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We analyze doubly magic trapping of Cs hyperfine transitions includingpreviously neglected contributions from the ground state hyperpolarizabilityand the interaction of the laser light and a static magnetic field. Extensivenumerical searches do not reveal any doubly magic trapping conditions for anypair of hyperfine states. However, including the hyperpolarizability revealslight intensity insensitive traps for a wide range of wavelengths at specificintensities. We then investigate the possibility of using bichromatic trappinglight fields. Deploying a bichromatic scheme, we demonstrate doubly magic redand blue detuned traps for pairs of states separated by one or two singlephoton transitions.

Doubly magic optical trapping for Cs atom hyperfine clock transitions