Permanent Electric Dipole Moment of the Cesium Atom. An Upper Limit to the Electric Dipole Moment of the Electron

Abstract

An atomic-beam magnetic-resonance apparatus has been employed to search for a linear Stark effect on the flop-in Zeeman transition ($F=4, {m}_{F}=\ensuremath{-}4)\ensuremath{\leftrightarrow}(F=4, {m}_{F}=\ensuremath{-}3$) of the ground state of the cesium atom. Such an effect could be interpreted in terms of a permanent electric dipole moment (EDM) of the cesium atom. The existence of an EDM in a nondegenerate physical system having well-defined angular momentum, such as the cesium atom in its ground state, would be direct evidence of a violation of parity and time-reversal invariance. To detect a possible linear Stark effect, a voltage of 10 kV is applied across two parallel metal plates located between the rf loops of a Ramsey double-hairpin structure. A beam of cesium atoms passes between the metal plates, where it is subjected to an electric field of approximately 5 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ V/cm. The flop-in Zeeman transition is observed for a magnetic field of 0.95 G. The signal generator which drives the rf loops is adjusted so that the detector signal corresponds to the point of maximum slope on one side of the central peak of the two-loop interference pattern. The direction of the electric field is reversed every 0.57 sec, and the resonance signal is accumulated in two counters (one for each direction of the electric field), gated synchronously with the electric field switching frequency. Thus, the quadratic Stark effect contributes the same signal to each counter, and a difference between the counters indicates the presence of a resonance shift linear in $E$. With the apparatus used in the present experiments, resonance shifts as small as 2 or 3 parts in ${10}^{6}$ of the linewidth (850 cps in cesium) could be observed with about 2 h of integration time. A linear resonance shift which simulates a linear Stark effect can be caused by the interaction between the atom's magnetic dipole moment and the magnetic field [$(\frac{\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}{c})\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$] due to the atom's motion through $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$. To separate this motional magnetic field effect from a possible linear Stark effect, the resonance shift linear in $E$ is studied as a function of the angle between $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$, and the angles corresponding to zero resonance shift are obtained in sodium and cesium. A difference between these angles for sodium and cesium would indicate the presence of a linear effect other than $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$. The magnitude of this difference can be used to set an upper limit on the linear Stark effect in cesium. A relativistic argument shows that if the electron possesses an EDM, the EDM of the Cs atom is approximately 119 times as large, whereas that of the sodium atom is 0.3 times as large. These results, together with the measured values of the angles which correspond to zero resonance shifts in Na and Cs, lead to the following upper limits on the EDM's of the Cs atom and the free electron: $\frac{{\ensuremath{\mu}}_{\mathrm{Cs}}}{e}<3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ cm and $\frac{{\ensuremath{\mu}}_{e}}{e}<2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ cm.