What's a Fermionic Condensate?

John Baez

January 31, 2004

This week the media have been talking in very vague terms about a new thing called a "fermionic condensate" - they say it's a new state of matter, but they're not saying much about what it is! Here's an article that's a bit clearer: Basically, there had been two known ways of getting fermions to form pairs, which act approximately like bosons, and can thus "condense" - meaning that a whole bunch of them get into the same state.

One way was for the fermions to literally stick together: for example, some protons, neutrons and electrons (all fermions) can stick together and form helium-4, which is a boson... and these bosons can then form a condensate known as "superfluid helium".

A fancy way of saying that the fermions stick together is to say that they have strongly correlated positions: if you know where one is, you've got a good idea where its mates are.

The other option was for the fermions to get strongly correlated momenta. The classic example is a superconductor, where electrons form "Cooper pairs", which are bosons. The two electrons in a Cooper pair aren't close together in position - after all, they repel each other due their electric charge. However, they have almost the same momentum!

The new "fermionic condensate" allows physicists to interpolate between these two extremes: they can now get some fermions to correlate in ways that are "between" position correlation and momentum correlation. Even better, they can adjust the type of correlation by changing an external magnetic field.

In more mathematical terms, we used to be able to form pairs of bosons in "position space" or in "momentum space". Now we can do it more generally. Yay!

The position space and momentum space representation of wavefunctions are important, and nicely related by the Fourier transform - but there are infinitely many other representations, and we can try to get correlations in any one. News reports about this being useful for new high-temperature superconductors are somewhat missing the point. It may ultimately be useful - but what it is right now is beautiful!

It's not surprising that the media are having a tough time explaining this, though!

© 2004 John Baez