Measurement of the ratio of the 6P$_{\mathrm{j}}\to $ 7S $_{\mathrm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }}$ matrix elements in atomic cesium

We report progress on a measurement of the ratio of transition matrix elements of the 6P$_{\mathrm{j}}\to $ 7S $_{\mathrm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \thinspace }}$ transition in atomic cesium. We use a 1.47 um diode laser and a Ti: Sapphire laser at 850 nm to drive the two photon 6S $\to $ 7S transition. We measure the ratio of the polarization-dependent intensities of the transition by changing the polarization of the diode laser. Since the 6S$\to $6P matrix elements are well known, the ratio of the 6P$_{\mathrm{j}}\to $ 7S $_{\mathrm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \thinspace }}$ matrix elements can be precisely determined. Combined with our recent measurement of the cesium 7S lifetime, a new measurement of this ratio allows us to determine the 6P$_{\mathrm{j}}\to $7S $_{\mathrm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \thinspace }}$ matrix elements.