Thermal dephasing and the echo effect in a confined Bose-Einstein condensate

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Abstract
Thermal fluctuations of the normal component induce dephasing—reversible damping of the low-energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where the Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence. It is weakly amplitude dependent, and is sensitive to the total number of atoms in the trap. The value of the rate belongs to the range of the damping rates observed by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)]. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of the Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo for the isotropic trap are calculated in the weak echo limit. Results of the numerical simulations of the echo are also presented.