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arXiv:cond-mat/0205474 · Physical Review A

Thermalization of an impurity cloud in a Bose-Einstein condensate

A. Montina

Published May 28, 2003• 4 citations
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Abstract

We study the thermalization dynamics of an impurity cloud inside a Bose-Einstein condensate at finite temperature, introducing a suitable Boltzmann equation. Some values of the temperature and of the initial impurity energy are considered. We find that below the Landau critical velocity, the stimulation effects reduce the depletion rate of the macroscopic initial impurity population. For appropriate parameters, the collisions cool the condensate. The maximum cooling per impurity atom is obtained with multiple collisions. A cooling method is outlined.

DOI
10.1103/physreva.67.053614

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We study the thermalization dynamics of an impurity cloud inside a Bose-Einstein condensate at finite temperature, introducing a suitable Boltzmann equation. Some values of the temperature and of the initial impurity energy are considered. We find that below the Landau critical velocity, the stimulation effects reduce the depletion rate of the macroscopic initial impurity population. For appropriate parameters, the collisions cool the condensate. The maximum cooling per impurity atom is obtained with multiple collisions. A cooling method is outlined.
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We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the temperature of the gas is very low compared to the Bose-Einstein condensation critical temperature. In particular, our system couples the density of the condensate from a Gross-Pitaevskii type equation to the kinetic equation through the dispersion relation in the kinetic model and the corresponding transition probability rate from pre to post collision momentum states. We rigorously show the following three properties (1) the well-posedness of the Cauchy problem for the system in the case of a radially symmetric initial configuration, (2) find qualitative properties of the solution such as instantaneous creation of exponential tails and, (3) prove the uniform condensate stability related to the initial mass ratio between condensed particles and quasi-particles. The stability result from (3) leads to global in time existence of the initial value problem for the quantum Boltzmann-Condensation system.
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In this thesis we measure and calculate the enhanced scattering rate for both cold thermal clouds and Bose-Einstein condensates. For Bose-Einstein condensates we find that the scattering rate is enhanced, due to the large densities and a temperature just below the critical temperature. The enhancement under typical experimental conditions with a Bose-Einstein condensate is up to a factor 3, while there is no enhancement for thermal clouds. The scattering rate influences both the number of particles and the average energy per particle. For both the energy and the number of particles a theoretical prediction is compared with an experimental result. For the number of particles in a cloud both with and without a Bose-Einstein condensate and the energy in a cloud without a Bose-Einstein condensate, we find that theory and experiment agree within their uncertainties. In the case of the energy per particle in a cloud with a Bose-Einstein condensate, we included a cooling effect for condensed atoms that become thermal, however our experimental results are not sufficient to confirm this theory.