Editing Fermionic condensate

{{Short description|State of matter}}
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{{Condensed matter physics|expanded=States of matter}}
A '''fermionic condensate''' (or '''Fermi–Dirac 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]]ic atoms 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.<ref>{{Cite journal |last1=DeMarco |first1=Brian |last2=Bohn |first2=John |last3=Cornell |first3=Eric |year=2006 |title=Deborah S. Jin 1968–2016 |journal=Nature |language=en |volume=538 |issue=7625 |pages=318 |doi=10.1038/538318a |doi-access=free |pmid=27762370 |issn=0028-0836}}</ref><ref name=":0" />

==Background==

===Superfluidity===
Fermionic condensates are attained at lower temperatures than Bose–Einstein condensates. 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 high velocities without dissipating any energy—i.e. zero [[viscosity]]. At lower 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-4]] whose atoms are [[boson]]s, not fermions.

=== 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: That mechanism is the [[BCS theory|BCS transition]], discovered in 1957 by [[John Bardeen|J.&nbsp;Bardeen]], [[Leon Neil Cooper|L.N.&nbsp;Cooper]], and [[John Robert Schrieffer|R.&nbsp;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, and the material through which it flows a superconductor.

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|D.D.&nbsp;Osheroff]] showed that helium-3 becomes a superfluid below 0.0025&nbsp;K. It was soon verified that the superfluidity of helium-3 arises from a BCS-like mechanism.{{efn|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.}}

=== Condensates of fermionic atoms ===
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 S. Jin|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, 2003, Jin managed to produce a condensate out of fermionic atoms for the first time. The experiment involved 500,000&nbsp;[[potassium]]-40 atoms cooled to a temperature of 5×10<sup>−8</sup>&nbsp;K, subjected to a time-varying magnetic field.<ref name=":0">{{Cite journal |last1=Regal |first1=C.A. |last2=Greiner |first2=M. |last3=Jin |first3=D.S. |date=2004-01-28 |df=dmy-all |title=Observation of resonance condensation of Fermionic atom pairs|journal=Physical Review Letters |volume=92 |issue=4 |pages=040403 |doi=10.1103/PhysRevLett.92.040403 |pmid=14995356 |arxiv=cond-mat/0401554|bibcode=2004PhRvL..92d0403R |s2cid=10799388 }}</ref>

==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|Quantum Chromodynamics]].

===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]]. 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 [[flavour (particle physics)|flavour]]s, there is an exact chiral {{nowrap|SU(''N'') × SU(''N'')}} 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 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 pair]]s which are bosonic and condense into a [[superfluid]]. These Cooper pairs are substantially larger than the interatomic separation.

== See also ==
* [[Fermi gas]]
* [[Bose gas]]

== Footnotes ==
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== References ==
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=== Sources ===
{{Refbegin}}
* {{cite book |author=Guenault, Tony |date=2003 |title=Basic superfluids |publisher=[[Taylor & Francis]] |isbn=978-0-7484-0892-4}}
* {{cite press release |publisher=University of Colorado |date=January 28, 2004 |url=http://www.colorado.edu/news/releases/2004/21.html |archive-url=https://web.archive.org/web/20061207131059/http://www.colorado.edu/news/releases/2004/21.html |archive-date=2006-12-07 |df=dmy-all |title=NIST/University of Colorado scientists create new form of matter: A Fermionic condensate}}
* {{cite web |last1=Rodgers |first1=Peter |last2=Dumé |first2=Bell |date=January 28, 2004 |url=https://physicsworld.com/a/fermionic-condensate-makes-its-debut/ |title=Fermionic condensate makes its debut |website=Physics World |access-date=29 Jun 2019}}
* {{cite journal |last=Hägler |first=Ph. |title=Hadron structure from lattice quantum chromodynamics |journal=Physics Reports |volume=490 |issue=3–5 |year=2010 |pages=49–175 |issn=0370-1573 |doi=10.1016/j.physrep.2009.12.008 |arxiv=0912.5483|bibcode=2010PhR...490...49H }}
{{Refend}}

{{Phase of matter}}

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