Measurements of the Ground-State Polarizabilities of Cs, Rb, and K using Atom Interferometry

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-nonconservation experiments. We measured ${\ensuremath{\alpha}}_{\mathrm{Cs}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}59.39(9)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3},{\ensuremath{\alpha}}_{\mathrm{Rb}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}47.39(8)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$, and ${\ensuremath{\alpha}}_{\mathrm{K}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}42.93(7)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$. In atomic units, these measurements are ${\ensuremath{\alpha}}_{\mathrm{Cs}}=401.2(7),{\ensuremath{\alpha}}_{\mathrm{Rb}}=320.1(6)$, and ${\ensuremath{\alpha}}_{\mathrm{K}}=290.0(5)$. We report ratios of polarizabilities ${\ensuremath{\alpha}}_{\mathrm{Cs}}/{\ensuremath{\alpha}}_{\mathrm{Rb}}=1.2532(10),{\ensuremath{\alpha}}_{\mathrm{Cs}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.3834(9)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.1040(9)$ 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.