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.
The static electric dipole polarizability of the
4s2(1S0) ground state of the calcium atom has been measured using an electric deflection technique. The result is normalized to the polarizability of lithium by comparing deflections of calcium and lithium beams passing through an inhomogeneous electrostatic field. We find (25 \ifmmode\pm\else\textpm\fi{} 2.5) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$
cm3 for the polarizability of calcium.
The atomic beam $E\ensuremath{-}H$ gradient-balance method has been employed to measure the
z-component ${\ensuremath{\alpha}}_{z}({m}_{J})$ of the electric polarizability tensors of the
mJ=+2 and
mJ=+1 magnetic substates of
3P2 metastable argon. The measurements were normalized to the polarizability of
3S1 metastable helium, which is calculable to within an accuracy of 1%. In this method, a metastable beam is passed through a region containing transverse, congruent, inhomogeneous electric and magnetic fields. The condition that atoms in a particular magnetic substate experience no deflection in such a field region is ${\ensuremath{\alpha}}_{z}({m}_{J})E(\frac{\ensuremath{\delta}E}{\ensuremath{\delta}z})={\ensuremath{\mu}}_{\mathrm{eff}}(\frac{\ensuremath{\delta}H}{\ensuremath{\delta}z})$, where ${\ensuremath{\mu}}_{\mathrm{eff}}$ is the magnetic moment in the field
H, and $\frac{\ensuremath{\delta}E}{\ensuremath{\delta}z}$, $\frac{\ensuremath{\delta}H}{\ensuremath{\delta}z}$ are the
z components of the gradients of the magnitudes of the electric and magnetic fields, respectively. Because of the congruency of the
E and
H fields $\frac{(\frac{\ensuremath{\delta}E}{\ensuremath{\delta}z})}{E}=\frac{(\frac{\ensuremath{\delta}H}{\ensuremath{\delta}z})}{H}$, and therefore ${\ensuremath{\alpha}}_{z}({m}_{J})=\frac{{\ensuremath{\mu}}_{\mathrm{eff}}H}{{E}^{2}}$. Because of the normalization, it was unnecessary to find either
E or
H. The results, in units of ${10}^{\ensuremath{-}24}$
cm3, are ${\ensuremath{\alpha}}_{z}(\ifmmode\pm\else\textpm\fi{}1)=50.4\ifmmode\pm\else\textpm\fi{}3.5$ and ${\ensuremath{\alpha}}_{z}(\ifmmode\pm\else\textpm\fi{}2)=44.5\ifmmode\pm\else\textpm\fi{}3.1$. The measured values of ${\ensuremath{\alpha}}_{z}(+1)$ and ${\ensuremath{\alpha}}_{z}(\ifmmode\pm\else\textpm\fi{}2)$ can be used to determine the polarizability tensors of each of the magnetic substates. The other components of the diagonalized tensors, with ${\ensuremath{\alpha}}_{x}({m}_{J})={\ensuremath{\alpha}}_{y}({m}_{J})$, in units of ${10}^{\ensuremath{-}24}$
cm3 are ${\ensuremath{\alpha}}_{x}(0)=46.4\ifmmode\pm\else\textpm\fi{}2.4$, ${\ensuremath{\alpha}}_{x}(\ifmmode\pm\else\textpm\fi{}1)=47.2\ifmmode\pm\else\textpm\fi{}2.3$, ${\ensuremath{\alpha}}_{x}(\ifmmode\pm\else\textpm\fi{}2)=50.4\ifmmode\pm\else\textpm\fi{}3.5$, and ${\ensuremath{\alpha}}_{z}(0)=52.4\ifmmode\pm\else\textpm\fi{}4.8$.
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 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 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.