Diffusion Dominated RF-Response of a Coated Rb-Vapor Cell in an Inhomogenous Magnetic Field

The magnetic resonance lineshape of Rb-vapor in a coated cylindrical cell [1] is modeled quantitatively. It is diffusion-dominated when l$^{3}$\textit{$\omega $}'$>$D. Here l is the cell thickness, D is the diffusion constant and \textit{$\omega $}' is the local gradient of the Lamor frequency (directed perpendicular to the cell's faces). We obtain the spectrum by averaging the path-dependent transition probability over all diffusion paths in a binomial ``hopping'' model. The resulting line shape also depends on the characteristics of the average interactions of a Rb atom with the coated cell surface. It agrees very well with the experimentally observed lineshape. The two most prominent peaks in the diffusion-dominated regime are due to modes concentrated at either face of the cell with a gradient-dependent contribution to the half-width c(\textit{$\omega $}'$^{2}$ D)$^{1/3}$, where c depends on the surface interactions but is $\sim $0.5 in most cases studied. This dependence of the line width on \textit{$\omega $}' allows one to measure the local gradient of the magnetic field without moving the magnetometer and should be particularly useful for measuring time-dependent field gradients. \newline [1] K. Zhao and Z. Wu, to be published.