Cooper pairing in ultracold40Kusing Feshbach resonances

We point out that the fermionic isotope ${}^{40}\mathrm{K}$ is a likely candidate for the formation of Cooper pairs in an ultracold atomic gas. Specifically, in an optical trap that simultaneously traps the spin states $|9/2,-9/2〉$ and $|9/2,-7/2〉,$ there exists a broad magnetic-field Feshbach resonance at ${B=196\mathrm{}}_{-21}^{+9\mathrm{}}$ G that can provide the required strong attractive interaction between atoms. An additional resonance, at ${B=191\mathrm{}}_{10}^{+5\mathrm{}}$ G, could generate p-wave pairing between identical $|9/2,-7/2〉$ atoms. A Cooper-paired degenerate Fermi gas could thus be constructed with existing ultracold-atom technology.