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arXiv:physics/0603127 · Physical Review A

Focusing a fountain of neutral cesium atoms with an electrostatic lens triplet

Juris G. Kalnins, Jason Amini, Harvey Gould

Published Oct 26, 2005• 19 citations

Abstract

An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.

DOI: 10.1103/physreva.72.043406

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An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.

A method of slowing, accelerating, cooling, and bunching molecules and neutral atoms using time-varying electric-field gradients is demonstrated with cesium atoms in a fountain. The effects are measured and found to be in agreement with our calculations. Time-varying electric-field-gradient slowing and cooling is applicable to atoms that have large dipole polarizabilities, including atoms that are not amenable to laser slowing and cooling, to Rydberg atoms, and to molecules, especially polar molecules with large electric dipole moments. The possible applications of this method include slowing and cooling thermal beams of atoms and molecules, launching cold atoms from a trap into a fountain, and measuring atomic dipole polarizabilities.

Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compared to the outcome of trajectory simulations.

In the field of atom optics, there has been much interests in developing components such as lenses, mirrors, beam splitters and waveguides to manipulate neutral atoms. Especially many clever methods to focus neutral atoms have been developed. The lenses have been constructed using the static electrical and magnetic fields, Fresnel zone plates, and radiation pressure forces. Before the laser cooling and trapping techniques were invented, the electrostatic fields could not be used for manipulating neutral atoms because of its weak interaction energy with atoms. After the cold atoms were available, it has been possible to manipulate atoms with weak electrostatic interaction energy. We developed an atom lens system using electrostatic fields.

Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compared to the outcome of trajectory simulations.

The imaging of a neutral atomic beam by electrostatic force has been demonstrated. An ultracold neon atomic beam in the

{1s}_{3}[{(2p)}^{5}{3s:}^{1}{P}_{0}]

state illuminated a transparent object, passed through a set of three electrostatic lenses, and formed the image on a microchannel plate detector with the magnification of unity. Each lens consisted of two parallel cylinders that functioned as a concave lens along one axis and as a convex lens along the other axis. The atomic polarizability of neon in the

{1s}_{3}

state has been also determined to be $2.8(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39} {\mathrm{Fm}}^{2}.$

Beams of polar molecules can be focused using an array of electrostatic lenses in alternating gradient (AG) configuration. They can also be accelerated or decelerated by applying an appropriate high-voltage switching sequence to the lenses. AG focusing is applicable to molecules in both low-field- and high-field-seeking states and is particularly well suited to the problem of decelerating heavy molecules and those in their ground rotational state. We describe the principles of AG deceleration and set out criteria to be followed in decelerator design, construction and operation. We calculate the longitudinal and transverse focusing properties of a decelerator, and exemplify this by 2D-imaging studies of a decelerated beam of metastable CO molecules.