A fermionic condensate (or Fermi–Dirac condensate) is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic particles under similar conditions. Examples of fermionic condensates include superconductors and the superfluid phase of helium-3. The first fermionic condensate in dilute atomic gases was created by a team led by Deborah S. Jin using potassium-40 atoms at the University of Colorado Boulder in 2003.
Examples
Chiral condensate
A chiral condensate is an example of a fermionic condensate that appears in theories of massless fermions with chiral symmetry breaking, such as the theory of quarks in Quantum Chromodynamics.
BCS theory
The BCS theory of superconductivity has a fermion condensate. A pair of electrons in a metal with opposite spins can form a scalar bound state called a Cooper pair. The bound states themselves then form a condensate. Since the Cooper pair has electric charge, this fermion condensate breaks the electromagnetic gauge symmetry of a superconductor, giving rise to the unusual 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 symmetry of the theory. The QCD vacuum breaks this symmetry to SU(N) by forming a quark condensate. The existence of such a fermion condensate was first shown explicitly in the lattice formulation of QCD. The quark condensate is therefore an order parameter of transitions between several phases of quark matter in this limit.
This is very similar to the BCS theory of superconductivity. The Cooper pairs are analogous to the pseudoscalar mesons. However, the vacuum carries no charge. Hence all the gauge symmetries are unbroken. Corrections for the masses of the quarks can be incorporated using chiral perturbation theory.
Helium-3 superfluid
A helium-3 atom is a fermion and at very low temperatures, they form two-atom Cooper pairs which are bosonic and condense into a superfluid. These Cooper pairs are substantially larger than the interatomic separation.
See also
- Fermi gas
- Bose gas