Abstract

The microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 \rangle \leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 \rangle$ transition in the $^{113}$Cd$^+$ ion has been reported as 15199862855.0192(10) Hz [Opt. Lett. {\bf 40}, 4249 (2015)]. Fractional systematic due to the black-body radiation (BBR) shift ($\beta$) arising from the Stark effect in the above clock transition was used as $-1.1 \times 10^{-16}$ from our unpublished preliminary estimation. We present here a precise value as $\beta=-1.815(77) \times 10^{-16}$ by carrying out rigorous calculations of third-order polarizabilities of the hyperfine levels associated with the clock transition. This is determined by evaluating matrix elements of the magnetic dipole hyperfine interaction Hamiltonian, electric dipole operator and energies between many low-lying states of $^{113}$Cd$^+$. We employ all-order relativistic many-body theories in the frameworks of Fock-space coupled-cluster and relativistic multi-configuration Dirac-Fock methods.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.