Parity-nonconserving interaction-induced light shifts in the 7S _1/2 -6D _3/2 transition of the ultracold ²¹⁰ 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 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 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.