On the conversion of ultracold fermionic atoms to bosonic molecules via feshbach resonances

It is demonstrated that symmetry plays an important roll in the production, through Feshbach sweep experiments, of diatomic bosonic molecules from fermionic atomic mixtures of two hyperfine spin-states by constructing the many-body state. It is shown that the experimental procedure employed to prepare these atomic mixtures, leads to a mixture of even and odd many body parity pair-states. The symmetry of the many body state is shown to be the reason behind the 0.5 limited transfer experimental efficiency observed independently by two experimental groups who studied the conversion of ultracold Fermi gases of ⁴⁰K and ⁶Li atoms into diatomic Bose gases. The higher than 50% transfer efficiency, as is currently experimentally obtained is achieved by a magnetic sweep rate which is much slower than the the collision rate in the gas, which is here related to a pair decorrelation rate.