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Journal de Physique IV (Proceedings)

Two experiments with Bose-Einstein condensates in magnetic micro traps

Claus Zimmermann, Sebastian Kraft, Andreas Günther, Herwig Ott, József Fortágh

Published Oct 1, 2004• 3 citations
Publisher

Abstract

\nBose-Einstein condensates are trapped in elongated magnetic traps made from\nmicro fabricated current conductors. By bringing the atoms close to the\nsurface of the substrate a periodic anomalous magnetic field is observed. It\nis oriented parallel to the conductor and depends on its current. In a second\nexperiment we study the motion of a condensate in an anharmonic wave guide.\nStrong collective excitations are observed which can be very well described by\ntheory. Simulations predict pronounced chaotic motion within the parameter\nrange of the experiment.\n

DOI
10.1051/jp4:2004116017

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\nBose-Einstein condensates are trapped in elongated magnetic traps made from\nmicro fabricated current conductors. By bringing the atoms close to the\nsurface of the substrate a periodic anomalous magnetic field is observed. It\nis oriented parallel to the conductor and depends on its current. In a second\nexperiment we study the motion of a condensate in an anharmonic wave guide.\nStrong collective excitations are observed which can be very well described by\ntheory. Simulations predict pronounced chaotic motion within the parameter\nrange of the experiment.\n
We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.
Collective excitations of a dilute Bose condensate have been observed. These excitations are analogous to phonons in superfluid helium. Bose condensates were created by evaporatively cooling magnetically trapped sodium atoms. Excitations were induced by a modulation of the trapping potential, and detected as shape oscillations in the freely expanding condensates. The frequencies of the lowest modes agreed well with theoretical predictions based on mean-field theory. Before the onset of Bose-Einstein condensation, we observed sound waves in a dense ultracold gas.
The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.
We theoretically study binary Bose-Einstein condensates trapped in a single-well harmonic potential to probe the dynamics of collective atomic motion. The idea is to choose tunable scattering lengths through Feshbach resonances such that the ground-state wave function for two types of the condensates are spatially immiscible where one of the condensates, located at the center of the potential trap, can be effectively treated as a potential barrier between bilateral condensates of the second type of atoms. In the case of small wave-function overlap between bilateral condensates, one can parametrize their spatial part of the wave functions in the two-mode approximation together with the time-dependent population imbalance zzz and the phase difference $\ensuremath{\phi}$ between two wave functions. The condensate in the middle can be approximated by a Gaussian wave function with the displacement of the condensate center $\ensuremath{\xi}$. As driven by the time-dependent displacement of the central condensate, we find the Josephson oscillations of the collective atomic motion between bilateral condensates as well as their anharmonic generalization of macroscopic self-trapping effects. In addition, with the increase in the wave-function overlap of bilateral condensates by properly choosing tunable atomic scattering lengths, the chaotic oscillations are found if the system departs from the state of a fixed point. The Melnikov approach with a homoclinic solution of the derived $z, \ensuremath{\phi}$, and $\ensuremath{\xi}$ equations can successfully justify the existence of chaos. All results are consistent with the numerical solutions of the full time-dependent Gross-Pitaevskii equations.