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arXiv:cond-mat/9909014 · Physical Review A

Limits to sympathetic evaporative cooling of a two-component Fermi gas

Michael Crescimanno, C. G. Kaoy, R. Peterson

Published Apr 5, 2000• 10 citations
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Abstract

We find a limit cycle in a quasiequilibrium model of evaporative cooling of a two-component trapped fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively $\ensuremath{\beta}\ensuremath{\mu}\ensuremath{\sim}O(1).$ We speculate that one may be able to cool an atomic Fermi gas further by photoassociating dimers near the bottom of the Fermi sea.

DOI
10.1103/physreva.61.053602

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We find a limit cycle in a quasiequilibrium model of evaporative cooling of a two-component trapped fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively \ensuremathβ\ensuremathμ\ensuremath∼O(1).\ensuremath{\beta}\ensuremath{\mu}\ensuremath{\sim}O(1).\ensuremathβ\ensuremathμ\ensuremath∼O(1). We speculate that one may be able to cool an atomic Fermi gas further by photoassociating dimers near the bottom of the Fermi sea.
The evaporative cooling of a two-component mixture of trapped atomic fermions into quantum degeneracy is investigated using the semiclassical Boltzmann equation for fermions. The influence of Fermi blocking for temperatures well below the Fermi temperature is discussed. Comparison between collisional and relaxation rates for a Fermi degenerate gas are made, and the similarities and differences between the cooling kinetics of the Fermi gas mixture and a mixture of classical gases is investigated, and discussed using a simple model. The latter also serves to clarify the processes which terminate the cooling in the quantum degenerate regime. Finally, a brief discussion of mean-field effects is given.
An evaporative cooling strategy that uses a two-component Fermi gas was employed to cool a magnetically trapped gas of 7 x 10(5) (40)K atoms to 0.5 of the Fermi temperature T(F). In this temperature regime, where the state occupation at the lowest energies has increased from essentially zero at high temperatures to nearly 60 percent, quantum degeneracy was observed as a barrier to evaporative cooling and as a modification of the thermodynamics. Measurements of the momentum distribution and the total energy of the confined Fermi gas directly revealed the quantum statistics.
The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below Tc{T}_{c}Tc​ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below Tc{T}_{c}Tc​ is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve T=0T=0T=0 and all of the particles must be evaporated.
Sympathetic cooling of an atomic Fermi gas by a Bose gas is studied by solution of the coupled quantum Boltzmann equations for the confined gas mixture. Results for equilibrium temperatures and relaxation dynamics are presented, and some simple models are developed. Our study illustrates that a combination of sympathetic and forced evaporative cooling enables the Fermi gas to be cooled to the degenerate regime where quantum statistics and mean-field effects are important. The influence of mean-field effects on the equilibrium spatial distributions is discussed qualitatively.
We measure the scaling laws for the number of atoms and the cloud size as a function of trap depth for evaporative cooling of a unitary Fermi gas in an optical trap. A unitary Fermi gas comprises a trapped mixture of atoms in two hyperfine states which is tuned to a collisional (Feshbach) resonance using a bias magnetic field. Near resonance, the zero energy s-wave scattering length diverges, and the s-wave scattering cross-section is limited by unitarity to be 4π/ k 2 , where k is the relative wavevector of the colliding particles. In this case, the collision cross-section for evaporation scales inversely with the trap depth, enabling runaway evaporation under certain conditions. We demonstrate high evaporation efficiency, which is achieved by maintaining a high ratio η of trap depth to thermal energy as the trap depth is lowered. We derive and demonstrate a trap lowering curve which maintains η constant for a unitary gas. This evaporation curve yields a quantum degenerate sample from a classical gas in a fraction of a second, with only a factor of three loss in atom number.
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.