New standard magnetic field values determined by cancellations of ${}^{85}\text{Rb}$ and ${}^{87}\text{Rb}$ atomic vapors $5{}^2{S}_{1/2} \rightarrow 6{}^2{P}_{1/2,~3/2}$ transitions

Abstract

In this article, we study the theoretical behaviour of all the possible hyperfine transitions ($\pi$, $\sigma^+$ and $\sigma^-$) between the $5S$ and $6P$ states of ${}^{87}\text{Rb}$ and ${}^{85}\text{Rb}$ atomic vapors under the influence of an external magnetic field $B$. We show that, for specific transitions, we obtain one or several $B$-values for which the transition intensity is cancelled. The precision of these values is limited to the uncertainty of the physical quantities that are involved in the problem, thus measuring precisely the $B$-values for the cancellations could be a way to determine these quantities more precisely. In the simplest cases involving $2\times 2$ hamiltonians, we give eigenvectors, eigenvalues and analytical formulas to determine the transition cancellation. By checking accuracy between formulas and numerical simulations, we conclude that it is possible to use the latter in order to determine all the cancellations even in the most complicated cases.