Atomic $CP$-violating polarizability

Searches for $CP$-violating effects in atoms and molecules provide important constrains on competing extensions to the standard model of elementary particles. In particular, $CP$ violation in an atom leads to the $CP$-odd (T,P-odd) polarizability ${\beta }^{\mathrm{CP}}$: a magnetic moment ${\mu }^{\mathrm{CP}}$ is induced by an electric field ${\mathcal{E}}_0$ applied to an atom, ${\mu }^{\mathrm{CP}}={\beta }^{\mathrm{CP}}{\mathcal{E}}_0$. We estimate the $CP$-violating polarizability for rare-gas (diamagnetic) atoms He through Rn. We relate ${\beta }^{\mathrm{CP}}$ to the permanent electric dipole moment (EDM) of the electron and to the scalar constant of the $CP$-odd electron-nucleus interaction. The analysis is carried out using the third-order perturbation theory and the Dirac-Hartree-Fock formalism. We find that, as a function of nuclear charge $Z,{\beta }^{\mathrm{CP}}$ scales steeply as $Z^{5}R\left(Z\right)$, where slowly varying $R\left(Z\right)$ is a relativistic enhancement factor. Finally, we evaluate the feasibility of setting a limit on electron EDM by measuring $CP$-violating magnetization of liquid Xe. We find that such an experiment could provide competitive bounds on electron EDM only if the present level of experimental sensitivity to ultraweak magnetic fields [Kominis et al., Nature 422, 596 (2003)] is improved by several orders of magnitude.

Figure 1

(Color online) Dependence of the $CP$-violating polarizability ${\beta }^{\mathrm{CP}}$ on the nuclear charge $Z$ for rare-gas atoms. $CP$ violation is due to the electron EDM, $d_e$. The ratio ${\beta }^{\mathrm{CP}}∕d_e$ is given in atomic units.

Figure 2

(Color online) A scheme for measuring $CP$-violating polarizability.