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.
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