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We achieve degeneracy in a mixture of the two lowest hyperfine states of Li by direct evaporation in a CO laser trap, yielding the first all-optically produced degenerate Fermi gas. More than atoms are confined at temperatures below K at full trap depth, where the Fermi temperature for each state is K. This degenerate two-component mixture is ideal for exploring mechanisms of superconductivity ranging from Cooper pairing to Bose condensation of strongly bound pairs.

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