Sympathetic cooling of trapped fermions by bosons in the presence of particle losses

¹ Istituto Nazionale per la Fisica della Materia, BEC-INFM Trento I-38050 Povo (TN), Italy
² Centrum Fizyki Teoretycznej, Polska Akademia Nauk - 02-668 Warsaw, Poland
³ Institut für Theoretische Physik III, Universität Stuttgart Pfaffenwaldring 57 V, D-70550 Stuttgart, Germany
⁴ Institut für Theoretische Physik, Universität Hannover D-30167 Hannover, Germany

Received: 26 January 2005
Accepted: 13 April 2005

Abstract

We study the sympathetic cooling of a trapped Fermi gas interacting with an ideal Bose gas below the critical temperature of the Bose-Einstein condensation. We derive the quantum master equation, which describes the dynamics of the fermionic component, and postulating the thermal distribution for both gases we calculate analytically the rate at which fermions are cooled by the bosonic atoms. The particle losses constitute an important source of heating of the degenerate Fermi gas. We evaluate the rate of loss-induced heating and derive analytical results for the final temperature of fermions, which is limited in the presence of particle losses.