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Review of Scientific Instruments

The Stark ball: A programmable multipolar environment

Keith B. MacAdam, C. S. Hwang

Published Mar 27, 2003• 3 citations
Publisher

Abstract

A device is described and mathematically analyzed which creates electrostatic multipole potentials at least up to rank 3 in a 2 cm diam spherical region. The fields in the Stark ball are produced by the application of programmed voltages to 24 conducting rods that are inserted symmetrically in an empty 5 cm conducting cavity. Three mutually orthogonal unobstructed paths through the center of the device between the rods are provided for access of light and particle beams, and four other tetrahedrally located openings can be added for beams, detectors, or imaging. The device is intended for application in atom or molecule trapping and cooling, recoil-ion momentum spectroscopy, particulate analysis, reactive scattering, and coherent control. Potential distributions can be established, altered, and rotated on subnanosecond time scales, and frequencies higher than 20 GHz can be introduced via the same electrodes. Uniform fields, i.e., first-rank multipoles, quadrupole, and octupole potentials can be programmed and superposed with arbitrary and independent time profiles, so that the device may be applied to the study of orientational properties of complex anisotropic molecules, pollens, grains of dust, and other particulates. The device is nonmagnetic. An extensive analysis of fields in the center region, fringing fields, and multipole purity up to rank 7 has been carried out, and recipes are given for pure (l,m)=(1,0), (2,0), and (3,0) multipoles. The principles and methods laid out here and applied to a “truncated octahedron” can be applied to the design of electrostatic environments having fewer or more independent electrodes in any polyhedral geometry.

