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We explore ways to use the ability to measure the populations of individualmagnetic sublevels to improve the sensitivity of magnetic field measurementsand measurements of atomic electric dipole moments (EDMs). When atoms areinitialized in the $m=0$ magnetic sublevel, the shot-noise-limited uncertaintyof these measurements is $1/\sqrt{2F(F+1)}$ smaller than that of a Larmorprecession measurement. When the populations in the even (or odd) magneticsublevels are combined, we show that these measurements are independent of thetensor Stark shift and the second order Zeeman shift. We discuss thecomplicating effect of a transverse magnetic field and show that when the ratioof the tensor Stark shift to the transverse magnetic field is sufficientlylarge, an EDM measurement with atoms initialized in the superposition of thestretched states can reach the optimal sensitivity.

Improving sensitivity to magnetic fields and electric dipole moments by using measurements of individual magnetic sublevels