A large class of cold neutral atoms and molecules is subject to magnetic field-gradient forces. In the presence of a field, hyperfine atomic states are split into several Zeeman levels. The slopes of these curves vs. field are the effective magnetic moments. By means of optical pumping in a field, Zeeman states of neutral lithium atoms and CaH molecules with effective magnetic moments of nearly {+-} one Bohr magneton can be selected. Particles in Zeeman states for which the energy increases with field are repelled by increasing fields; particles in states for which the energy decreases with field are attracted to increasing fields. For stable magnetic confinement, field-repelled states are required. Neutral-particle velocities in the present study are on the order of tens to hundreds of m/s and the magnetic fields needed for transport and injection are on the order of in the range of 0.01-1T. Many of the general concepts of charged-particle beam transport carry over into neutral particle spin-force optics, but with important differences. In general, the role of bending dipoles in charged particle optics is played by quadrupoles in neutral particle optics; the role of quadrupoles is played by sextupoles. The neutralparticle analog of charge-exchange injection into storage rings is the use of lasers to flip the state of particles from field-seeking to field-repelled. Preliminary tracking results for two neutral atom/molecule storage ring configurations are presented. It was found that orbit instabilities limit the confinment time in a racetrack-shaped ring with discrete magnetic elements with drift spaces between them; stable behavior was observed in a toroidal ring with a continuous sextupole field. An alternative concept using a linear sextupole or octupole channel with solenoids on the ends is presently being considered.
A large class of cold neutral atoms and molecules is subject to magnetic field-gradient forces. In the presence of a field, hyperfine atomic states are split into several Zeeman levels. The slopes of these curves vs. field are the effective magnetic moments. By means of optical pumping in a field, Zeeman states of neutral lithium atoms and CaH molecules with effective magnetic moments of nearly {+-} one Bohr magneton can be selected. Particles in Zeeman states for which the energy increases with field are repelled by increasing fields; particles in states for which the energy decreases with field are attracted to increasing fields. For stable magnetic confinement, field-repelled states are required. Neutral-particle velocities in the present study are on the order of tens to hundreds of m/s and the magnetic fields needed for transport and injection are on the order of in the range of 0.01-1T. Many of the general concepts of charged-particle beam transport carry over into neutral particle spin-force optics, but with important differences. In general, the role of bending dipoles in charged particle optics is played by quadrupoles in neutral particle optics; the role of quadrupoles is played by sextupoles. The neutralparticle analog of charge-exchange injection into storage rings is the use of lasers to flip the state of particles from field-seeking to field-repelled. Preliminary tracking results for two neutral atom/molecule storage ring configurations are presented. It was found that orbit instabilities limit the confinment time in a racetrack-shaped ring with discrete magnetic elements with drift spaces between them; stable behavior was observed in a toroidal ring with a continuous sextupole field. An alternative concept using a linear sextupole or octupole channel with solenoids on the ends is presently being considered.
We have been studying the use of inhomogeneous magnetic fields for the trapping of neutral atoms via the interaction with their magnetic moments. Apart from gravitational forces (which may turn out to be of great importance in atom traps), only electromagnetic forces are of real interest for trapping neutral atoms, and these forces must necessarily arise from the interaction of multipole moments and inhomogeneous fields. In this paper we restrict ourselves to static traps and magnetic dipoles, even though optical, quasi‐static, and Stark effect traps have been discussed. We present some discussion of the field configurations that might be used, of the motion of ‘‘warm’’ trapped atoms (about 1 K), and of the states of ‘‘cold’’ trapped atoms (about 0.1 μK). The basic scale of the interaction is set by the ratio of the Bohr magneton to the Boltzmann constant, about 1.5 Tesla/Kelvin.
