Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses

Details Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses

2003-05-19

arxiv.org/abs/cond-mat/0305441v2

Phys. Rev. A 69, 033603 (2004)

Physics

Condensed Matter

Soft Condensed Matter

14 pages, 7 figures. Phys. Rev. A in press

Scientific paper

10.1103/PhysRevA.69.033603

It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic cooling of fermions by bosons. Both a quantum Boltzmann equation and a quantum Boltzmann \emph{master} equation are used to study the evolution of the occupation number distribution. It is shown that, in the thermodynamic limit, the Fermi gas cools to a minimal temperature $k_{{\rm B}}T/\mu\propto(\gamma_{{\rm loss}}/\gamma_{{\rm coll}})^{0.44}$, where $\gamma_{{\rm loss}}$ is a constant loss rate, $\gamma_{{\rm coll}}$ is the bare fermion--boson collision rate not including the reduction due to Fermi statistics, and $\mu\sim k_{{\rm B}}T_{{\rm F}}$ is the chemical potential. It is demonstrated that, beyond the thermodynamic limit, the discrete nature of the momentum spectrum of the system can block cooling. The unusual non-thermal nature of the number distribution is illustrated from several points of view: the Fermi surface is distorted, and in the region of zero momentum the number distribution can descend to values significantly less than unity. Our model explicitly depends on a constant evaporation rate, the value of which can strongly affect the minimum temperature.

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