Section 9: Conclusions and a Look Ahead
Macroscopic quantum fluids, or superfluids, can be formed from cold bosons. Many types of composite entities fulfill the basic bosonic requirement of integral spin. So, the gaseous quantum superfluid can consist of bosonic atoms, and quite newly bosonic molecules, all of which contain an even overall number of spin-1/2 fermions, be they electrons, protons, or neutrons. All are uncharged superfluids. In the dilute gaseous superfluid phase, they display fully quantum properties, such as interference on the length scale of around a millimeter, which are visible to the naked eye. So, they are certainly macroscopic. Dense liquid superfluids such as 4He, of course, contain many more atoms than gaseous BECs in laboratory traps, and have a myriad of unusual properties. But, they do not directly display their fundamental quantum nature quite so directly, even though it underlies their superfluid behavior.
Figure 32: A fountain of superfluid 4He
Source: © Peter Taborek, Low Temperature Materials Laboratory, University of California, Irvine. More info
Two fermions can pair to make a boson: This allows fermionic 3He to become a superfluid, albeit at a much lower temperature than its bosonic neighbor 4He. The pair interaction between these 3He atoms is far too weak to allow formation of molecules in the liquid, so the pair formed is rather ephemeral, and is best described in analogy to what happens to electrons in a superconductor rather than atoms in 4He.
Famously, and unexpectedly, even two electrons can pair in a metallic free-electron "sea" to make a composite boson inside a superconductor. This seems odd at first, as these electrons have like charges and thus repel each other. Thus, their pairing is not at all like making bosonic 6Li2 from fermionic 6Li, as those atoms actually attract and form molecules in physical space. The pairing of electrons to make bosonic pairs of electrons, called "Cooper pairs," is indeed more complex. It does not even take place in the three-dimensional coordinate space in which we live. Rather, the pairing occurs in a more abstract "momentum" space. We leave that description to Unit 8, simply noting that it is yet another example of the pairing concepts that we have introduced here. And, because a bosonic pair of electrons carries two units of negative electrical charge, the Bose condensate of such paired electrons is not only a superfluid, but also a superconductor.