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

Abstract

It has been suggested by Timmermans [Phys. Rev. Lett. 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 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 kBT /µ ∝ (γ loss /γ coll ) 0.44 , where γ loss is a constant loss rate, γ coll is the bare fermion-boson collision rate not including the reduction due to Fermi statistics, and µ ∼ kBTF 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 nonthermal 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.

Thermodynamics of Ultracold Fermi Gases

“…As soon as the gas enters the Fermi degeneracy regime, the atom number decreases more sharply when the trap depth is lowered (see Fig.2.12). This is expected as Pauli blocking plays an increasing role [107]. …”

All-Optical Production of Quantum Degeneracy and Molecular Bose-Einstein Condensation of 6 Li

“…In our case, as the trap laser power is further decreased we don't see the apparent decrease of the temperature and on the contrary we see a little increase of the temperature of the gas. The mechanism of such the heating is not so clear currently and one possible reason is due to the losses of Fermions at the very shallow dipole trap depth [12].…”

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

“…This has been sufficient to reach the Mott insulator regime as discussed above. When entering the quantum degenerate regime, the thermalization slows down owing to the Pauli blocking of collisions and to inelastic processes, which lead to hole heating [157] and make cooling beyond this value hardly possible. The gas is subsequently loaded into the optical lattice potential adiabatically, hence conserving the total entropy.…”