Analysis of a Magnetically Trapped Atom Clock

We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.