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arXiv:cond-mat/0202369 · Physical Review A

Dynamics of a Bose-Einstein condensate at finite temperature in an atom-optical coherence filter

Francesca Ferlaino, P. Maddaloni, Sven Burger, F. S. Cataliotti, C. Fort, Michele Modugno, M. Inguscio

Published Jul 22, 2002• 37 citations
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Abstract

The macroscopic coherent tunneling through the barriers of a periodic potential is used as an atom-optical filter to separate the center of mass of the condensate and the thermal components of a ${}^{87}\mathrm{Rb}$ mixed cloud. We condense in the combined potential of a laser standing wave superimposed on the axis of a cigar-shaped magnetic trap and induce condensate dipole oscillation in the presence of a static thermal component. The oscillation is damped due to the interaction with the thermal fraction and we investigate the role played by the periodic potential in the damping process.

DOI
10.1103/physreva.66.011604

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•Jan 1, 2001•1 citation
The macroscopic coherent tunneling through the barriers of a periodic potential is used as an atom-optical filter to separate the center of mass of the condensate and the thermal components of a 87Rb{}^{87}\mathrm{Rb}87Rb mixed cloud. We condense in the combined potential of a laser standing wave superimposed on the axis of a cigar-shaped magnetic trap and induce condensate dipole oscillation in the presence of a static thermal component. The oscillation is damped due to the interaction with the thermal fraction and we investigate the role played by the periodic potential in the damping process.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
We create Bose-Einstein condensates of 87Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the Bose-Einstein condensate and accounts for the main features of the observed behavior.
We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
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