Blackbody-radiation shift in a⁸⁸Sr⁺ion optical frequency standard

Abstract

The blackbody radiation (BBR) shift of the 5s − 4d 5/2 clock transition in 88 Sr + is calculated to be 0.250(9) Hz at room temperature, T = 300 K, using the relativistic all-order method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. The BBR shift is a major component in the uncertainty budget of the optical frequency standard based on the 88 Sr + trapped ion. The scalar polarizabilities of the 5s and 4d 5/2 levels, as well as the tensor polarizability of the 4d 5/2 level, are presented together with the evaluation of their uncertainties. The lifetimes of the 4d 3/2 , 4d 5/2 , 5p 1/2 , and 5p 3/2 states are calculated and compared with experimental values.

Black-body radiation shifts and theoretical contributions to atomic clock research

“…The resulting uncertainty of the 5s polarizability is 1%. Our theoretical LCCSD 5p 1/2,3/2 lifetimes [20] are in agreement with 1% experiment conducted in 1995 [37]. The contribution of the 5s − 5p transitions to the lifetimes is dominant (94%).…”

“…The LCCSD values for the primary ns−np transitions in Li, Na, K, Rb, and Cs agree with various types of high-precision experiments to 0.1% -0.4% [33]. There is no reason to expect reduced theoretical accuracy in the cases of either Ca + or Sr + , and 0.5% uncertainty was assigned to the 5s−5p 1/2 and 5s−5p 3/2 Sr + matrix elements [20]. The resulting uncertainty of the 5s polarizability is 1%.…”

“…The agreement of results in Table I obtained with dis- In this section, we discuss the calculation of the BBR shifts for optical frequency standards based on the 4s − 3d 5/2 transition in Ca + [19] and the 5s − 4d 5/2 transition in Sr + [20]. We note that while the calculations were conducted for 43 Ca + and 88 Sr + , we have verified that the results given in this section do not depend on the particular isotope.…”

“…(3) [19], [20]. The dynamic correction was estimated for Sr + to be η = 0.0013 and η = 0.0064 for the 5s and 4d 3/2 states, respectively, using formulas from [24].…”

“…New preliminary result for the BBR shift of the ground-state hyperfine microwave transition in 87 Rb is presented [18]. The evaluation of BBR shifts and their uncertainties in optical frequency standards in monovalent ions, such as Ca + [19] and Sr + [20] is discussed. New method for accurate calculations of the BBR shifts in divalent atoms such as Sr is outlined.…”