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arXiv:cond-mat/0309010 · Physical Review Letters

Weakly Bound Dimers of Fermionic Atoms

Dmitry S. Petrov, Ch Salomon, Gora V. Shlyapnikov

Published Aug 24, 2004• 642 citations
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Abstract

We discuss the behavior of weakly bound bosonic dimers formed in a two-component cold Fermi gas at a large positive scattering length a for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing a. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.

DOI
10.1103/physrevlett.93.090404

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We discuss the behavior of weakly bound bosonic dimers formed in a two-component cold Fermi gas at a large positive scattering length a for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing a. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.
We consider weakly bound diatomic molecules (dimers) formed in a two-component atomic Fermi gas with a large positive scattering length for the interspecies interaction. We develop a theoretical approach for calculating atom-dimer and dimer-dimer elastic scattering and for analyzing the inelastic collisional relaxation of the molecules into deep bound states. This approach is based on the single-channel zero-range approximation, and we find that it is applicable in the vicinity of a wide two-body Feshbach resonance. Our results draw prospects for various interesting manipulations of weakly bound dimers of fermionic atoms.
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We discuss a major theoretical generalization of existing techniques for handling the three-body problem that accurately describes the interactions among four fermionic atoms. Application to a two-component Fermi gas accurately determines dimer-dimer scattering parameters at finite energies and can give deeper insight into the corresponding many-body phenomena. To account for finite temperature effects, we calculate the energy-dependent complex dimer-dimer scattering length, which includes contributions from elastic and inelastic collisions. Our results indicate that strong finite-energy effects and dimer dissociation are crucial for understanding the physics in the strongly interacting regime for typical experimental conditions. While our results for dimer-dimer relaxation are consistent with experiment, they confirm only partially a previously published theoretical result.
We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.