Magnetic trapping of laser-cooled neutral atoms has been demonstrated at NBS and is progressing in other laboratories. Confinement of any object requires exchanging kinetic for potential energy, and for neutral atoms, this necessarily derives from shifts of internal energy levels. This is implemented through the force experienced by the atomic magnetic moment in a carefully designed, highly inhomogeneous field. Since magnetic fields of convenient strength can shift atomic energy levels by only a few gigahertz (temperature ≌ 0.1 K), neutral atom traps are very shallow and must be loaded with very cold atoms. We present some motivations for using magnetic traps and then discuss the constraints and optimal configurations of various arrangements. For example, no trap can be isotropic. Next we discuss both the classical and quantum mechanical motions of trapped atoms. These motions are important for at least two reasons: First, several schemes under study for further cooling depend on knowing the position and velocity of the atoms, as well as the vector field at each point along the orbit. Second, magnetic traps depend on the atomic moment remaining aligned with the field as the atom orbits in the trap, and this precludes rapid motion through a low-field region.
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 have demonstrated a storage ring for ultracold neutral atoms. Atoms with mean velocities of 1 m/s corresponding to kinetic energies of approximately 100 neV are confined to a 2 cm diameter ring by magnetic forces produced by two current-carrying wires. Up to 10(6) atoms are loaded at a time in the ring, and seven revolutions are clearly observed. Additionally, we have demonstrated multiple loading of the ring and deterministic manipulation of the longitudinal velocity distribution of the atoms using applied laser pulses. Applications of this ring include large area atom interferometers and monochromatic atomic beam generation.
Slowing down atoms using laser cooling, together with techniques like magnetic trapping and evaporative cooling, has led to numerous exciting results over the last decade [1], with the realization of Bose-Einstein condensation as the most spectacular achievement [2]. Laser-cooling schemes are applicable to atoms since closed multilevel systems can be realized and many consecutive absorptionemission cycles can be induced. This leads to a significant momentum transfer from the photons of the laser to the atom, resulting in a change of the velocity of the atom. There currently is a great interest in producing cold molecules for the study of cold molecule-molecule collisions, molecular quantum collective effects, Doppler-free spectroscopy, frequency standards, as well as many other applications already realized for atoms [3]. Slowing down of neutral molecules, a prerequisite for being able to trap them, has proven to be considerably more difficult to be achieved, however. The above-mentioned laser-cooling scheme cannot be applied to slow down molecules as no simple closed-level systems can be found; the unavoidable off-resonant radiative decay of molecules from the excited state to other vibrational levels in the electronic ground state hampers efficient momentum transfer [4]. Once molecules are present at sufficiently low kinetic energies, below a fraction of a cm21, they can be trapped in various ways. Trapping of neutral molecules in inhomogeneous magnetic [3] and electric fields [5] and trapping based on the use of evanescent fields close to the dielectricvacuum interface have been proposed [6]. It has also been suggested that extremely high laser powers might be used to induce a dipole moment in polarizable molecules, leading to trapping of these molecules in the laser beam [7]. Other methods to produce slow molecules have been put forward and have recently been successfully applied to produce the first samples of trapped molecules. By injecting molecules in a cold buffer gas, sufficiently low kinetic energies of the injected molecules can be obtained after thermalization that they can subsequently be trapped in an inhomogeneous magnetic field. This has recently been demonstrated for CaH injected in 3He buffer gas at temperatures of around 0.3 K [8]. Associative collisions between ultracold trapped atoms [9] have proven to be
A thermal atomic Na beam is opposed by a resonantly tuned laser beam. The radiation pressure decelerates and compresses the thermal velocity distribution, bringing the average velocity to zero and reducing the width from ~1000 m/s to a few tens of m/s or less.1 The density of stopped atoms is > 106/cm3 within a bandwidth of a few m/ s. These densities and velocities are suitable for trapping by a number of proposed optical and magnetic traps. Using these stopped atoms, we have demonstrated the first electromagnetic trapping of neutral atoms. The trap, a magnetic quadrupole formed by two separated, coaxial, opposed current loops, confines the atoms by virtue of the force exerted on the Na magnetic dipole moment by the inhomogeneous magnetic field. The time constant for exponential decay of the atomic population in the trap is 0.83(7) s and is limited mainly by collisions with fast background gas atoms. The maximum velocity of atoms contained in the trap is 3.5 m/s, corresponding to a maximum energy of 17 mK.