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Journal of Experimental and Theoretical Physics

Dynamics of cold atoms in a quadrupole magnetic trap with an orbiting potential

Vladimir G. Minogin, Maksim V. Subbotin, Павел Николаевич Мелентьев

Published Jul 1, 1998• 1 citation
Publisher

Abstract

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.

DOI
10.1134/1.558624

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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.
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.
The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This allows to evaluate the effect that reversing of the bias field rotation produces on the vertical position of the atomic orbit, a displacement that is closely related to the adiabatic character of the trap motion. The present investigation has been motivated by a similar experimental test previously carried out in the actual magnetic time orbiting potential trap. We find that the non-adiabatic effects provided by the classical model are extremely small. Thus, we conclude that the theoretical explanation of the experimental measures, requires a quantum description of the dynamics in magnetic traps.
We study the translational motions of homonuclear diatomic molecules prepared in their 3Σ electronic states, deeply bound vibrational states, and rotational states of well-defined parity. The trapping potential arises due to the interaction of the total spin of electrons and orbital angular momentum of nuclei with the trap's quadrupole magnetic field. The translational motion of a molecule is treated classically. We examine the Hamilton equations that govern the center-of-mass dynamics both numerically and analytically. Using data of a hydrogen molecule at the ground vibrational state, we present global dynamics using the Poincaré section method and various types of trajectories: periodic, quasiperiodic, and chaotic. We prove that the Hamiltonian system governing this motion is non-integrable. The particle's orbits are confined to a bound region of space that grows with energy, but for small energies (<1.8 K), the motion is restricted to a processing chamber (a few centimeters). Solutions of equations of motion occurring on the symmetry axis and the horizontal plane are expressed in terms of Jacobi elliptic functions.
Single-particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective time-averaged potential. We show that the trapping is possible when the frequency of the rotations exceeds some threshold. Slightly above this threshold the weakly interacting gas of the trapped atoms acquires the properties of a quasi-one-dimensional system in the frame rotating together with the field. The role of the atom-atom interaction in changing the ideal gas solution is discussed. We show that in the limit of large numbers of particles the rotating field whose frequency is appropriately modulated can be utilized as a driving force principally for the center-of-mass motion as well as for the angular momentum L=2 normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed.
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.
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.