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Physical Review A

Centrifugal effects in a Bose-Einstein condensate in the time-orbiting-potential magnetic trap

Anatoly B. Kuklov, N. Chencinski, Alfred M. Levine, W. M. Schreiber, Joseph L. Birman

Published Jan 1, 1997• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.55.488

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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.
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-1D 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 angular 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=2L = 2L=2 normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed.
We report on the manipulation of the center-of-mass motion (``sloshing'') of a Bose-Einstein condensate in a time-averaged orbiting potential (TOP) trap. We start with a condensate at rest in the center of a static trapping potential. When suddenly replacing the static trap with a TOP trap centered about the same position, the condensate starts to slosh with an amplitude much larger than the TOP micromotion. We show, both theoretically and experimentally, that the direction of sloshing is related to the initial phase of the rotating magnetic field of the TOP. We show further that the sloshing can be quenched by applying a carefully timed and sized jump in the phase of the rotating field.
A study is made of the quantum mechanics of a gas of spin-polarized (b-state) atomic hydrogen confined in a three-dimensional dynamic (ac) magnetic trap. A previous classical treatment indicated that evaporative cooling from such a trap could be used to attain conditions for Bose-Einstein condensation (BEC). An approximate solution is developed for the quantum mechanics of a single atom in an ac trap. This solution is then used to treat the statistical mechanics of the BEC in an ac trap. The ideal-gas limit is briefly considered, and this is compared with the more realistic approximation of a nonideal gas described by the finite-temperature Hartree-Fock equations with an s-wave scattering-length interaction. The threshold temperature for BEC differs only slightly from the value for an ideal gas. However, the nature of the condensate is strongly dependent on the scattering length.
By numerically solving the single-particle stationary Schrödinger equation and the Gross-Pitaevskii equation with mean-field interactions at zero temperature, the ground state properties of the rotating spin-orbital-angular-momentum coupled Bose-Einstein condensates in a harmonic trapping potential are investigated in this work. The results show that the rotation lifts the double degeneracy of the single-particle energy spectrum in the angular momentum space, and leads to the vortex state. The angular momentum of the vortex depends on the rotating frequency, the intensity of the laser beam, and the spin-orbital-angular-momentum coupling. In particular, if the rotating frequency is below a critical value, the angular momentum of the ground state vortex remains unaffected by the rotating frequency. When the rotating frequency exceeds the critical value, the angular momentum of the ground state vortex will increase with the rotating frequency increasing. By assuming that the system is confined in a ring trap, the expression of the single-particle energy spectrum in the angular momentum space can be obtained, which clarifies how the rotation frequency affects the angular momentum of the ground state. In the presence of atomic interactions, similar phenomena can also be observed in the mean-field ground state at zero temperature.
A rigorous time independent Hamiltonian for rotating atomic traps is discussed. The steady states carry a mass current and thereby an angular momentum. It is shown that the rotation positions the atoms away from the rotation axis (after taking both the time and quantum mechanical averages) as in a conventional centrifuge. Some assert that the rotation for Bose condensates cause the atoms to move towards the rotation axis; i.e. act oppositely to fluids in a centrifuge. The opposing physical pictures are reminiscent of the difference between the rotational motion views of Newton and Cassini.
Nonadiabatic motion of Bose-Einstein condensates of rubidium atoms arising from the dynamical nature of a time-orbiting-potential (TOP) trap was observed experimentally. The orbital micromotion of the condensate in velocity space at the frequency of the rotating bias field of the TOP was detected by a time-of-flight method. A dependence of the equilibrium position of the atoms on the sense of rotation of the bias field was observed. We have compared our experimental findings with numerical simulations. The nonadiabatic following of the atomic spin in the trap rotating magnetic field produces geometric forces acting on the trapped atoms.