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arXiv:1009.5565 · Physical Review A

Manipulation of a Bose-Einstein condensate by a time-averaged orbiting potential using phase jumps of the rotating field

Paul W. Cleary, Tom W. Hijmans, Jook T. M. Walraven

Published Dec 30, 2010• 8 citations
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Abstract

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.

DOI
10.1103/physreva.82.063635

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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.
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.
We have observed Bose-Einstein condensation of large numbers of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in a magnetic time-averaged orbiting potential (TOP) trap. Over $1.5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ atoms are captured in the trap and evaporatively cooled to produce condensates containing up to $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms. We discuss special considerations relating to the production of large Bose-Einstein condensates in a TOP trap, and present measurements of the condensate fraction for this case.
We present a detailed theoretical analysis of micromotion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time-dependent behavior of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular center of mass motion in the laboratory frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.
We report on the realization of a stiff magnetic trap with independently adjustable trap frequencies, ω z and ω r , in the axial and radial directions, respectively. This has been achieved by applying an axial modulation to a time-averaged orbiting potential (TOP) trap. The frequency ratio of the trap, ω z /ω r , can be decreased continuously from the original TOP trap value of 2.83 down to 1.6. We have transferred a Bose-Einstein condensate (BEC) into this trap and obtained very good agreement between its observed anisotropic expansion and the hydrodynamic predictions. Our method can be extended to obtain a spherical trapping potential, which has a geometry of particular theoretical interest.
We present an experimental method for rotating a Bose-Einstein condensate trapped in an axisymmetric magnetic potential. This method is based on the anharmonicity of the trapping potential, which couples the center-of-mass motion of the condensate to its internal motion. By circularly shaking the trapping potential, we generate a circular center-of-mass motion of the condensate around the trap center. The circulating condensate undergoes rotating shape deformation and eventually relaxes into a rotating condensate with a vortex lattice. We discuss the vortex nucleation mechanism and, in particular, the role of the thermal cloud in the relaxation process. Finally, we investigate the dependence of the vortex nucleation on the elliptical polarization of the trap shaking. The response of the condensate is asymmetric with respect to the sign of the shaking polarization, demonstrating the gauge-field effect due to the spin texture of the condensate in the magnetic potential.