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arXiv:cond-mat/0308318 · Physical Review Letters

Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas

Kevin E. Strecker, Guthrie B. Partridge, Randall G. Hulet

Published Aug 22, 2003• 545 citations
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Abstract

We have converted an ultracold Fermi gas of $^{6}\mathrm{L}\mathrm{i}$ atoms into an ultracold gas of $^{6}\mathrm{L}\mathrm{i}_{2}$ molecules by adiabatic passage through a Feshbach resonance. Approximately $1.5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ molecules in the least-bound, $v=38$, vibrational level of the ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.

DOI
10.1103/physrevlett.91.080406

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We have converted an ultracold Fermi gas of 6Li^{6}\mathrm{L}\mathrm{i}6Li atoms into an ultracold gas of 6Li2^{6}\mathrm{L}\mathrm{i}_{2}6Li2​ molecules by adiabatic passage through a Feshbach resonance. Approximately 1.5\ifmmode×\else\texttimes\fi1051.5\ifmmode\times\else\texttimes\fi{}{10}^{5}1.5\ifmmode×\else\texttimes\fi105 molecules in the least-bound, v=38v=38v=38, vibrational level of the X1\ensuremathΣg+{X}^{1}{\ensuremath{\Sigma}}_{g}^{+}X1\ensuremathΣg+​ singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.
In some recent experiments an ultracold gas of 40^{40}40K2_22​ (or 6^{6}6Li2_22​) molecules has been produced from a degenerate two-component Fermi gas of 40^{40}40K (or 6^{6}6Li) atoms by adiabatic passage through a Feshbach resonance. The maximum atom-molecule transfer efficiency is reported to be about 50%. We propose a simple microscopic model to characterize the ground state of the gas in the vicinity of the resonance, and show that the term describing the atom-molecule coupling is responsible for the observed efficiency 50%. Our result also suggests that the experiments have produced a molecular condensate.
We determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in the harmonic trap by using the local density approximation. The adiabatic phase diagram shows the fermionic condensate fraction composed of condensed molecules and Cooper pair atoms. The key idea of our work is conservation of entropy through the adiabatic process, extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123 (2004)] for an ideal gas mixture to include the resonant interaction in a mean-field theory. We also calculate the molecular conversion efficiency as a function of initial temperature. Our work helps to understand recent experiments on the BCS-BEC crossover, in terms of the initial temperature measured before a sweep of the magnetic field.
Atomic Feshbach resonances have recently been used to produce a strongly interacting Fermi gas, where the BCS/BEC crossover can be explored. We have used both narrow and broad Feshbach resonances to convert a quantum degenerate Fermi gas of 6Li atoms into an ultracold gas of Li2 molecules. For the narrow resonances, the molecules are formed by coherent adiabatic passage through the resonance. We find that 50% of the atoms are converted to molecules. Furthermore, the lifetime of these molecules was measured to be surprisingly long, 1 s. We will discuss these measurements in the context of the present theoretical understanding. Molecules can also be formed using static fields near the broad Feshbach resonance. The lifetime of these molecules is again long, and sufficient to enable their evaporation to a Bose‐Einstein condensate. Phase contrast images of the molecular condensate are presented. The BCS/BEC crossover may be explored by starting with a pure molecular condensate on the low‐field side of the Feshbach resonance, and adiabatically changing the field to any final value around resonance. We combine this ability with optical spectroscopy on a bound‐bound molecular transition to probe the nature of the many‐body wavefunction in the crossover regime.