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arXiv:cond-mat/0204129 · Physical Review A

Impurity scattering in a Bose-Einstein condensate at finite temperature

A. Montina

Published Aug 26, 2002• 10 citations
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Abstract

We consider the effects of finite temperature on the scattering of impurity atoms in a Bose-Einstein condensate, showing that the scattering rate is enhanced by the thermal atoms. Collisions can increase or decrease the impurity energy. Below the Landau velocity only the first process occurs, i.e., the collisions cool the condensate. Above the critical velocity the dissipative collisions prevail over the cooling ones for sufficiently low temperatures. These considerations are applied to a recent experiment.

DOI
10.1103/physreva.66.023609

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We consider the effects of finite temperature on the scattering of impurity atoms in a Bose-Einstein condensate, showing that the scattering rate is enhanced by the thermal atoms. Collisions can increase or decrease the impurity energy. Below the Landau velocity only the first process occurs, i.e., the collisions cool the condensate. Above the critical velocity the dissipative collisions prevail over the cooling ones for sufficiently low temperatures. These considerations are applied to a recent experiment.
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.
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.
Impurity atoms propagating at variable velocities through a trapped Bose-Einstein condensate were produced using a stimulated Raman transition. The redistribution of momentum by collisions between the impurity atoms and the stationary condensate was observed in a time-of-flight analysis. The collisional cross section was dramatically reduced when the impurity velocity was reduced below the condensate speed of sound, in agreement with the Landau criterion for superfluidity. For large numbers of impurity atoms, we observed an enhancement of atomic collisions due to bosonic stimulation. This enhancement is analogous to optical super-radiance.
We discuss the cooling dynamics of heavy impurity atoms in a Bose-Einstein condensate (BEC) by emission of Cherenkov phonons from scattering with the condensate. In a weakly interacting low-temperature condensate, different scattering processes result in a separation of time scales of the thermalization dynamics. Prethermalized states are formed with distinct regions of impurity momenta determined by the mass ratio of impurity and BEC atoms. This can be employed to detect the mass renormalization of the impurity upon the formation of a polaron and paves the way to preparing nonequilibrium impurity-momentum distributions.
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The motion of single quantum particle through Bose-Einstein condensate (BEC) is considered within perturbation theory with respect to the particle-BEC interaction. The Hamiltonian of BEC is diagonalized by means of Bogoliubov's method. The process of dissipation due to the creation of excitation in BEC is analyzed and the dissipation rate is calculated in the lowest order of perturbation theory. The Landau's criterion for energy dissipation in BEC is then recovered. The energy spectrum of the impurity particle due to the interaction with BEC and its effective mass are evaluated.