Estimation of BBR shift due to Stark effect for the Microwave ${}^{113}$Cd${}^{+}$ Ion Clock

Abstract

The microwave clock frequency of the $|5s{}^2{S}_{1/2},F=0,m_F=0⟩\leftrightarrow |5s{}^2{S}_{1/2},F=1,m_F=0⟩$ 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shift ($\beta$) arising from the Stark effect in the above clock transition was used as $-1.1\times 10^{-16}$ from our unpublished preliminary estimation.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.

arXiv comment6 pages

References in corpus (12)

• Frequency Comparison of Two High-Accuracy Al+ Optical Clocks
• Single-Ion Atomic Clock with $3\times 10^{-18}$ Systematic Uncertainty
• A quantum information processor with trapped ions
• Ion Trap in a Semiconductor Chip
• High-accuracy calculation of black-body radiation shift in ${}^{133}$Cs primary frequency standard
• Relativistic general-order coupled-cluster method for high-precision calculations: Application to Al+ atomic clock
• Multipolar Black Body Radiation Shifts for the Single Ion Clocks
• Comparative studies of dipole polarizabilities in Sr${}^{+}$, Ba${}^{+}$ and Ra${}^{+}$ and their applications to optical clocks
• Precision lifetime measurements of a single trapped ion with ultrafast laser pulses
• Conforming the measured lifetimes of the $5d{}^2{D}_{3/2,5/2}$ states in Cs with theory
• Evaluation of blackbody radiation shift with temperature associated fractional uncertainty at 10E-18 level for 40Ca+ ion optical clock
• Energy shift due to anisotropic black body radiation

Cited by in corpus (5)

• Precision determination of the ground-state hyperfine splitting of trapped ${}^{113}$Cd${}^{+}$ ions
• Relativistic coupled-cluster theory analysis of energies, hyperfine structure constants, and dipole polarizabilities of Cd${}^{+}$
• Roles of electron correlation effects for accurate determination of $g_j$ factors of low-lying states of ${}^{113}$Cd${}^{+}$ and their applications to atomic clock
• High-precision Electric Dipole Polarizabilities of the Clock States in ${}^{133}$Cs
• Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes