Cesium and francium fountain EDM experiments

Our approach to guard against false positives and false negatives:

The Physics of Cs and Fr is well understood

cesium and francium

Fig. 1. Cs and Fr. The lighter alkali metals appear silver-white but Cs appears slightly golden due to relativistic effects. The reflectivity of Fr has not been determined.

The ground state hyperfine splitting is also a relativistic effect. The 43.6 GHz value for 211Fr could allow a Fr fountain frequency standard to be nearly a factor of five more precise than the Cs standard.

Cs and Fr, are alkali atoms. They have atomic structure that is simple, reliably calculated, and experimentally well understood. The Cs ground state hyperfine splitting defines the S.I. unit of the second.

Cs and Fr have large relativistic effects which scale as high powers of the atomic number Z. Among these effects is the atomic EDM induced by the electron EDM, an entirely relativistic effect that has been calculated from field theory. It puts this relationship on the same footing as other Standard Model calculations such as the calculations of radiative corrections that give rise to an EDM of any fundamental particle.

Because Fr is radioactive and in limited supply, Cs will be used both developing the experiment and for testing systematic effects. A Cs fountain proof-of-principle experiment has previously been completed and published. Reprint here.

Measurements on atoms in free space

Cs and Fr fountains allow the measurements to be done in free space and in free fall, with no collisions with gasses or walls; with no confining lasers or A.C. Stark shifts; with no applied static or time-varying magnetic fields; with only a static electric field between optical state preparation and optical state analysis, and with state preparation and analysis in a region free of both applied magnetic and applied electric fields.

Electric field quantization

Electric field quantization uses the electric field through the atom's tensor polarizability to lift the degeneracy between states of different magnetic sublevels |M|. With no applied magnetic field, motional magnetic field effects appear in second order and scale differently with electric field and with M than does an EDM. This tensor polarizability is a relativistic effect, larger in Fr than in Cs, reducing francium's sensitivity, relative to Cs, to motional systematic effects.

A novel feature of our experiment is the preparation of superpositions of different ±M states whose composition can be changed by rotating the laser polarization. Because different ±M states have different sensitivities to motional systematic effects and to an electron EDM, we can change the sensitivity to an EDM and to motional systematic effects (including making the EDM sensitivity zero). This is developed in great detail in: B. J. Wundt, C. T. Munger, Jr., and U. D. Jentschura Quantum dynamics in atomic- fountain experiments for measuring the electric dipole moment of the electron with improved sensitivity, Phys. Rev. X, 2:041009 (2012) for Cs and in it’s supplement for Fr.

Direct measurement of sensitivity

Because both the electron's electric and magnetic dipole moments couple to the atom's spin, the atom's sensitivity to a tiny magnetic field reversal serves as an estimate its sensitivity to an EDM.

To demonstrate the sensitivity to a very small effect, it is not generally sufficient to detect a large effect and declare, that with sufficient counting time, a small effect would be detectable. One must confront issues of noise, thresholds, nonlinearities, and cancellations. A substantial investment of experimental time is needed.

Incomplete electric field reversal does not lead to a systematic effect

An incomplete reversal of the electric field does not lead to a systematic effect because we use a superposition of +M and -M states. Unless there is an EDM, +M and -M states have the identical interaction with the electric field.

We also adjust the electric field so that the phase advance due to the Stark effect is, for every M state a multiple of π. We used this previously in the proof-of-principle cesium fountain EDM experiment.