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arXiv:physics/9712009 · Physical Review A

Nonadiabatic dynamics of atoms in nonuniform magnetic fields

Vyacheslav I. Yukalov

Published Dec 1, 1997• 17 citations
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Abstract

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 $z$ 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 $z$ 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.

DOI
10.1103/physreva.56.5004

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Reply to “Comment on ‘Nonadiabatic dynamics of atoms in nonuniform magnetic fields’ ”

Vyacheslav I. Yukalov

Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered in my earlier paper [V. I. Yukalov, Phys. Rev. A 56, 5004 (1997)]. The main result of this paper is that an unusual semiconfining regime of motion was found, when atoms are confined from one side of an axis, but are not confined from another side. The author of the Comment [V. E. Shapiro, Phys. Rev. A 60, 719 (1999)] expressed doubts on the validity of this result, advancing several concrete questions. In the present reply I answer all of these questions and show that they do not invalidate the possibility of realizing the semiconfining regime of motion.

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The problem of creating well-collimated beams of atoms escaping from a trap is studied. This problem is of high importance for the realization of atom lasers. Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered. The main result of this report is that an unusual semiconfining regime of motion is found, when atoms are confined from one side of an axis but are not confined from another side. This regime can be achieved by means of only magnetic fields. The formed atomic beam can be forwarded in arbitrary direction.

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

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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.

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Quantized motion of atoms in a quadrupole magnetostatic trap

T. H. Bergeman, Patrick J. McNicholl, Jan B. Kycia +2 more

We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all quantum levels have a nonzero decay rate. The Schrödinger equation associated with the potential gμB · S (S is the total atomic spin) takes the form of coupled equations in r when the spinor components are expanded in spherical harmonics. We integrate the multichannel problem numerically to obtain asymptotic phase shifts, resonance energies, and widths. For S = 1/2, the lowest levels have widths somewhat less than their spacing. Thus the trap quantum-level structure might possibly be observable if the atoms are sufficiently cold, namely, in the 0.1-μK regime for most atoms and attainable trap field gradients. The width decreases rapidly with increasing MJ, the angular momentum about the symmetry axis. Spectroscopic linewidths of a few hertz are possible if there is enough population in the lowest levels with a few MJ quanta. The decay rate of the lowest levels, however, is probably too rapid for studying Bose–Einstein condensation in such a trap.

Journal of the Optical Society of America B•Nov 1, 1989•70 citations
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.
Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered in my earlier paper [V. I. Yukalov, Phys. Rev. A 56, 5004 (1997)]. The main result of this paper is that an unusual semiconfining regime of motion was found, when atoms are confined from one side of an axis, but are not confined from another side. The author of the Comment [V. E. Shapiro, Phys. Rev. A 60, 719 (1999)] expressed doubts on the validity of this result, advancing several concrete questions. In the present reply I answer all of these questions and show that they do not invalidate the possibility of realizing the semiconfining regime of motion.
The problem of creating well-collimated beams of atoms escaping from a trap is studied. This problem is of high importance for the realization of atom lasers. Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered. The main result of this report is that an unusual semiconfining regime of motion is found, when atoms are confined from one side of an axis but are not confined from another side. This regime can be achieved by means of only magnetic fields. The formed atomic beam can be forwarded in arbitrary direction.
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.
In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed onto an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the nonadiabatic effects arising from the spin dynamics about the local magnetic field. Geometric like magnetic fields determined by Berry's phase appear within the quantum description. Application of the time-dependent variational principle on the original quantum equation leads to a set of dynamical evolution equations for the quantum average value of the position operator and spin variables. Within this approximation we derive the quantum-mechanical ground-state configuration matching the classical adiabatic solution and perform some numerical simulations.
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.
We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all quantum levels have a nonzero decay rate. The Schrödinger equation associated with the potential gμB · S (S is the total atomic spin) takes the form of coupled equations in r when the spinor components are expanded in spherical harmonics. We integrate the multichannel problem numerically to obtain asymptotic phase shifts, resonance energies, and widths. For S = 1/2, the lowest levels have widths somewhat less than their spacing. Thus the trap quantum-level structure might possibly be observable if the atoms are sufficiently cold, namely, in the 0.1-μK regime for most atoms and attainable trap field gradients. The width decreases rapidly with increasing MJ, the angular momentum about the symmetry axis. Spectroscopic linewidths of a few hertz are possible if there is enough population in the lowest levels with a few MJ quanta. The decay rate of the lowest levels, however, is probably too rapid for studying Bose–Einstein condensation in such a trap.