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arXiv:quant-ph/0506106 · Physical Review A

Measurement of the electric polarizability of lithium by atom interferometry

Alain Miffre, Marion Jacquey, M Büchner, G. Trénec, J. Vigué

Published Jan 30, 2006• 63 citations
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Abstract

We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium $\ensuremath{\alpha}=(24.33\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}$ with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for our largest field, is measured with a ${10}^{\ensuremath{-}3}$ accuracy.

DOI
10.1103/physreva.73.011603

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We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium \ensuremathα=(24.33\ifmmode±\else\textpm\fi0.16)\ifmmode×\else\texttimes\fi10\ensuremath−30m3\ensuremath{\alpha}=(24.33\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}\ensuremathα=(24.33\ifmmode±\else\textpm\fi0.16)\ifmmode×\else\texttimes\fi10\ensuremath−30m3 with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to 4\ifmmode×\else\texttimes\fi10\ensuremath−94\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}4\ifmmode×\else\texttimes\fi10\ensuremath−9 for our largest field, is measured with a 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 accuracy.
\nWe have built an atom interferometer of the Mach Zehnder type. The\natomic wave (lambdaitdB=54\\lambda_{\\it dB}=54lambdaitdB​=54 pm) is a supersonic beam of\nlithium seeded in argon. The realization of mirrors and beams\nsplitters for the atomic wave relies on elastic Bragg diffraction on\nlaser standing waves at lambda=671\\lambda= 671lambda=671 nm. We first present our\nexperimental setup and signals with atomic fringes which exhibit a\nvery high visibility, up to 84.5pm184.5 \\pm 1 \\%84.5pm1, and a very large phase\nsensitivity. This phase sensitivity is then used to perform an\nabsolute measurement of the lithium atom electric polarizability by\napplying an electric field on only one atomic beam in the\ninterferometer. Our result, $\\alpha= (24.33 \\pm 0.16) \\times\n10^{-30}$ m3^33, reduces by a factor three the uncertainty of the\nbest previous measurement.\n
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)statistical{)}_{\mathrm{statistical}})statistical​(6)systematic{)}_{\mathrm{systematic}})systematic​\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ cm3{\mathrm{cm}}^{3}cm3.
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 fikf_{ik}fik​, Einstein coefficients AikA_{ik}Aik​, state lifetimes τkτ_{k}τk​, transition dipole matrix elements DikD_{ik}Dik​, line strengths SikS_{ik}Sik​, and van der Waals C6C_6C6​ coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6C_6C6​ values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal nsnsns-npJnp_JnpJ​ 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).
We have constructed an atom interferometer using three 200 nm period transmission gratings. The two interfering portions of each atom’s wave pass on opposite sides of a stretched metal foil. A fringe amplitude of up to 900 cps is observed, which allows us to determine the phase to 15 milliradians in 1 minute. By applying different interactions to the two sides of the interferometer, we have determined the electric polarizability of the ground state of sodium, the coherence length of our beam, and the differential phase shifts and coherences of the different Zeeman ground states in a magnetic field. Some future prospects of separated beam experiments are discussed.
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.