Atomic-Beam Resonance Measurement of the Differential Polarizability between Zeeman Substates in the Ground State of the Cesium Atom

A large 25-cps voltage is applied across two parallel metal plates situated between the loops of a Ramsey double-hairpin structure, in an atomic-beam magnetic-resonance apparatus adjusted to observe flop-in transitions. A beam of cesium atoms passes between the plates and is subject to an electric field of about 5×${10}^4$ V/cm. The flop-in transition $\mathrm{}(4,-3)\mathrm{}\leftrightarrow \mathrm{}(4,-4)\mathrm{}$ is observed at a low magnetic field with the rf oscillator adjusted so that the signal at the detector corresponds to the point of maximum slope on either side of the central peak of the Ramsey pattern. A small quadratic Stark shift is observed in two ways, using phase-sensitive detection, by measuring (1) the 50-cps component in the signal, and (2) the 25-cps component when a dc bias is superimposed on the ac voltage. The width of the central Ramsey peak is about 2 kc/sec, and shifts of the order of a few parts in ${10}^5$ of this are easily detected. The measured result for the quadratic Stark shift is $\delta f=-127\mathrm{}\pm 20$ cps at ${10}^5$ V/cm. A detailed discussion of instrumental effects which might be responsible for the large uncertainty is included. In particular, the major contribution to the uncertainty is believed to arise from an undetermined motion of the magnet pole pieces of the C magnet. This motion is probably due to either electrostrictive effects in the insulators of the electric-field-plate structure, or electrostatic attraction between the plates or between the plates and the pole pieces. A theory of the quadratic Stark effect involving mixing by both the dipole and the quadrupole part of the hfs operator in the first excited state is given. The theoretical estimate is $\delta f=-118\mathrm{}$ cps at ${10}^5$ V/cm, which is in agreement with the measured result.