Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1001.3888 · Physical Review A

Absolute and ratio measurements of the polarizability of Na, K, and Rb with an atom interferometer

William F. Holmgren, Melissa Revelle, Vincent Lonij, Alexander D. Cronin

Published May 10, 2010• 100 citations
arXivHTMLPDF

Abstract

We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find ${\ensuremath{\alpha}}_{\mathrm{Na}}=24.11(2){}_{\mathrm{stat}}(18){}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}{\mathrm{cm}}^{3}$, ${\ensuremath{\alpha}}_{\mathrm{K}}=43.06(14)(33)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(12)(42)$. Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with $0.3%$ uncertainty. We find ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.959(5)$, ${\ensuremath{\alpha}}_{\mathrm{K}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.786(6)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.097(5)$. We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find ${\ensuremath{\alpha}}_{\mathrm{K}}=43.06(21)$ and ${\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(21)$.

DOI
10.1103/physreva.81.053607

Related papers

Measurements of the ground-state polarizabilities of Cs, Rb, and K using atom interferometry

Maxwell D. Gregoire, Ivan Hromada, William F. Holmgren +2 more

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.

arXiv:1509.07091•Physical Review A•Nov 20, 2015•78 citations

Analysis of polarizability measurements made with atom interferometry

Maxwell D. Gregoire, Nathan J. Brooks, Raisa Trubko +1 more

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 $f_{ik}$, Einstein coefficients $A_{ik}$, state lifetimes $τ_{k}$, transition dipole matrix elements $D_{ik}$, line strengths $S_{ik}$, and van der Waals $C_6$ coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and $C_6$ values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal $ns$-$np_J$ transitions for alkali metal atoms.

arXiv:1606.01963•Jun 6, 2016•0 citations

Analysis of Polarizability Measurements Made with Atom Interferometry

Maxwell D. Gregoire, Nathan J. Brooks, Raisa Trubko +1 more

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.

Atoms•Jul 6, 2016•17 citations

Measurement of the electric polarizability of sodium with an atom interferometer

Christopher R. Ekstrom, Jörg Schmiedmayer, Michael Chapman +2 more

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{}${10}^{\mathrm{\ensuremath{-}}24}$ ${\mathrm{cm}}^{3}$.

Physical Review A•May 1, 1995•261 citations

Measurement of alkali-metal polarizabilities by deflection of a velocity-selected atomic beam

William Davis Hall, Jens C. Zorn

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 $\ensuremath{\alpha}(\mathrm{Cs})=63.3\ifmmode\pm\else\textpm\fi{}4.6$ ${\mathrm{\AA{}}}^{3}$.

Physical Review A•Oct 1, 1974•103 citations

Polarizability and Magic-Zero Wavelength Measurements of Alkali Atoms

William F. Holmgren

Atomic polarizability plays an essential role in topics ranging from van der Waals interactions, state lifetimes, and indices of refraction, to next generation atomic clocks and atomic parity non-conservation experiments. Polarizability measurements, such as the ones described in this thesis, provide valuable input to these subjects and serve as benchmark tests for sophisticated atomic structure calculations. We measured the static polarizability of potassium and rubidium with record precision and 0.5% uncertainty using a Mach-Zehnder atom interferometer with an electric-field gradient. To support future precision measurements of polarizability, we developed a new atom beam velocity measurement technique called phase choppers. Using phase choppers, we demonstrated measurements of mean atom beam velocity with an uncertainty of 0.1%. We also developed a new way to probe atomic structure: a measurement of a zero-crossing of the dynamic polarizability of potassium, known as a magic-zero wavelength. We measured the first magic-zero wavelength of potassium with 1.5 pm uncertainty and established a new benchmark measurement for the ratio of the D1 and D2 line strengths. Finally, we propose the use of a resonant photoionization detector for measurements of strontium polarizability, and the use of contrast interferometry for measurements of alkali dimer tensor polarizabilities.

•Jan 1, 2013•4 citations
We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find \ensuremathαNa=24.11(2)stat(18)sys\ifmmode×\else\texttimes\fi10\ensuremath−24cm3{\ensuremath{\alpha}}_{\mathrm{Na}}=24.11(2){}_{\mathrm{stat}}(18){}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}{\mathrm{cm}}^{3}\ensuremathαNa​=24.11(2)stat​(18)sys​\ifmmode×\else\texttimes\fi10\ensuremath−24cm3, \ensuremathαK=43.06(14)(33){\ensuremath{\alpha}}_{\mathrm{K}}=43.06(14)(33)\ensuremathαK​=43.06(14)(33), and \ensuremathαRb=47.24(12)(42){\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(12)(42)\ensuremathαRb​=47.24(12)(42). Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with 0.30.3%0.3 uncertainty. We find \ensuremathαRb/\ensuremathαNa=1.959(5){\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.959(5)\ensuremathαRb​/\ensuremathαNa​=1.959(5), \ensuremathαK/\ensuremathαNa=1.786(6){\ensuremath{\alpha}}_{\mathrm{K}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.786(6)\ensuremathαK​/\ensuremathαNa​=1.786(6), and \ensuremathαRb/\ensuremathαK=1.097(5){\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.097(5)\ensuremathαRb​/\ensuremathαK​=1.097(5). We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find \ensuremathαK=43.06(21){\ensuremath{\alpha}}_{\mathrm{K}}=43.06(21)\ensuremathαK​=43.06(21) and \ensuremathαRb=47.24(21){\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(21)\ensuremathαRb​=47.24(21).
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 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.
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.
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.
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 $\ensuremath{\alpha}(\mathrm{Na})=24.4\ifmmode\pm\else\textpm\fi{}1.7$ A˚3{\mathrm{\AA{}}}^{3}A˚3, $\ensuremath{\alpha}(\mathrm{K})=45.2\ifmmode\pm\else\textpm\fi{}3.2$ A˚3{\mathrm{\AA{}}}^{3}A˚3, $\ensuremath{\alpha}(\mathrm{Rb})=48.7\ifmmode\pm\else\textpm\fi{}3.4$ A˚3{\mathrm{\AA{}}}^{3}A˚3, and $\ensuremath{\alpha}(\mathrm{Cs})=63.3\ifmmode\pm\else\textpm\fi{}4.6$ A˚3{\mathrm{\AA{}}}^{3}A˚3.
Atomic polarizability plays an essential role in topics ranging from van der Waals interactions, state lifetimes, and indices of refraction, to next generation atomic clocks and atomic parity non-conservation experiments. Polarizability measurements, such as the ones described in this thesis, provide valuable input to these subjects and serve as benchmark tests for sophisticated atomic structure calculations. We measured the static polarizability of potassium and rubidium with record precision and 0.5% uncertainty using a Mach-Zehnder atom interferometer with an electric-field gradient. To support future precision measurements of polarizability, we developed a new atom beam velocity measurement technique called phase choppers. Using phase choppers, we demonstrated measurements of mean atom beam velocity with an uncertainty of 0.1%. We also developed a new way to probe atomic structure: a measurement of a zero-crossing of the dynamic polarizability of potassium, known as a magic-zero wavelength. We measured the first magic-zero wavelength of potassium with 1.5 pm uncertainty and established a new benchmark measurement for the ratio of the D1 and D2 line strengths. Finally, we propose the use of a resonant photoionization detector for measurements of strontium polarizability, and the use of contrast interferometry for measurements of alkali dimer tensor polarizabilities.