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arXiv:cond-mat/0206582 · Physical Review Letters

Accidental Suppression of Landau Damping of the Transverse Breathing Mode in Elongated Bose-Einstein Condensates

B. Jackson, E. Zaremba

Published Sep 19, 2002• 42 citations
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Abstract

We study transverse radial oscillations of an elongated Bose-Einstein condensate using finite-temperature simulations, in the context of a recent experiment at ENS [F. Chevy, Phys. Rev. Lett. 88, 250402 (2002)]]. The mode observed experimentally corresponds to an in-phase collective oscillation of both the condensate and the thermal cloud. Our simulations are in excellent agreement with experiment, accounting for the very small damping rates observed. In contrast to other condensate modes, interatomic collisions are found to be the dominant damping mechanism in this case.

DOI
10.1103/physrevlett.89.150402

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We study transverse radial oscillations of an elongated Bose-Einstein condensate using finite-temperature simulations, in the context of a recent experiment at ENS [F. Chevy, Phys. Rev. Lett. 88, 250402 (2002)]]. The mode observed experimentally corresponds to an in-phase collective oscillation of both the condensate and the thermal cloud. Our simulations are in excellent agreement with experiment, accounting for the very small damping rates observed. In contrast to other condensate modes, interatomic collisions are found to be the dominant damping mechanism in this case.
We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.
We discuss the collective modes in a harmonically trapped, highly-elongated Bose condensed gas. The transverse breathing mode exhibits a number of interesting features, such as the insensitivity of the condensate mode frequency to the interaction strength, and the closeness of the frequency to that of the non-condensed thermal cloud in the collisionless limit. Using finite temperature simulations, we show that these features are responsible for the very small damping rate observed experimentally. Our results for the temperature dependence of the damping rate and frequency shift are in excellent agreement with experiment. We also demonstrate that the unusually small damping rate does not arise for the m=2m=2m=2 mode or for more isotropic trap potentials, suggesting further possible experimental tests of our theory.
We study experimentally the transverse monopole mode of an elongated rubidium condensate. Because of the scaling invariance of the nonlinear Schr\"odinger (Gross-Pitaevskii) equation, the oscillation is monochromatic and sinusoidal at short times, even under strong excitation. For ultralow temperatures, the quality factor $Q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\omega}}_{0}/{\ensuremath{\gamma}}_{0}$ can exceed 2000, where ${\ensuremath{\omega}}_{0}$ and ${\ensuremath{\gamma}}_{0}$ are the mode angular frequency and damping rate. This value is much larger than any previously reported for other eigenmodes of a condensate. We also present the temperature variation of ${\ensuremath{\omega}}_{0}$ and ${\ensuremath{\gamma}}_{0}$.
We have measured the damped motion of a trapped Bose-Einstein condensate, oscillating with respect to a thermal cloud.The cigar-shaped trapping potential provides enough transverse confinement that the dynamics of the system are intermediate between three-dimensional and onedimensional.We find that the scaling of the damping rate with temperature is consistent with Landau theory, but that the damping rate for axial oscillations at a given temperature is consistently smaller than expected for a three-dimensional gas.We attribute this to the suppressed density of states for low-energy transverse excitations (essential excitations for axial Landau damping), which results from the quantization of the radial motion.
The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.
The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified. © 2007 The American Physical Society.