Parity-nonconserving interaction-induced light shifts in the \bf{7S}_{1/2}–\bf{6D}_{3/2} transition of the ultracold {^{210}\bf{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 \(7S_{1/2}\)–\(6D_{3/2}\) 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 \(7S_{1/2}\) and \(6D_{3/2}\) 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.