From Cooper Pairs to Molecules: Effective field theories for ultra-cold atomic gases near Feshbach resonances

<p>Feshbach resonances in dilute atomic gases are a powerful tool used to control the strength of atom-atom interactions. In practice, the tuning is accomplished by varying a magnetic field, aording experiments on dilute atomic gases a knob with which they can arbitrarily adjust the interactions. This precision control makes atomic gases an ideal place to study many-body phenomena. The resonance works by introducing a closed channel containing a bound, molecular state within the open channel of contin- uum scattering states. The molecular state greatly modifies the scattering responsible for the interactions, as it is tuned near resonance, introducing pair correlations through- out the sample. The size of these correlations may range from either very small, where they appear as molecules, to very large, where they resemble Cooper pairs. This leads to a "crossover" problem of connecting the Bardeen-Cooper-Schrieffer theory of Cooper pairing, which describes conventional superconductors, to the process of Bose-Einstein condensation of molecules. To answer this question, it is necessary to develop an ap- propriate field theory for both Bosons and Fermions that can account for the Feshbach processes and, therefore, properly describe resonant, ultra-cold atomic gases.</p>