Precise measurements of atomic g factor ratios using trapped Rb

We have measured the dephasing time of a coherence grating and inferred the temperature of a cloud of trapped atoms. The grating involves a spatially periodic superposition of adjacent magnetic sublevels of the F = 3 ground state in $^{85}$Rb. The dephasing exhibits Larmor oscillations in the presence of a magnetic field. We initially measured the frequency of Larmor oscillations to a precision of $\sim$0.1$\%$ using pulsed magnetic fields. We have improved the precision by over two orders of magnitude by using steady B fields. A precise measurement of the Zeeman shift of the atomic levels would require an absolute measurement of the B field at the location of the trap. Nevertheless, we show that it is possible to measure of the g factor ratios for $^{85}$Rb and $^{87}$Rb that are precise to ~50 parts per million.