Quadratic Zeeman shift of a clock transition
= Quadratic Zeeman shift of a clock transition
{title2=$\Delta\nu=(g_J-g_I)^2\mu_B^2B^2/(2h\Delta_{\rm hf})$}
For the two $m=0$ branches of the <Breit-Rabi formula>, their splitting is $\sqrt{\Delta_{\rm hf}^2+[(g_J-g_I)\mu_BB]^2}$. Expanding at small field gives the quadratic <frequency> shift displayed above. Vanishing linear <frequency> sensitivity at zero field therefore does not eliminate field-gradient <dephasing> at a finite bias field.