DOI
10.1063/1.1544085

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A device is described and mathematically analyzed which creates electrostatic multipole potentials at least up to rank 3 in a 2 cm diam spherical region. The fields in the Stark ball are produced by the application of programmed voltages to 24 conducting rods that are inserted symmetrically in an empty 5 cm conducting cavity. Three mutually orthogonal unobstructed paths through the center of the device between the rods are provided for access of light and particle beams, and four other tetrahedrally located openings can be added for beams, detectors, or imaging. The device is intended for application in atom or molecule trapping and cooling, recoil-ion momentum spectroscopy, particulate analysis, reactive scattering, and coherent control. Potential distributions can be established, altered, and rotated on subnanosecond time scales, and frequencies higher than 20 GHz can be introduced via the same electrodes. Uniform fields, i.e., first-rank multipoles, quadrupole, and octupole potentials can be programmed and superposed with arbitrary and independent time profiles, so that the device may be applied to the study of orientational properties of complex anisotropic molecules, pollens, grains of dust, and other particulates. The device is nonmagnetic. An extensive analysis of fields in the center region, fringing fields, and multipole purity up to rank 7 has been carried out, and recipes are given for pure (l,m)=(1,0), (2,0), and (3,0) multipoles. The principles and methods laid out here and applied to a “truncated octahedron” can be applied to the design of electrostatic environments having fewer or more independent electrodes in any polyhedral geometry.
A cylindrical arrangement of electrodes, together with control electronics, is described that provides uniform electric fields over cm3 volumes in a vacuum, whose angle and magnitude can be switched on a μs time scale. Full 360° field rotation is achieved, and the device allows access for particle or light beams from all sides. Both numerical and analytic descriptions of the general fields are given. Extension to full three-dimensional field control and other variations are described. The device, which was originally designed for crossed-beam collision experiments with keV energy ions and laser-excited Rydberg atoms in field-directed Stark states or coherent-elliptic states, may be more generally useful in atom trapping and cold collisions or in materials and surface science.
We propose a novel optical-access opened electrostatic trap to study the Stark-potential evaporative cooling of polar molecules by using two charged disk electrodes with a central hole of radius r 0 =1.5 mm, and derive a set of new analytical equations to calculate the spatial distributions of the electrostatic field in the above charged-disk layout. Afterwards, we calculate the electric-field distributions of our electrostatic trap and the Stark potential for cold ND 3 molecules, and analyze the dependences of both the electric field and the Stark potential on the geometric parameters of our charged-disk scheme, and find an optimal condition to form a desirable trap with the same trap depth in the x , y , and z directions. Also, we propose a desirable scheme to realize an efficient loading of cold polar molecules in the weak-field-seeking states, and investigate the dependences of the loading efficiency on both the initial forward velocity of the incident molecular beam and the loading time by Monte Carlo simulations. Our study shows that the maximal loading efficiency of our trap scheme can reach about 95%, and the corresponding temperature of the trapped cold molecules is about 28.8 mK. Finally, we study the Stark-potential evaporative cooling for cold polar molecules in our trap by the Monte Carlo method, and find that our simulated evaporative cooling results are consistent with our developed analytical model based on trapping-potential evaporative cooling.
A four electrode electrostatic trap geometry is demonstrated that can be used to combine a dipole, quadrupole, and hexapole field. A cold packet of 15ND3^{15}\mathrm{ND}_{3}15ND3​ molecules is confined in both a purely quadrupolar and hexapolar trapping field and additionally, a dipole field is added to a hexapole field to create either a double-well or a donut-shaped trapping field. The profile of the 15ND3^{15}\mathrm{ND}_{3}15ND3​ packet in each of these four trapping potentials is measured, and the dependence of the well-separation and barrier height of the double-well and donut potential on the hexapole and dipole term are discussed.
We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric field. We first give the two-ball scheme and derive the analytical solution of the electric field. In order to make a comparison, we also give the numerical solution calculated by the finite element software (Ansoft Maxwell). Considering the loading of cold polar molecules into the trap, we give the three-ball scheme. We first give the analytical and numerical solutions of the distribution of the electric field. Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method. We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency. After that, we give the temperature of the trapped cold molecules. Our study shows that the loading efficiency can reach 82%, and the corresponding temperature of the trapped molecules is about 24.6 mK. At last, we show that the single well divides into two ones by increasing the bias electric field or decreasing the voltages applied to the spherical electrodes.
To meet some demands for realizing precise measurements of an electric dipole moment of electron (eEDM) and examining cold collisions or cold chemical physics, we have proposed a novel, versatile electrostatic Stark decelerator with an array of true 3D electric potential wells, which are created by a series of horizontally-oriented, U-shaped electrodes with time-sequence controlling high voltages (± HV) and two guiding electrodes with a constant voltage. We have calculated the 2D electric field distribution, the Stark shifts of the four lowest rotational sub-levels of PbF molecules in the X1(2)Π1/2(v = 0) electronic and vibrational ground states as well as the population in the different rotational levels. We have discussed the 2D longitudinal and transverse phase-space acceptances of PbF molecules in our decelerator. Subsequently, we have simulated the dynamic processes of the decelerated PbF molecules using the 3D Monte-Carlo method, and have found that a supersonic PbF beam with a velocity of 300 m s(-1) can be efficiently slowed to about 5 m s(-1), which will greatly enhance the sensitivities to research a parity violation and measure an eEDM. In addition, we have investigated the dependences of the longitudinal velocity spread, longitudinal temperature and bunching efficiency on both the number of guiding stages and high voltages, and found that after bunching, a cold packet of PbF molecules in the J = 7/2, MΩ = -7/4 state with a longitudinal velocity spread of 0.69 m s(-1) (corresponding to a longitudinal temperature of 2.35 mK) will be produced by our high-efficient decelerator, which will generate a high energy-resolution molecular beam for studying cold collision physics. Finally, our novel decelerator can also be used to efficiently slow NO molecules with a tiny electric dipole moment (EDM) of 0.16 D from 315 m s(-1) to 28 m s(-1). It is clear that our proposed new decelerator has a good slowing performance and experimental feasibility as well as wide applications in the field of precise measurements and cold molecule physics.
We propose an optically accessible electrostatic trap scheme to confine cold polar molecules by using two charged spherical electrodes, and we calculate the corresponding electric field distribution and the Stark trapping potential for ND3 molecules. We also propose a desirable scheme to realize an efficient loading of cold polar molecules in weak-field-seeking states, and our simulated results show that the maximal loading efficiency can reach ∼14%. In addition, we briefly discuss some potential applications of our proposed trap scheme in the studies of optical-potential evaporative cooling and electrostatic surface traps for cold polar molecules.