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It would be really helpful if somebody could describe what does one mean by a BEC-BCS Crossover. I was going through articles available on the topic, but I was unable to grasp the gist of the topic.

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In the context of ultracold Fermi gases, a BEC-BCS crossover means that by tuning the interaction strength (the s-wave scattering length), one goes from a BEC state to a BCS state without encountering a phase transition (thus the word "crossover").

It is also useful to know that the BEC state is a Bose-Einstein condensate of two-atom molecules, while the BCS state is made up of pair of atoms. The different between the pairs and the molecules is that the molecules are localized in the real (position) space, whereas the BCS pairs are made of two particles with opposite momenta. Thus, the BCS pairs are large (much larger than the inter-particle spacing), whereas the BEC molecules are small.

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  • $\begingroup$ @FraSchelle I had read the review, but was not quite able to get the whole idea. But after reading ffc 's comment, I think I will read the reviews again. $\endgroup$ – Abhijit Apr 16 '15 at 5:47
  • $\begingroup$ So, you mean to say that for negative scattering lengths, the particles are described by BCS state, but when you crossover from zero to positive side of scattering length, then they form composite bosons (or bosons made from two fermions)? For what all systems has this been observed till date? Further, since there is no phase transition, can we expect that BCS and BEC can be explained by a single theory? $\endgroup$ – Abhijit Apr 16 '15 at 5:53
  • $\begingroup$ Yes, it seems that you have understood it correctly :) It has been observed for several different ultracold gases, please take a look at the references 1-7 in the recent review arXiv:1306.5785. And yes, both BCS and BEC can be understood in a single framework. As it is eloquently put in this recent review, "There is now a clear recognition that the BCS and BEC paradigms are not as distinct as they were once thought to be, but rather are the two extrema of a continuum.". $\endgroup$ – ffc Apr 16 '15 at 9:23
  • $\begingroup$ Minor remark: the BCS condensate is made up of pairs of electrons ("Cooper pairs"), not atoms. $\endgroup$ – Betohaku Feb 12 '18 at 14:15
  • $\begingroup$ @Betohaku historically you are right, but now people do it with atoms as well, see eg cmt.harvard.edu/demler/TEACHING/Physics284/chapter11.pdf $\endgroup$ – ffc Mar 13 '18 at 10:56

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