Quadratic Stark Shift between Zeeman Substates inCs133,Rb87,Rb85,K39, andNa23

An atomic-beam magnetic-resonance apparatus with separated oscillatory fields has been used to make precision measurements of the quadratic Stark shift between "flop-in" Zeeman levels in the ground-state hyperfine structure of ${\mathrm{Cs}}^{133}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{K}}^{39}$, and ${\mathrm{Na}}^{23}$. The shift was measured as a function of the applied electric field and as a function of the rf power used to induce transitions. At magnetic fields of 1 G, the Stark shifts in cesium and ${\mathrm{Rb}}^{85}$ increased when the rf power was decreased. This observation has been explained by including multiple-quantum effects. The effects were eliminated in ${\mathrm{Rb}}^{85}$ by operating at low rf power, but in cesium it was necessary to extrapolate to zero rf power to obtain the final result. Systematic error due to uncertainties in the electric field and the filling factor are less than 2%. The results in units of ${10}^{-10\mathrm{}}$ $H_z{E}^{-2\mathrm{}}$, where $E$ is in V/cm, are: Cs=-137.2±7.9, ${\mathrm{Rb}}^{87}$ =-104.4±6.7, ${\mathrm{Rb}}^{85}$=-22.8±1.2, ${\mathrm{K}}^{39}$=-4.8±0.31, and ${\mathrm{Na}}^{23}$=-11.18±0.96.