Abstract
BCS-BEC crossover regimes can be studied using three approaches (i) from 1D and 2D Hubbard model (ii) from two-channel model for system of ultra-cold alkali atoms (iii) via Feshbach resonance method. It has been observed that in 40K, the appearance of the condensate in BCS regime is accompanied by a significant decrease in the width of the non-condensate fraction. The origin of this phenomenon is yet unknown and requires further study. Another important aspect of the BCS-BEC transition is that one studies the nature of the condensate formed when the system is taken across the resonance. It is not known if the condensate is in the intermediate region of resonance then what will happen whether one will take the linear combination of Cooper pairs and tightly bound molecules or some complex state.
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