Triply magic conditions for microwave transitions of optically trapped alkali-metal atoms

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.