Fermionic condensate

Background

Superfluidity

Fermionic condensates are a type of superfluid. As the name suggests, a superfluid possesses fluid properties similar to those possessed by ordinary quantized vortices, which act as "holes" in the medium where superfluidity breaks down.

Superfluidity was originally discovered in liquid gas.

Fermionic superfluids

It is far more difficult to produce a fermionic superfluid than a bosonic one, because the Pauli exclusion principle prohibits fermions from occupying the same quantum state. However, there is a well-known mechanism by which a superfluid may be formed from fermions. This is the Leon Cooper and Robert Schrieffer for describing superconductivity. These authors showed that, below a certain temperature, electrons (which are fermions) can pair up to form bound pairs now known as Cooper pairs. As long as collisions with the ionic lattice of the solid do not supply enough energy to break the Cooper pairs, the electron fluid will be able to flow without dissipation. As a result, it becomes a superfluid.

The BCS theory was phenomenally successful in describing superconductors. Soon after the publication of the BCS paper, several theorists proposed that a similar phenomenon could occur in fluids made up of fermions other than electrons, such as helium-3 atoms. These speculations were confirmed in 1971, when experiments performed by Douglas D. Osheroff showed that helium-3 becomes a superfluid below 0.0025 K. It was soon verified that the superfluidity of helium-3 arises from a BCS-like mechanism. (The theory of superfluid helium-3 is a little more complicated than the BCS theory of superconductivity. These complications arise because helium atoms repel each other much more strongly than electrons, but the basic idea is the same.)

Creation of the first fermionic condensates

When Eric Cornell and Carl Wieman produced a Bose-Einstein condensate from atoms in 1995, there naturally arose the prospect of creating a similar sort of condensate made from fermionic atoms, which would form a superfluid by the BCS mechanism. However, early calculations indicated that the temperature required for producing Cooper pairing in atoms would be too cold to achieve. In 2001, Murray Holland at JILA suggested a way of bypassing this difficulty. He speculated that fermionic atoms could be coaxed into pairing up by subjecting them to a strong magnetic field.

In 2003, working on Holland's suggestion, Deborah Jin at JILA, Rudolf Grimm at the University of Innsbruck, and Wolfgang Ketterle at MIT managed to coax fermionic atoms into forming molecular bosons, which then underwent Bose-Einstein condensation. However, this was not a true fermionic condensate. Later that year, Jin managed to produce a condensate out of fermionic atoms for the first time. The experiment involved 500,000 potassium-40 atoms cooled to a temperature of 5×10⁻⁸ K, subjected to a time-varying magnetic field. The findings were published in the online edition of Physical Review Letters on January 24 2004.

Examples

BCS theory

The electric charge, this fermion condensate breaks the electromagnetic gauge symmetry of a superconductor, giving rise to the wonderful electromagnetic properties of such states.

QCD

In Quantum chromodynamics (QCD) the chiral condensate is also called the quark condensate. This property of the QCD vacuum is partly responsible for giving masses to hadrons (along with other condensates like the gluon condensate).

In an approximate version of QCD, which has vanishing quark masses for N quark flavours, there is an exact chiral SU(N)xSU(N) symmetry of the theory. The QCD vacuum breaks this symmetry to SU(N) by forming a quark condensate. The quark condensate is therefore an quark matter in this limit.

This is very similar to the quarks can be incorporated using chiral perturbation theory.

Helium-3 superfluid

A superfluid. These Cooper pairs are substantially larger than the interatomic separation.

See also

• BCS theory.
• The QCD vacuum and the gluon condensate.
• diquark condensate and the pion condensate.
• The top quark condensate and Technicolor models.
• Nambu-Jona-Lasinio model
• Gross-Neveu model
• gaugino condensate

References

• Guenault, Tony (2003). Basic superfluids. Taylor & Francis. ISBN 0-7484-0892-4. 
• University of Colorado (January 28, 2004). NIST/University of Colorado Scientists Create New Form of Matter: A Fermionic Condensate. Press Release.
• Rodgers, Peter & Dumé, Bell (January 28, 2004). Fermionic condensate makes its debut. PhysicWeb.