The electric dipole polarizability of the alkali-metal atoms Na, K, Rb, and Cs are determined by measuring the deflection of a velocity-selected beam by an inhomogeneous electric field. It is shown experimentally that scattering of slower beam atoms by background gas in the apparatus is an important systematic error in measurements of this kind if a beam-velocity selector is not used, and that this scattering is responsible for the discrepancies between different, earlier beam-deflection measurements of polarizability. The polarizability values obtained in this work are $\ensuremath{\alpha}(\mathrm{Na})=24.4\ifmmode\pm\else\textpm\fi{}1.7$ ${\mathrm{\AA{}}}^{3}$, $\ensuremath{\alpha}(\mathrm{K})=45.2\ifmmode\pm\else\textpm\fi{}3.2$ ${\mathrm{\AA{}}}^{3}$, $\ensuremath{\alpha}(\mathrm{Rb})=48.7\ifmmode\pm\else\textpm\fi{}3.4$ ${\mathrm{\AA{}}}^{3}$, and $\ensuremath{\alpha}(\mathrm{Cs})=63.3\ifmmode\pm\else\textpm\fi{}4.6$ ${\mathrm{\AA{}}}^{3}$.
The electric dipole polarizability of the alkali-metal atoms Na, K, Rb, and Cs are determined by measuring the deflection of a velocity-selected beam by an inhomogeneous electric field. It is shown experimentally that scattering of slower beam atoms by background gas in the apparatus is an important systematic error in measurements of this kind if a beam-velocity selector is not used, and that this scattering is responsible for the discrepancies between different, earlier beam-deflection measurements of polarizability. The polarizability values obtained in this work are \ensuremathα(Na)=24.4\ifmmode±\else\textpm\fi1.7A˚3, \ensuremathα(K)=45.2\ifmmode±\else\textpm\fi3.2A˚3, \ensuremathα(Rb)=48.7\ifmmode±\else\textpm\fi3.4A˚3, and \ensuremathα(Cs)=63.3\ifmmode±\else\textpm\fi4.6A˚3.
The static dipole polarizability of helium atoms in the metastable 23S1 and 21S0 states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\ensuremath{\alpha}(2^{3}S_{1})=(44.6\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm3 and $\ensuremath{\alpha}(2^{1}S_{0})=(108\ifmmode\pm\else\textpm\fi{}13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm3, agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths fik, Einstein coefficients Aik, state lifetimes τk, transition dipole matrix elements Dik, line strengths Sik, and van der Waals C6 coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6 values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal ns-npJ transitions for alkali metal atoms.
The static electric dipole polarizabilities of barium and strontium atoms have been measured using an electric deflection technique. The results are normalized to the polarizability of lithium by comparing deflections of the alkaline-earth beams to deflections of a lithium beam passing through an inhomogeneous electrostatic field. The measured polarizabilities are (39.7 \ifmmode\pm\else\textpm\fi{} 3.2) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$ cm3 for barium and (27.6 \ifmmode\pm\else\textpm\fi{} 2.2) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$ cm3 for strontium.
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.
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then, we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths fik, Einstein coefficients Aik, state lifetimes τk, transition dipole matrix elements Dik, line strengths Sik, and van der Waals C6 coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6 values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal ns-npJ transitions for alkali metal atoms.
Atom interferometers, in which de Broglie waves are coherently split and recombined to make interference fringes, now serve as precision measurement tools for several quantities in physics. Examples include measurements of Newton's constant, the fine structure constant, van der Waals potentials, and atomic polarizabilities. To make next-generation measurements of static electric dipole atomic polarizabilities with an atom beam interferometer, I worked on new methods to precisely measure the velocity distribution for atom beams. I will explain how I developed and used phase choppers to measure lithium, sodium, potassium, and cesium atomic beam velocities with 0.07% accuracy. I also present new measurements of polarizability for these atoms. I classify systematic errors into two broad categories: (1) fractional errors that are similar for all different types of atoms in our experiments, and (2), errors that scale with de Broglie wavelength or inverse atomic momentum in our experiments. This distinction is important for estimating the uncertainty in our measurements of ratios of atomic polarizabilities, e.g., αCs / αNₐ = 2.488(12).