Magic wavelengths for optically trapped atoms

The ability to trap neutral atoms inside high-Q cavities in the strong coupling regime is of particular importance for quantum computation and communication schemes, where it is essential to precisely localize and control neutral atoms with minimum decoherence. In a far-detuned optical dipole trap, the potentials experienced by an atom in its ground and excited states may be of opposite sign affecting the fidelity of experiments in which excited states are temporarily occupied. ``Magic wavelengths'' are those for which such potentials are equal. Single-laser schemes offer few cases in which magic wavelengths exist for Rb [Arora et al. PRA 76, 052509 (2007).] Here we explore bichromatic schemes for state-insensitive optical trapping of the Rb. We describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We have also identified wavelengths $\lambda_{\rm{zero}}$ where the ground state frequency-dependent polarizabilities in alkali-metal atoms are zero. These are relevant for cooling and trapping experiments involving mixtures such as Rb/Yb, where the vanishing lattice potential for Rb facilitates interesting applications.