Abstract In a trap operating with a voltage of 10 = 500 V, singly-charged ions have a maximum ‘binding’ energy of order 500eV.3 This trap depth corresponds to the kinetic energy at a temperature of 6 x 106 K. This is more than enough to trap ions, even if the ions do receive a large recoil kick during the ionization process-to load an ion trap experimenters send a weak (neutral) atomic beam through the trapping region where an electron beam ionizes a few of the atoms by knocking an electron off. These ions created by electron bombardment have much greater kinetic energy than the thermal energy of atoms at room temperature (equivalent to only 1 / 40 eV). It would be unwise to try to be more precise about the typical energy of an ion since it depends on the voltage used. In contrast, a magnetic trap for neutrals has a maximum depth of only 0.07K.
Abstract In a trap operating with a voltage of 10 = 500 V, singly-charged ions have a maximum ‘binding’ energy of order 500eV.3 This trap depth corresponds to the kinetic energy at a temperature of 6 x 106 K. This is more than enough to trap ions, even if the ions do receive a large recoil kick during the ionization process-to load an ion trap experimenters send a weak (neutral) atomic beam through the trapping region where an electron beam ionizes a few of the atoms by knocking an electron off. These ions created by electron bombardment have much greater kinetic energy than the thermal energy of atoms at room temperature (equivalent to only 1 / 40 eV). It would be unwise to try to be more precise about the typical energy of an ion since it depends on the voltage used. In contrast, a magnetic trap for neutrals has a maximum depth of only 0.07K.
In order to confine any object, it is necessary to exchange kinetic for potential energy in the trapping field, and in neutral atom traps, the potential energy must be stored as internal atomic energy. Thus practical traps for ground-state neutral atoms are necessarily very shallow compared with thermal energy because the energy level shifts that result from conveniently sized fields are typically considerably smaller than k B T , even for T = 1 K. Neutral atom trapping therefore depends on substantial cooling of a thermal atomic sample, and is often connected with the cooling process. In most practical cases, atoms are loaded from magneto-optical traps, where they have been efficiently accumulated and cooled to mK temperatures (see Sec. 20.3), or from optical molasses, where they have been optically cooled to μK temperatures (see Sec. 19.4). The small depth of typical neutral atom traps dictates stringent vacuum requirements, because an atom cannot remain trapped after a collision with a thermal energy background gas molecule. Since these atoms are vulnerable targets for thermal energy background gas, the mean free time between collisions must exceed the desired trapping time. The cross-section for destructive collisions is quite large because even a gentle collision (i.e. large impact parameter) can impart enough energy to eject an atom from a trap. At pressure P sufficiently low to be of practical interest, the trapping time is ~(10 -8 / P ) s, where P is in torr. This chapter begins with a discussion of ordinary, single-center traps, but also considers arrays of traps. Such “optical lattices” are playing an increasingly important role in research in atomic physics, so discussion of their properties is an appropriate part of the education of a student of the subject. Dipole force optical traps Single-beam optical traps for two-level atoms The simplest imaginable optical trap consists of a single, strongly focused Gaussian laser beam (see Fig. 20.1) [214, 215] whose intensity at the focus varies transversely with r as where is the beam waist size. Such a trap has a well-studied and important macroscopic classical analog in a phenomenon called optical tweezers (see App. 1.C) [216–218].
We recently used a compact Penning trap to capture and isolate highly charged ions extracted from an electron beam ion trap (EBIT) at the National Institute of Standards and Technology. Isolated charge states of highly stripped argon and neon ions with total charge $Q\ensuremath{\ge}10$, extracted at energies of up to $4\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}Q$ eV, are captured in a trap with well depths of $\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}(4--12)Q$ eV. Here we discuss in detail the process to optimize velocity tuning, capture, and storage of highly charged ions in a unitary Penning trap designed to provide easy radial access for atomic or laser beams in charge exchange or spectroscopic experiments, such as those of interest for proposed studies of one-electron ions in Rydberg states or optical transitions of metastable states in multiply charged ions. Under near-optimal conditions, ions captured and isolated in such rare-earth Penning traps can be characterized by an initial energy distribution that is $\ensuremath{\approx}60$ times narrower than typically found in an EBIT. This reduction in thermal energy is obtained passively, without the application of any active cooling scheme in the ion-capture trap.
We produce large numbers of low-energy ions by photoionization of laser-cooled atoms inside a surface-electrode-based Paul trap. The isotope-selective trap's loading rate of $4\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.3em}{0ex}}{\mathrm{Yb}}^{+}\phantom{\rule{0.3em}{0ex}}\mathrm{ions}∕\mathrm{s}$ exceeds that attained by photoionization (electron-impact ionization) of an atomic beam by three (six) orders of magnitude. Traps as shallow as 0.13eV are easily loaded with this technique. The ions are confined in the same spatial region as the laser-cooled atoms, which will allow the experimental investigation of interactions between cold ions and cold atoms or Bose-Einstein condensates.
Abstract Atomic beams, pioneered by Stern (Episodes 30 and 52), opened the way to study non-interacting atoms which, essentially, have only one component in velocity, namely, that in beam direction. Ions could even be confined in a trap(Episode 80) with small values of all three velocity components. We shall see now how that was achieved also for neutral atoms. A measure of quality for a gas of trapped atoms is its temperature, i.e., the average kinetic energy of the atoms expressed in Kelvin. By carefully exploiting the inner structure of atoms it became possible, with the help of laser light and magnetic fields, to cool and trap small samples of highly dilute atomic gases, reaching temperatures as low as 180 nK (180 × 10‒9 K).
The kinetic energy distribution of a cloud of ions stored in a RF trap has been investigated by use of two methods based on phase-stopped ejection. The oscillation of the RF voltage is stopped at a phase corresponding to zero field Value inside the trap. After their subsequent ejection from the trap, the ions are detected by an electron multiplier. The instantaneous ion cloud temperature value corresponding to the phase-stopping time can be deduced from the recorded profile of the ion signal. An alternative method consists in submitting the ejected ions to a repulsive field, applied before the detector, which allows us to discriminate the velocity classes. In both cases, the experiments are interpreted thanks to a simple theoretical description of a cloud of ions at thermal equilibrium in a RF trap and to a precise calculation of the ejection process. Both methods are compared, for the various trap working points. In all cases, the ion cloud average temperature is of the order of a tenth of the potential well depth.
A kinetic theory based on the Boltzmann equation is developed for the trapping of atomic ions in a radio-frequency quadrupole ion trap containing enough neutral atoms that ion-neutral collisions cannot be ignored. The collisions are treated at the same level of sophistication and detail as is used to deal with the time- and space-dependent electric fields in the trap. As a result, microscopic definitions are obtained for the damping and stochastic forces that originate from such collisions. These definitions contrast with corresponding phenomenological terms added ad hoc in previous treatments to create damped Mathieu and Langevin equations, respectively. Furthermore, the theory indicates that either collisional cooling or heating of the ions is possible, depending upon details of the ion-neutral mass ratios and interaction potential. The kinetic theory is not dependent on any special assumptions about the electric field strengths, the ion-neutral interaction potentials, or the ion-neutral mass ratio. It also provides an ab initio way to describe the ion kinetic energies, temperatures, and other properties by a series of successive approximations.