The two-photon transition ${6S}_{1/2}\ensuremath{\rightarrow}{6D}_{5/2}$ is investigated for trapped atomic cesium excited by squeezed light. The rate
R of two-photon excitation versus intensity
I is observed to be consistent with the functional form $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\beta}}_{1}I+{\ensuremath{\beta}}_{2}{I}^{2}$, extending into a region with slope 1.3. This departure from the quadratic form for classical light sources is due to the fundamental alteration of atomic radiative processes by the nonclassical field.