Measurement of the electric polarizability of sodium with an atom interferometer

We have constructed an atom interferometer with interfering beams that are physically isolated by a metal foil. By applying an interaction to one of the two interfering beams, we can measure ground-state energy shifts with a spectroscopic precision of 6.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}14}$ eV/\ensuremath{\surd}min , or 16 Hz/\ensuremath{\surd}min . Applying an electric field to one beam of the interferometer, we have measured the phase shift induced from the quadratic Stark effect. By analyzing these phase shifts, we have determined the ground-state polarizability of sodium, with much improved accuracy, to be 24.11(6${)}_{\mathrm{statistical}}$(6${)}_{\mathrm{systematic}}$\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ ${\mathrm{cm}}^{3}$.