Parity-Nonconserving Interaction-Induced Light Shifts in the \( \mathbf{{7S}}_{\mathbf{1/2}} \)–\( \mathbf{6 D}_{\mathbf{3/2}} \) Transition of the Ultracold \( ^{\mathbf{210}}{\mathbf{Fr}} \) Atoms to Probe New Physics Beyond the Standard Model

We present an experimental technique to measure light shifts due to the nuclear spin independent (NSI) parity-nonconserving (PNC) interaction in the \( 7{S}_{1/2} \)–\( 6{D}_{3/2} \) transition in ultracold \( {}^{210}\mathrm{Fr} \) atoms. The approach we propose is similar to the one by Fortson (Phys Rev Lett 70:2383, 10) to measure the PNC-induced light shift which arises from the interference of parity nonconserving electric dipole transition and electric quadrupole transition amplitudes. Its major advantage is that it can treat more than \( {10}^4 \) ultracold \( {}^{210}\mathrm{Fr} \) atoms to enhance the shot noise limit. A relativistic coupled-cluster method has been employed to calculate the electric dipole transition amplitudes arising from the PNC interaction. Based on these calculations, we have evaluated the PNC-induced light shifts for transitions between the hyperfine levels of the \( 7{S}_{1/2} \) and \( 6{D}_{3/2} \) states and suitable transitions are identified for carrying out PNC measurements. It is possible in principle to probe new physics beyond the standard model with our proposed experimental scheme.