Atom-to-molecule conversion efficiency and adiabatic fidelity

The efficiency of converting two-species fermionic atoms into bosonic molecules is investigated in terms of mean-field Lagrangian density. We find that the STIRAP technique aided by Feshbach resonance is more effective than the bare Fechbach resonance for $^6$Li atoms rather than $^{40}$K atoms. We also make general consideration on the symmetry and its relevant conservation law, which enable us to introduce a natural definition of adiabatic fidelity for CPT state. The calculated values of the fidelity then provide an interpretation on why the conversion efficiencies for $^{40}$K and $^6$Li are distinctly different.