Oscillating nuclear electric dipole moment induced by axion dark matter produces atomic and molecular electric dipole moments and nuclear spin rotation

Abstract

According to the Schiff theorem, a static nuclear electric dipole moment (EDM) does not produce atomic and molecular EDMs. However, interaction with the axion dark matter field generates nuclear EDMs ${\mathbf{d}}_{N}={\mathbf{d}}_{N}^{0}\mathrm{cos}(\ensuremath{\omega}t)$ which oscillate with the frequency $\ensuremath{\omega}={m}_{a}{c}^{2}/\ensuremath{\hbar}$. These oscillating nuclear EDMs generate atomic and molecular EDMs proportional to ${\ensuremath{\omega}}^{2}$. The resulting atomic and molecular EDMs do not, however, lead to nuclear spin rotation in constant external electric fields. On the other hand, an oscillating electric field penetrates atoms and molecules and can interact with nuclear EDMs. Moreover, if the nuclear EDM oscillation frequency is in resonance with the external field, nuclear spin rotation happens, with the rotation angle growing linearly with time.