Optical frequency standard with $Sr^+$: A theoretical many-body approach

Demands from several areas of science and technology have lead to a worldwide search for accurate optical clocks with an uncertainty of 1 part in $10^{18}$, which is $10^{3}$ times more accurate than the present day cesium atomic clocks based on microwave frequency regime. In this article we discuss the electric quadrupole and the hyperfine shifts in the $5s ^{2}S_{1/2}\longrightarrow4d ^{2}D_{5/2}$ clock transition in $\mathrm{Sr^{+}}$, one of the most promising candidates for next generation optical clocks. We have applied relativistic coupled cluster theory for determining the electric quadrupole moment of the $4d ^{2}D_{5/2}$ state of $\mathrm{^{88}Sr^{+}}$ and the magnetic dipole ($A$) and electric quadrupole ($B$) hyperfine constants for the $5s ^{2}S_{1/2}$ and $4d ^{2}D_{5/2}$ states which are important in the study of frequency standards with $\mathrm{Sr^{+}}$. The effects of electron correlation which are very crucial for the accurate determination of these quantities have been discussed.