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 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.
The term of atom optics is due to the natural analogy with light optics or the optics of photons. Some elements of the optics of atoms and molecules, based on the interaction between spatially nonuniform static magnetic or electrical fields and the magnetic or electrical dipole moment of the particles, have long been known and used fairly successfully in experimental physics. In the presence of a magnetic or electric field, the quantum state of atom or molecule is shifted, the shift depending on the initial quantum state of the particle and the field strength. A particle in nonuniform magnetic field is acted upon by the force directed along the field strength gradient. The focusing properties of a magnetic lens depend on the magnetic sublevel of atoms.
A proof-of-principle electron electric-dipole-moment $(e\text{\ensuremath{-}}\mathrm{EDM})$ experiment using slow cesium atoms, nulled magnetic fields, and electric-field quantization has been performed. With the ambient magnetic fields seen by the atoms reduced to less than
200pT, an electric field of
6MV∕m lifts the degeneracy between states of unequal $\ensuremath{\mid}{m}_{F}\ensuremath{\mid}$ and, along with the low $(\ensuremath{\approx}3\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ velocity, suppresses the systematic effect from the motional magnetic field. The low velocity and small residual magnetic field have made it possible to induce transitions between states and to perform state preparation, analysis, and detection in regions free of applied static magnetic and electric fields. This experiment demonstrates techniques that may be used to improve the $e\text{\ensuremath{-}}\mathrm{EDM}$ limit by two orders of magnitude, but it is not in itself a sensitive $e\text{\ensuremath{-}}\mathrm{EDM}$ search, mostly due to limitations of the laser system.