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arXiv:cond-mat/0212593 · Journal of the Physical Society of Japan

Stability of Magnetically Trapped Bose–Einstein Condensates

Yuki Kawaguchi, Tetsuo Ohmi

Published May 15, 2003• 0 citations
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Abstract

According to the adiabatic approximation atoms moving in a magnetic trap keep their magnetic states. We investigate the validity of this approximation for quantum condensates, where a change of field's direction generates effective interactions between hyperfine angular momentum states. Condensates in general traps are found to be stable because they are confined in the vicinity of the trap center. A decay of a condensate is observable in a trap with extremely large field gradient.

DOI
10.1143/jpsj.72.1118

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According to the adiabatic approximation atoms moving in a magnetic trap keep their magnetic states. We investigate the validity of this approximation for quantum condensates, where a change of field's direction generates effective interactions between hyperfine angular momentum states. Condensates in general traps are found to be stable because they are confined in the vicinity of the trap center. A decay of a condensate is observable in a trap with extremely large field gradient.
The rotational properties of Bose–Einstein condensates in a synthetic magnetic field are studied by numerically solving the Gross–Pitaevskii equation and comparing the results to those of condensates confined in a rotating trap. It appears to be more difficult to add a large angular momentum to condensates spun up by the synthetic magnetic field than by the rotating trap. However, strengthening the repulsive interaction between atoms is an effective and realizable route to overcoming this problem and can at least generate vortex-lattice-like structures. In addition, the validity of the Feynman rule for condensates in the synthetic magnetic field is verified.
For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this Letter we investigate the relationship between the values of the sum or difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.
We demonstrate that atoms in magnetically insensitive hyperfine states (m=0) can be trapped efficiently by a Bose-Einstein Condensate of the same atomic species occupying a different hyperfine state. The latter is trapped magnetically. Hyperfine state changing collisions, and therefore loss of the trapped (m=0) atoms, are shown to be strongly inhibited in case of a low density of the confined atomic cloud. We monitor the transition from a 'soft' to a 'hard' effective potential by studying the backaction of the trapped (m=0) atoms onto the condensate which provides their confinement. The controlled outcoupling of the trapped atoms by shaping the condensate's wavefunction is explored. We observe a pulsed emission of atoms from the trapping region reminiscent of an atom laser.
We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of a coherent atom-atom interaction. We find that stable vortices can be supported and vortex stability can be controlled by changing the interparticle interaction strength. At unstable regimes, a vortex will spontaneously disintegrate into states with different angular momenta even without external perturbations, with the lifetime determined by its imaginary excitation frequencies.
We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.
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.