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

Abstract

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 $k_{\mathrm{B}}T/\mu \propto ({\gamma }_{\mathrm{loss}}/{\gamma }_{\mathrm{coll}}{)}^{0.44}$, where ${\gamma }_{\mathrm{loss}}$ is a constant loss rate, ${\gamma }_{\mathrm{coll}}$ is the bare fermion--boson collision rate not including the reduction due to Fermi statistics, and $\mu \sim k_{\mathrm{B}}{T}_{\mathrm{F}}$ 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.

arXiv comment14 pages, 7 figures. Phys. Rev. A in press

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