Fermionic condensate
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{{expert-portal|Physics}}
A '''fermionic condensate''' is a [[superfluid]] [[Phase (matter)|phase]] formed by [[fermion]]ic particles at low [[temperature]]s. It is closely related to the [[Bose-Einstein condensate]], a superfluid phase formed by [[boson|bosonic]] atoms under similar conditions. Unlike the Bose-Einstein condensates, fermionic condensates are formed using [[fermion]]s instead of bosons. The earliest recognized fermionic condensate described the state of [[electron]]s in a [[superconductivity|superconductor]]; the physics of other examples including recent work with fermionic [[atom]]s is analogous. The first atomic fermionic condensate was created by [[Deborah S. Jin]] in [[2003]]. A '''chiral condensate''' is an example of a fermionic condensate that appears in theories of massless fermions with [[chiral symmetry]] breaking.
== Background ==
=== Superfluidity ===
Fermionic condensates are a type of superfluid. As the name suggests, a superfluid possesses fluid properties similar to those possessed by ordinary [[liquid]]s and [[gas]]es, such as the lack of a definite shape and the ability to flow in response to applied forces. However, superfluids possess some properties that do not appear in ordinary matter. For instance, they can flow at low velocities without dissipating any energy—i.e. zero [[viscosity]]. At higher velocities, energy is dissipated by the formation of [[quantized vortex|quantized vortices]], which act as "holes" in the medium where superfluidity breaks down.
Superfluidity was originally discovered in liquid [[Helium|helium-4]], in [[1938]], by [[Pyotr Leonidovich Kapitsa|Pyotr Kapitsa]], [[John F. Allen|John Allen]] and [[Don Misener]]. Superfluidity in helium-4, which occurs at temperatures below 2.17 [[kelvin]]s (K), has long been understood to result from Bose condensation, the same mechanism that produces the Bose-Einstein condensates. The primary difference between superfluid helium and a Bose-Einstein condensate is that the former is condensed from a [[liquid]] while the latter is condensed from a [[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 [[BCS theory|BCS transition]], discovered in [[1957]] by [[John Bardeen]], [[Leon Neil Cooper|Leon Cooper]] and [[John Robert Schrieffer|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 pair]]s. 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 [[rubidium]] [[atom]]s 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. On December 16<sup>th</sup> of the same 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<sup>−8</sup> 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 [[BCS theory]] of [[superconductivity]] has a fermion condensate. A pair of [[electron]]s in a [[metal]], with opposite spins can form a [[scalar (physics)|scalar]] [[bound state]] called a [[Cooper pair]]. Then, the bound states themselves 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 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 [[flavour (particle physics)|flavour]]s, 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 [[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 meson]]s. However, the vacuum carries no charge. Hence all the [[gauge symmetry|gauge symmetries]] are unbroken. Corrections for the masses of the [[quark]]s 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==
* [[Superconductivity]] and the [[BCS theory]].
* The [[QCD vacuum]] and the [[gluon condensate]].
* [[Quark matter]], [[diquark condensate]] and the [[pion condensate]].
* The [[top quark condensate]] and [[Technicolor (physics)|Technicolor]] models.
*[[Nambu-Jona-Lasinio model]]
*[[Gross-Neveu model]]
*[[gaugino condensate]]
== References ==
* {{cite book|author=Guenault, Tony|year=2003|title=Basic superfluids|publisher=Taylor & Francis|id=ISBN 0-7484-0892-4}}
* University of Colorado (January 28, 2004). ''[http://www.colorado.edu/news/releases/2004/21.html NIST/University of Colorado Scientists Create New Form of Matter: A Fermionic Condensate]''. Press Release.
* Rodgers, Peter & Dumé, Bell (January 28, 2004). ''[http://physicsweb.org/articles/news/8/1/14 Fermionic condensate makes its debut]''. PhysicWeb.
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[[Category:Condensed matter physics]]
[[Category:phases of matter]]
[[Category:Quantum field theory]]
[[Category:Quark matter]]
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