  We report a measurement of the ratio of electric dipole transition matrix
elements of cesium for the $6p\,^2P_{1/2} \rightarrow 7s\,^2S_{1/2}$ and
$6p\,^2P_{3/2} \rightarrow 7s\,^2S_{1/2}$ transitions. We determine this ratio
of matrix elements through comparisons of two-color, two-photon excitation
rates of the $7s\,^2S_{1/2}$ state using laser beams with polarizations
parallel to one another vs.\ perpendicular to one another. Our result of $R
\equiv \langle 7s\ ^2S_{1/2} || r || 6p\ ^2P_{3/2} \rangle / \langle 7s\
^2S_{1/2} || r || 6p\ ^2P_{1/2} \rangle = 1.5272 \ (17)$ is in excellent
agreement with a theoretical prediction of $R=1.5270 \ (27)$. Moreover, the
accuracy of the experimental ratio is sufficiently high to differentiate
between various theoretical approaches. To our knowledge, there are no prior
experimental measurements of $R$. Combined with our recent determination of the
lifetime of the $7s\,^2S_{1/2}$ state, we determine reduced matrix elements for
these two transitions, $\langle 7s\ ^2S_{1/2} || r || 6p\ ^2P_{3/2} \rangle =
-6.489 \ (5) \ a_0$ and $\langle 7s\ ^2S_{1/2} || r || 6p\ ^2P_{1/2} \rangle =
-4.249 \ (4) \ a_0$. These matrix elements are also in excellent agreement with
theoretical calculations. These measurements improve knowledge of Cs properties
needed for parity violation studies and provide benchmarks for tests of
high-precision theory.
