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Physical Review A

Time-orbiting-potential quadrupole magnetic trap for cold atoms

Vladimir G. Minogin, James T. Richmond, Geoffrey I. Opat

Published Oct 1, 1998• 15 citations
Publisher

Abstract

An analytical theory of the time-orbiting-potential quadrupole magnetic trap for cold atoms is developed. It is shown that the rotating magnetic field used to create the time-averaged harmonic potential is responsible for the formation of quasienergy states of an atom in the trap. It is found that the motion of an atom near the origin of the trap can be represented as consisting of slow motion in the time-averaged potential and fast oscillations with small amplitude. Eigenstates and eigenfunctions for the motion are found. The eigenfunctions are used to calculate the coordinate and momentum distributions for a single atom. It is concluded that at low temperature the quantum-statistical momentum distribution for a single atom exhibits a ring shaped structure due to the fast oscillations in the atomic linear momentum.

DOI
10.1103/physreva.58.3138

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An analytical theory of the time-orbiting-potential quadrupole magnetic trap for cold atoms is developed. It is shown that the rotating magnetic field used to create the time-averaged harmonic potential is responsible for the formation of quasienergy states of an atom in the trap. It is found that the motion of an atom near the origin of the trap can be represented as consisting of slow motion in the time-averaged potential and fast oscillations with small amplitude. Eigenstates and eigenfunctions for the motion are found. The eigenfunctions are used to calculate the coordinate and momentum distributions for a single atom. It is concluded that at low temperature the quantum-statistical momentum distribution for a single atom exhibits a ring shaped structure due to the fast oscillations in the atomic linear momentum.
We study the dynamics of atoms confined to a quadrupole magnetic trap with an orbiting potential. For typical values of the experimental parameters of the trap, the rotating magnetic field is shown to produce high-frequency modulation of atomic momenta with an amplitude comparable to the widths of the momentum distributions for the lowest oscillation states of atoms in the time-averaged potential. We find the quantum-statistical momentum and position distributions of atoms and show that at temperatures much higher than the effective vibrational temperature of the atoms in the trap the quantum-statistical momentum and position distributions are Gaussian. We also establish that at temperatures comparable to the effective vibrational temperature of the atoms the quantum-statistical momentum distribution has an annular structure in the trap’s symmetry plane, which is due to the deep modulation of the atomic momenta caused by the rotating magnetic field.
We report the experimental realization of a versatile ring trap for ultracold atoms. The ring geometry is created by the time-averaged adiabatic potential resulting from the application of an oscillating magnetic bias field to a rf-dressed quadrupole trap. Lifetimes for a Bose-Einstein condensate in the ring exceed 11s11\mathrm{s}11s and the ring radius was continuously varied from $50 \ensuremath{\mu}\text{m}$ to $262 \ensuremath{\mu}\text{m}$. An efficient method of loading the ring from a conventional time-averaged orbiting potential trap is presented together with a rotation scheme which introduces angular momentum into the system. The ring presents an opportunity to study the superfluid properties of a condensate in a multiply connected geometry and also has applications for matter-wave interferometry.
We investigate classical motions of cold atoms in three types (harmonic, linear, and Gaussian) of off-axis rotating traps in the presence of damping forces. When the radius of rotation of the trap is within the trap volume, the atoms are always attracted towards the rotation’s origin if the damping rate Γ is larger than the trap frequency ω ( i.e. , Γ > ω ). This is opposed to being repelled by the centrifugal force in a rotating reference frame. Contrarily, when the trap’s rotation radius is larger than the trap size, the atoms experience a time-averaged ring-shape trap at a high rotational frequency. These anomalous properties can be used to realize high-speed rotation sensors and effective static ring-trap potentials for manipulating cold atoms.
We describe a new type of magnetic trap whose time-averaged, orbiting potential (TOP) supplies tight and harmonic confinement of atoms. The TOP trap allows for long storage times even for cold atom samples by suppressing the loss due to nonadiabatic spin flips which limits the storage time in an ordinary magnetic quadrupole trap. In preliminary experiments on evaporative cooling of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the TOP trap, we obtain a phase-space density enhancement of up to 3 orders of magnitude and temperatures as low as 200 nK.
In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields have been theoretically investigated for trapping and manipulating of cold atoms in a two-dimensional (2D) geometry. In this scheme, the RF fields of some particular polarizations and phases are shown to give rise to some novel static and time-dependent anisotropic two-dimensional potentials that are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on a circular ring, can be used to control the rotation and the oscillation of the cold-atom cloud on the path of the circular ring. The ultracold atoms trapped in these potentials may be used to investigate interesting physics phenomena, such as tunnelling and superfluidity.
Since the first proposal and the first experiment on magneto-optical trapping of atoms, magneto-optical traps (MOT) became the most popular traps for cold atoms. Despite the numerous successful applications of MOT it is still unclear what ultimate parameters could be expected for atoms trapped in MOT. We develop the theory of MOT for cold atoms under the multilevel dipole interaction schemes. Theory is based on consideration of one-dimensional motion of atoms which have three ground-state sublevels (F/sub g/=1) and five upper-state sublevels (F/sub e/=2) and are in inhomogeneous magnetic field and in the field of two counter-propagating circular polarized laser waves. It is shown that in multilevel interaction schemes two-photon processes are responsible for formation of a narrow velocity and spatial structure in the radiation force. It is found that two-photon coherent process enhances considerably the friction force and the oscillation frequency at negative detuning. Single-photon and two-photon processes are shown to produce the two-component structure of the MOT potential and accordingly the two-component coordinate distribution.