Electric-dipole-moment searches: Reexamination of frequency shifts for particles in traps

In experiments searching for a nonzero electric dipole moment of trapped particles, frequency shifts correlated with an applied electric field can be interpreted as a false signal. One such effect, referred to as the geometric phase effect, is known to occur in a magnetic field that is nonperfectly homogeneous. The increase in sensitivity of experiments demands improved theoretical description of this effect. In the case of fast particles, like atoms at room temperature and low pressure, the validity of established theories was limited to a cylindrical confinement cell in a uniform gradient with cylindrical symmetry. We develop a more general theory valid for an arbitrary shape of the magnetic field as well as for arbitrary geometry of the confinement cell. Our improved theory is especially relevant for experiments measuring the neutron electric dipole moment with an atomic comagnetometer. In this context, we have reproduced and extended earlier numerical studies of the geometric phase effect induced by localized magnetic impurities.

Figure 1

Enhancement of the geometric phase effect calculated for the OILL trap for a magnetic dipole on the axis as a function of the distance from the bottom plate of the trap. The analytical result (29) is compared to the heuristic and numerical results [13].

Figure 2

False neutron EDM signal due to a dipole of strength $p=0.5{\mathrm{nT}\mathrm{cm}}^3$ at the lower surface of the cell for different radial positions and different orientations. The left-hand-side plot shows the main contribution around the circumference of the cell. The right-hand-side plot is a zoom for smaller radii.