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Physical Review A

Proposals for improved methods for magnetic trapping and measurements of neutral atoms

V. E. Shapiro

Published Feb 11, 2000• 2 citations
Publisher

Abstract

The magnetic methods most successful so far for tight, stable confinement of cold neutral atoms in the dark explore three-dimensional-nonuniform magnetic configurations. A different method, using revolving planar-nonuniform fields, is developed in the present work. The paper gives an idea of the method, describes its basic features, and shows its superiority, such as (i) a greater product of curvatures of the trap well in the three spatial directions by a factor of two orders of magnitude given the same magnitude of field gradient, (ii) tight, stable, and more isotropic confinement in both the trap center and an easy-to-change orbit, (iii) vast possibilities to change the form of the trap well, and (iv) the possibility to separately detect the effective spin and translational motion temperatures of the cloud via observations of its density distribution.

DOI
10.1103/physreva.61.035401

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The magnetic methods most successful so far for tight, stable confinement of cold neutral atoms in the dark explore three-dimensional-nonuniform magnetic configurations. A different method, using revolving planar-nonuniform fields, is developed in the present work. The paper gives an idea of the method, describes its basic features, and shows its superiority, such as (i) a greater product of curvatures of the trap well in the three spatial directions by a factor of two orders of magnitude given the same magnitude of field gradient, (ii) tight, stable, and more isotropic confinement in both the trap center and an easy-to-change orbit, (iii) vast possibilities to change the form of the trap well, and (iv) the possibility to separately detect the effective spin and translational motion temperatures of the cloud via observations of its density distribution.
Methods of trapping neutral spin-polarized particles are proposed using highly nonuniform magnetic fields rotating at low frequencies, down to the resonance of the particle's orbiting motion. Such fields beget new trapping mechanisms of vast possibilities. The new resonance methods and the new traps of zero-size equilibrium orbit should give much tighter and more stable confinement than previously known. They also give the possibility of a high, resonance selectivity in magnetic separation and evaporative cooling. A general analysis of trapping with rotating fields is given.
Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the adiabatic approximation and, thus, permits one to check the limits of the latter and also to analyze nonadiabatic regimes of motion. An unusual nonadiabatic regime is found when atoms are confined from one side of the zzz axis but are not confined from another side. The lifetime of atoms in a trap in this semiconfining regime can be sufficiently long for accomplishing experiments with a cloud of such atoms. At low temperature, the cloud is ellipsoidal, being stretched in the axial direction and moving along the zzz axis. The possibility of employing the semiconfining regime for studying the relative motion of one component through another in a binary mixture of gases is discussed.
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.
We propose two double-well magnetic traps for cold neutral atoms that use current-carrying wires. These traps can be used to trap two different atomic species. The spatial distributions of the magnetic fields, gradients, and curvatures from these two wire configurations were calculated and analyzed. Our study shows that the double-well traps proposed here can be continuously changed into single-well traps by reduction of the current in a wire (or a coil) and vice versa and that a maximum field gradient greater than 5×104 G/cm and a maximum field curvature (at each trap center) greater than 2.5×107 G/cm2 can be generated in our double-well traps and used to achieve two-species Bose–Einstein condensations and study the properties of double-well Bose–Einstein condensations or to achieve sympathetic cooling between two atomic samples or even to achieve two-species magneto-optical traps and study cold collisions between two atomic samples.
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 describe planar and mostly planar current geometries for constructing microscopic magnetic traps for neutral atoms. These geometries are well-suited for fabrication from superconductors using standard microfabrication techniques. Magnetic-field gradients greater than 5\ifmmode\times\else\texttimes\fi{}105{10}^{5}105 G/cm, and field curvatures greater than 108{10}^{8}108 G/cm2{\mathrm{cm}}^{2}cm2 can be produced in microscopic traps. Trap loading could be accomplished by constructing a nested series of traps, and compressing atom clouds from larger traps into smaller ones. In the smallest magnetic microtraps the motional ground-state energy of atoms in the trap can exceed the recoil energy from resonant photons, which may allow direct laser cooling to the trap ground state. If a number of atoms can be simultaneously cooled to the ground state, the resulting ``Bose clusters'' should exhibit interesting optical behavior, since their spatial extent would be less than the resonant light wavelength.