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Physical Review Letters

Light-force technique for measuring polarizabilities

Michael A. Kadar-Kallen, Keith Bonin

Published Mar 30, 1992• 19 citations
Publisher

Abstract

We have developed a light-force technique for measuring polarizabilities. This new method uses the polarizaton forces experienced by an atom in the intense, inhomogeneous electric field of a standing-wave laser to deduce the polarizability. Using a Nd:YAG laser at ${\ensuremath{\lambda}}_{\mathrm{SW}}$=1.064 \ensuremath{\mu}m for the light force, we measured the polarizability of rubidium at this wavelength to be \ensuremath{\alpha}(${\mathrm{\ensuremath{\omega}}}_{\mathrm{SW}}$)=114\ifmmode\pm\else\textpm\fi{}9 A${\mathrm{\r{}}}^{3}$ (\ensuremath{\sigma}). Conversion of this ac polarizability to a static value using a semiempirical formula gives a value of ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{dc}}$=52 A${\mathrm{\r{}}}^{3}$, within 10% of the best published experimental results.

DOI
10.1103/physrevlett.68.2015

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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
We have developed a light-force technique for measuring polarizabilities. This new method uses the polarizaton forces experienced by an atom in the intense, inhomogeneous electric field of a standing-wave laser to deduce the polarizability. Using a Nd:YAG laser at \ensuremathλSW{\ensuremath{\lambda}}_{\mathrm{SW}}\ensuremathλSW​=1.064 \ensuremath{\mu}m for the light force, we measured the polarizability of rubidium at this wavelength to be \ensuremath{\alpha}(\ensuremathωSW{\mathrm{\ensuremath{\omega}}}_{\mathrm{SW}}\ensuremathωSW​)=114\ifmmode\pm\else\textpm\fi{}9 A˚3{\mathrm{\r{}}}^{3}˚3 (\ensuremath{\sigma}). Conversion of this ac polarizability to a static value using a semiempirical formula gives a value of \ensuremathαdc{\mathrm{\ensuremath{\alpha}}}_{\mathrm{dc}}\ensuremathαdc​=52 A˚3{\mathrm{\r{}}}^{3}˚3, within 10% of the best published experimental results.
The theory of a method to measure electric-dipole polarizabilities is presented. The method uses two-stage laser ablation to produce a pulsed beam of atoms from a solid target. A pair of slits makes the velocity distribution of the atomic beam nonuniform in a way that is well characterized. The light-force technique uses the polarization forces experienced by an atom in the intense, inhomogeneous electromagnetic field of a standing-wave laser to change the velocity distribution of the atomic beam. The large forces cause measurable Doppler shifts in the resonant frequency of the atoms. These frequency shifts change the amount of absorption of resonant light, yielding information about the change in the velocity distribution of the atoms. The detailed shape of the final absorption distribution is polarizability dependent. In the classical picture of the light force, the standing-wave electric field induces a time-varying dipole moment in each atom. Each atom then experiences a Lorentz force due to coherent interaction of the oscillating dipole moment with the time-varying magnetic field. The quantum-mechanical picture corresponds to the Kapitza-Dirac effect for atoms: an atom absorbs a photon from one of the two beams which form the standing wave, and is then stimulated to emit this photon by the other, counterpropagating beam. This paper provides a classical treatment of the light force experienced by an atom in a standing-wave light field; the polarizability is treated quantum mechanically. The theory presented here can be applied to atoms with a scalar polarizability, such as rubidium, and to atoms with significant tensor components, such as uranium. Experimental results from application of the light-force technique to a measurement of the polarizability of rubidium are also presented.
A light-force technique for measuring polarizabilities is being used to measure the polarizability of the uranium atom. The technique uses a pulsed Nd:YAG laser to produce an intense, standing-wave field that provides velocity kicks to atoms that traverse the field region. These velocity kicks result in Doppler-shifted absorption by the atoms. The change in absorption of resonant light, provided by a tunable diode laser is measured. This measurement and a measurement of the standing-wave laser fluence allow determination of the polarizability. We plan to report the results of our measurements, along with a new scheme for generating a dense beam of uranium atoms.
We have been working on the development of a technique for determining the static polarizabilities of refractory metal atoms. The technique involves producing a dense, cold atomic beam (n {approx equal}10{sup 11} {minus} 10{sup 12} atoms/cm{sup 3}, T {perpendicular} {approx equal} 5 mK) that is illuminated for a short time by a standing wave formed by a Nd:YAG laser. This technique would have an impact on laser isotope separation, ion mobility physics, and theoretical atomic physics. The interaction between the atoms and the laser light results in velocity kicks to the atoms along the two directions defined by the photons in the laser standing wave. The velocity kicks force the atoms to form into planes of alternating high and low density downstream. By Bragg scattering near-resonant light off these planes the static polarizability can be determined. The velocity kicks will also cause the atomic density distribution further downstream to take on a bimodal appearance. A measurement of the separation of the peaks of this distribution can be used to determine the polarizability. Here we report our progress on this technique and the present status of the experiments. A new method for producing focused beams of neutrals, ions, and clusters usingmore » two-stage laser ablation has been developed as a result of our experiments. 7 refs., 12 figs.« less
We use double-resonant two-photon laser spectroscopy to measure the dynamic scalar polarizability of the rubidium 5D3/25{D}_{3/2}5D3/2​ level, ${\ensuremath{\alpha}}_{5{D}_{3/2}}^{S}$, at a wavelength of $\ensuremath{\lambda}=1064$ nm. Since $\ensuremath{\lambda}$ is shorter than the photoionization (PI) limit of the Rb 5D3/25{D}_{3/2}5D3/2​ level, this state undergoes significant broadening due to PI. The 1064-nm field is applied in the form of a deep optical lattice ($\ensuremath{\sim}{10}^{5}$ photon recoils) generated by an in-vacuum field-enhancement cavity. In our spectroscopic method, we use known dynamic polarizabilities to eliminate the need to measure the light intensity. Our method yields, in atomic units, ${\ensuremath{\alpha}}_{5{D}_{3/2}}^{S}=\ensuremath{-}524(17)$, in agreement with estimates. Additionally, we extract the 5D3/25{D}_{3/2}5D3/2​ photoionization cross section $\ensuremath{\sigma}$ at 1064 nm from spectral linewidths; we find $\ensuremath{\sigma}=44(1)$ Mb.
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.
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.