoms with specially engineered, "magic" optical fields.
At the magic trapping conditions, the relevant atomic properties remain immune
to strong perturbations by the trapping fields. Here we develop a theoretical
analysis of a recently observed magic trapping for especially valuable
Zeeman-insensitive clock transitions in alkali-metal atoms. The involved
mechanism relies on applying "magic" bias B-field along circularly polarized
trapping laser field. We map out these B-fields as a function of trapping laser
wavelength for all commonly-used alkalis.
