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International Laser Science Conference

Magnetic trapping of neutral atoms

Thomas H. Bergeman, Harold J. Metcalf

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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.

DOI
10.1364/ils.1986.wf6

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Magnetic trapping of neutral atoms

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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.

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In view of the recent successful confinement of decelerated sodium atoms in a magnetostatic trap, it is of interest to evaluate possible trap-field configurations. Neutral atoms in a Zeeman sublevel whose energy increases with field can be confined by a field whose magnitude \ensuremath{\Vert}B\ensuremath{\Vert} increases with distance from the center. Because this same basic requirement applies also to traps for neutrons and for plasmas (in the guiding-center approximation), trap configurations developed previously for these purposes are of interest for neutral atoms. However, the desired properties differ considerably because of very different objectives and different behavior of very cold atoms as compared with hot plasmas. We characterize basic trap configurations using both the exact expressions for the field, and a multipole polynomial expansion that facilitates studies of symmetry properties and classical or quantum orbits. Polynomial terms for the field components are derived and coefficients obtained by comparison with Taylor-series expansions and by global fit. Contours of \ensuremath{\Vert}B\ensuremath{\Vert} for various trap configurations are also presented. Under certain restrictive conditions, \ensuremath{\Vert}B\ensuremath{\Vert}, and hence the effective potential, can be made isotropic to second order.

Physical Review A•Feb 1, 1987•280 citations
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.
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.
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].
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.
In view of the recent successful confinement of decelerated sodium atoms in a magnetostatic trap, it is of interest to evaluate possible trap-field configurations. Neutral atoms in a Zeeman sublevel whose energy increases with field can be confined by a field whose magnitude \ensuremath{\Vert}B\ensuremath{\Vert} increases with distance from the center. Because this same basic requirement applies also to traps for neutrons and for plasmas (in the guiding-center approximation), trap configurations developed previously for these purposes are of interest for neutral atoms. However, the desired properties differ considerably because of very different objectives and different behavior of very cold atoms as compared with hot plasmas. We characterize basic trap configurations using both the exact expressions for the field, and a multipole polynomial expansion that facilitates studies of symmetry properties and classical or quantum orbits. Polynomial terms for the field components are derived and coefficients obtained by comparison with Taylor-series expansions and by global fit. Contours of \ensuremath{\Vert}B\ensuremath{\Vert} for various trap configurations are also presented. Under certain restrictive conditions, \ensuremath{\Vert}B\ensuremath{\Vert}, and hence the effective potential, can be made isotropic to second order.