Magic Wavelengths for a Lattice Trapped Rubidium Four-Level Active Optical Clock

After being pumped from the 5s_1/2 ground state to the 6p_1/2 state, the population inversion between 6s_1/2 and 5p_1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10⁻¹⁸.