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arXiv:cond-mat/0308384 · Physical Review A

Degenerate atom-molecule mixture in a cold Fermi gas

S. J. J. M. F. Kokkelmans, Georgy V. Shlyapnikov, Ch Salomon

Published Mar 23, 2004• 31 citations
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Abstract

We show that the atom-molecule mixture formed in a degenerate atomic Fermi gas with interspecies repulsion near a Feshbach resonance constitutes a peculiar system where the atomic component is almost nondegenerate but quantum degeneracy of molecules is important. We develop a thermodynamic approach for studying this mixture, explain experimental observations, and predict optimal conditions for achieving molecular Bose-Einstein condensation.

DOI
10.1103/physreva.69.031602

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We show that the atom-molecule mixture formed in a degenerate atomic Fermi gas with interspecies repulsion near a Feshbach resonance constitutes a peculiar system where the atomic component is almost nondegenerate but quantum degeneracy of molecules is important. We develop a thermodynamic approach for studying this mixture, explain experimental observations, and predict optimal conditions for achieving molecular Bose-Einstein condensation.
The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature T=0.1TF0T=0.1{T}_{F}^{0}T=0.1TF0​, where TF0{T}_{F}^{0}TF0​ is the noninteracting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T\ensuremath{\lesssim}0.01{T}_{F}^{0}$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules.
We test a non equilibrium approach to study the behavior of a Bose-Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations of motion for, the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that bosonic depletion plays in the Bose-Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose-Fermi mixtures is driven by three point and higher order correlations in the gas, unlike any other resonant system studied in the context of ultra-cold atomic physics.
We report on the formation of a stable quantum degenerate mixture of fermionic ^{6}Li and bosonic ^{133}Cs in an optical trap by sympathetic cooling near an interspecies Feshbach resonance. New regimes of quantum degenerate Bose-Fermi mixtures are identified. With moderate attractive interspecies interactions, we show that a degenerate Fermi gas of Li can be fully confined in a Cs Bose-Einstein condensate without external potentials. For stronger attraction where mean-field collapse is expected, no such instability is observed. Potential mechanisms to explain this phenomenon are discussed.
Recent experiments performed with fermionic /sup 6/Li and /sup 40/K atoms, which possess both Feshbach resonances at convenient magnetic fields are discussed. When /sup 40/K is mixed with a Bose-Einstein condensate of /sup 87/Rb, for sufficient atom numbers of both species, a collapse of the Fermi gas is observed. This is the result of the strong interspecies attractive interaction which overcomes the Fermi pressure in the quantum degenerate regime. As for the case of phonon-induced interaction between electrons in superconductors, it is predicted that the boson-fermion attractive interaction favors Cooper pairing of fermions when prepared in a mixture of two states.
Experimental realization of a quantum degenerate gas of molecules would provide access to a wide range of phenomena in molecular and quantum sciences. However, the very complexity that makes ultracold molecules so enticing has made reaching degeneracy an outstanding experimental challenge over the past decade. We now report the production of a degenerate Fermi gas of ultracold polar molecules of potassium-rubidium. Through coherent adiabatic association in a deeply degenerate mixture of a rubidium Bose-Einstein condensate and a potassium Fermi gas, we produce molecules at temperatures below 0.3 times the Fermi temperature. We explore the properties of this reactive gas and demonstrate how degeneracy suppresses chemical reactions, making a long-lived degenerate gas of polar molecules a reality.
We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.