  We measured the ground-state static electric-dipole polarizabilities of Cs,
Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam
interferometer. Our measurements provide benchmark tests for atomic structure
calculations and thus test the underlying theory used to interpret atomic
parity non-conservation experiments. We measured $\alpha_{\mathrm{Cs}} =
4\pi\epsilon_0 \times 59.45(11) \AA^3$, $\alpha_{\mathrm{Rb}} = 4\pi\epsilon_0
\times 47.44(9) \AA^3$, and $\alpha_{\mathrm{K}} = 4\pi\epsilon_0 \times
42.97(8) \AA^3$. In atomic units, these measurements are $\alpha_{\mathrm{Cs}}
= 401.2(7)$, $\alpha_{\mathrm{Rb}} = 320.1(6)$, and $\alpha_{\mathrm{K}} =
290.0(5)$. We report ratios of polarizabilities
$\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{Rb}} = 1.2532(10)$,
$\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{K}} = 1.3835(9)$, and
$\alpha_{\mathrm{Rb}}/\alpha_{\mathrm{K}} = 1.1040(9)$ with smaller fractional
uncertainty because the systematic errors for individual measurements are
largely correlated. Since Cs atom beams have short de Broglie wavelengths, we
developed measurement methods that do not require resolved atom diffraction.
Specifically, we used phase choppers to measure atomic beam velocity
distributions, and we used electric field gradients to give the atom
interference pattern a phase shift that depends on atomic polarizability.
