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arXiv:cond-mat/9907222 · Physical Review A

Evaporative cooling of trapped fermionic atoms

W. Geist, A. Idrizbegovic, M. Marinescu, T. A. B. Kennedy, Li You

Published Dec 13, 1999• 13 citations
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Abstract

We propose an efficient mechanism for the evaporative cooling of trapped fermions directly into quantum degeneracy. Our idea is based on an electric field induced elastic interaction between trapped atoms in spin symmetric states. We discuss some novel general features of fermionic evaporative cooling and present numerical studies demonstrating the feasibility for the cooling of alkali-metal fermionic species ${}^{6}\mathrm{Li},$ ${}^{40}\mathrm{K},$ and ${}^{82,84,86}\mathrm{Rb}.$ We also discuss the sympathetic cooling of fermionic hyperfine spin mixtures, including the effects of anisotropic interactions.

DOI
10.1103/physreva.61.013406

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We propose an efficient mechanism for the evaporative cooling of trapped fermions directly into quantum degeneracy. Our idea is based on an electric field induced elastic interaction between trapped atoms in spin symmetric states. We discuss some novel general features of fermionic evaporative cooling and present numerical studies demonstrating the feasibility for the cooling of alkali-metal fermionic species 6Li,{}^{6}\mathrm{Li},6Li, 40K,{}^{40}\mathrm{K},40K, and 82,84,86Rb.{}^{82,84,86}\mathrm{Rb}.82,84,86Rb. We also discuss the sympathetic cooling of fermionic hyperfine spin mixtures, including the effects of anisotropic interactions.
We investigate sympathetic cooling fermions 40 K by evaporatively cooling bosonic 87 Rb atoms in a magnetic trap with microwave and radio frequency induced evaporations in detail. The mixture of bosonic and fermionic atoms is prepared in their polarized spin states | F = 9/2, m F = 9/2〉 for 40 K and | F = 2, m F = 2〉 for 87 Rb, which is trapped in Quadrupole—Ioffe—Configuration trap. Comparing microwave with radio frequency evaporatively cooling bosonic 87 Rb atoms with sympathetically cooling Fermi gas 40 K, we find that the presence of rubidium atoms in the |2, 1〉 Zeeman states, which are generated in the evaporative process, gives rise to a significant loss of 40 K due to inelastic collisions. Thus, the rubidium atoms populated in the |2, 1〉 Zeeman states should be removed in order to effectively perform sympathetically cooling 40 K with the evaporatively cooled 87 Rb atoms.
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.
A dual species electromagnetic trap has been developed for the purpose of studying quantum degeneracy and the BCS phase transition in 6Li. Since the symmetry requirements of quantum mechanics forbid collisions between identical ultra-cold fermions, the standard method of cooling atoms in a magnetic trap, evaporative cooling, will not work. To circumvent this obstacle we evaporatively cool 7Li, the boson, and allow sympathetic collisions between the bosons and fermions to cool the 6Li to quantum degeneracy. This thesis will cover the experimental details pertaining to capturing, cooling, and probing a mixture of atomic 7Li and 6Li.
Summary form only given. The last five years has seen an explosive growth in activity in the field of quantum degenerate gases, and there are now many realizations of Bose-Einstein condensation (BEC) of trapped atomic gasses. However, only one experiment has produced a quantum degenerate Fermi gas. The ultimate goal of the experiment discussed here is to achieve a BCS phase transition in a trapped gas of fermionic /sup 6/Li atoms. This requires a phase-space density that is much higher than that needed for BEC, as the temperature must be made much less than the Fermi temperature.BEC in trapped gases has only been achieved using forced evaporative cooling. Since this method depends on elastic collisions, however, it fails for an ultracold Fermi gas, as the Pauli principle forbids s-wave collisions between identical fermions. To circumvent this obstacle, we simultaneously trap a /sup 7/Li-/sup 6/Li mixture, and use rf-induced evaporation to cool /sup 7/Li. /sup 6/Li is then cooled via thermalizing elastic collisions with the /sup 7/Li. The clover-leaf-type magnetic trap is loaded from a two-species magneto-optical trap (MOT).
We discuss cooling efficiency for different-species Fermi-Bose mixtures in magnetic traps. A better heat capacity matching between the two atomic species is achieved by a proper choice of the Bose cooler and the magnetically trappable hyperfine states of the mixture. When a partial spatial overlap between the two species is also taken into account, the deepest Fermi degeneracy is obtained for an optimal value of the trapping frequency ratio between the two species. This can be achieved by assisting the magnetic trap with a deconfining light beam, as shown in the case of fermionic 6Li^{6}\mathrm{Li}6Li mixed with 23Na^{23}\mathrm{Na}23Na, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs, with optimal conditions found for the not yet explored $^{6}\mathrm{Li}\penalty1000-\hskip0pt^{87}\mathrm{Rb}$ mixture.
The standard approach for generating deeply degenerate quantum gases is evaporative or sympathetic cooling in a harmonic trap, after which the gas has reached its minimum entropy. All subsequent state transformations rely on adiabatic changes of a closed system, and coupling to the environment or non-adiabatic processes monotonically increase the entropy. Here, we demonstrate that this experimental paradigm can be bypassed by utilizing species-selective trapping with a low-dissipation optical tune-out trap in a dual-species mixture. We successfully reduce the entropy of a two-component fermionic quantum gas via isothermal compression within a bosonic bath, reaching deep quantum degeneracy of T/TF=0.024+0.007T/T_F = 0.024^{+0.007}T/TF​=0.024+0.007, with TFT_FTF​ the Fermi temperature. By characterizing the cross-dimensional relaxation and thermalization, we demonstrate that cooling light fermions with heavy bosons remains efficient and fast, even deep in the degenerate regime, where the thermalization time is found to be independent of T/TFT/T_FT/TF​. Our results pave the way for direct cooling within optical lattices, box traps, or other complex potentials, thereby eliminating the reliance on adiabatic state transformations to reach strongly interacting many-body regimes.