Roles of electron correlation effects for the accurate determination of gj factors of low-lying states of Cd+113 and their applications to atomic clocks

Abstract

We investigate roles of electron correlation effects in the determination of gj factors of the ns 2 S 1/2 (n=5,6,7), np 2 P 1/2,3/2 (n=5,6), 5d 2 D 3/2,5/2 , and 4f 2 F 5/2,7/2 states of the singly ionized cadmium (Cd + ) ion. Single and double excited configurations along with important valence triple excited configurations through relativistic coupled-cluster (RCC) theory are taken into account for incorporating electron correlation effects in our calculations. We find significant contributions from the triples to the lower S and P states for attaining high accuracy results. The contributions of Breit interaction and lower-order quantum electrodynamics effects, such as vacuum polarization and self-energy corrections, are also estimated using the RCC theory and are quoted explicitly. In addition, we present energies of the aforementioned states from our calculations and compare them with the experimental results to validate gj values. Using the gj factor of the ground state, systematical shift due to the Zeeman effect in the microwave clock frequency of the |5s 2 S 1/2 , F = 0, mF = 0 ↔ |5s 2 S 1/2 , F = 1, mF = 0 transition in 113 Cd + ion has been estimated.

Determination of hyperfine splittings and Landé $g_J$ factors of $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ states of $^{111,113}$Cd$^+$ for a microwave frequency standard

“…Accurate calculations of Landé g J factors has proven complicated even for alkali atoms and alkali-like ions because they are sensitive to electron correlations. Those calculated in this work using the MCDHF method show strong deviations from previous RCC results [24]. The ground state Landé g J factor calculated in this work (2.002257(1)) agrees with the recent result calculated using the Λ-RCC theory (2.002291( 4)) [36] to the fourth decimal place, although there is no overlap within their margins of uncertainty.…”

“…The HFSs and Landé g J factors determined in this work can further improve the efficiency of the optical pumping procedure and the accuracy of the second-order Zeeman correction, and the stability and accuracy of the microwave frequency standard based on trapped Cd + ions. [24]…”

“…Among all the systematic frequency shifts of a frequency standard, one dominant shift is the second-order Zeeman shift (SOZS) induced by the external magnetic field [15,22,23]. The precise estimation of this SOZS and the calibration of the external magnetic field require accurate knowledge of the ground-state Landé g j factor [24]. The external magnetic field in our latest laser-cooled microwave-frequency standard based on trapped 113 Cd + ions is approximately 8000 nT [15].…”

“…The external magnetic field in our latest laser-cooled microwave-frequency standard based on trapped 113 Cd + ions is approximately 8000 nT [15]. However, only two theoretical studies have provided a value of the ground-state Landé g J factor of Cd + , one giving 2.00286(53), calculated using the relativisticcoupled-cluster (RCC) theory [24], and the other giving 2.002291(4), calculated by the Λ-approach RCC (Λ-RCC) theory [25]. The two Landé g J factors have a difference of 0.0006 that generates a relative frequency shift of 6.6 × 10 −14 .…”

Sympathetic cooling of $^{113}$Cd$^+$ by laser-cooled $^{40}$Ca$^+$ in a linear Paul trap for Microwave Ion Clocks

“…A great deal of progress has been achieved. In the past ten years, our group has been committed to developing a microwave atomic clock based on 113 Cd + [11,[16][17][18][19][20]. At present, the short-term frequency instability has reached 6.1 × 10 −13 / √ τ , and the uncertainty associated with ground-state hyperfine splitting has reached 6.6 × 10 −14 [11].…”