  We report the finding of "triply magic" conditions (the doubly magic
frequency-intensity conditions of an optical dipole trap plus the magic
magnetic field) for the microwave transitions of optically trapped alkali-metal
atoms. The differential light shift (DLS) induced by a degenerate two-photon
process is adopted to compensate a DLS associated with the one-photon process.
Thus, doubly magic conditions for the intensity and frequency of the optical
trap beam can be found. Moreover, the DLS decouples from the magnetic field in
a linearly polarized optical dipole trap, so that the magic condition of the
magnetic field can be applied independently. Therefore, the "triply magic"
conditions can be realized simultaneously. We also experimentally demonstrate
the doubly magic frequency-intensity conditions as well as the independence of
the magnetic field. When the triply magic conditions are fulfilled, the
inhomogeneous and homogeneous decoherences for the optically trapped atom will
be dramatically suppressed, and the coherence time can be extended
significantly.
