Theoretical Calculation of the Quadratic Zeeman Shift Coefficient of the 3P0 clock state for Strontium Optical Lattice Clock

TL;DR

This paper combines theoretical derivation and experimental measurement to accurately determine the quadratic Zeeman shift coefficient of the 3P0 clock state in strontium, enhancing precision in optical lattice clocks.

Contribution

It provides a new theoretical expression and calculated values for the quadratic Zeeman shift coefficients, validated by experimental measurements, improving understanding of magnetic field effects in strontium clocks.

Findings

Calculated quadratic Zeeman shift coefficient for 88Sr: -23.38(5) MHz/T^2

Experimental measurement of the shift coefficient for 87Sr agrees with calculations

Calculated coefficients for other magnetic states relevant to clock transitions

Abstract

The quadratic Zeeman shift coefficient of 3P0 clock state for strontium is determined in theory and experiment. In theory, we derived the expression of the quadratic Zeeman shift of 3P0 clock state for 88Sr and 87Sr in the weak-magnetic-field approximation. By using the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. To determine the calculated results, the quadratic Zeeman shift coefficient of 3P0,F=9/2,MF=+/-9/2 clock state was measured in our 87Sr optical lattice clock. The calculated results C2=-23.38(5) MHz/T2 for 88Sr and the 3P0,F=9/2,MF=+/-9/2 clock state for 87Sr agree well with the other experimental and theoretical values, especially the most accurate measurement recently. As the 1S0,F=9/2,MF=+/-5/2-3P0,F=9/2,MF=+/-3/2 transitions have been used as another clock transition for less sensitive to the magnetic field noise, we also calculated the quadratic Zeeman shift coefficients for the other magnetic states.