A
fermionic condensate is a
superfluidSuperfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
phaseIn the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
formed by
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
ic particles at low
temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
s. It is closely related to the
Bose–Einstein condensateA Bose–Einstein condensate is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at...
, a superfluid phase formed by
bosonIn particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
ic atoms under similar conditions. Unlike the Bose–Einstein condensates, fermionic condensates are formed using
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s instead of bosons. The earliest recognized fermionic condensate described the state of
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in a
superconductorSuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
; the physics of other examples including recent work with fermionic
atomThe atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s is analogous. The first atomic fermionic condensate was created by
Deborah S. JinDeborah S. Jin is a physicist with the National Institute of Standards and Technology ; Professor Adjoint, Department of Physics at the University of Colorado; a fellow of the JILA, a NIST joint laboratory with the University of Colorado. In 2003, Dr. Jin's team at JILA made the first fermionic...
in 2003. A
chiral condensate is an example of a fermionic condensate that appears in theories of massless fermions with
chiral symmetryIn quantum field theory, chiral symmetry is a possible symmetry of the Lagrangian under which the left-handed and right-handed parts of Dirac fields transform independently...
breaking.
Superfluidity
Fermionic condensates are called the sixth state of matter. They are attained at temperatures lower 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
liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
s and
gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
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
viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
. At higher velocities, energy is dissipated by the formation of quantized vortices, which act as "holes" in the medium where superfluidity breaks down.
Superfluidity was originally discovered in liquid
helium-4Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
, in 1938, by Pyotr Kapitsa, John Allen and
Don MisenerDon Misener was a physicist. Along with Pyotr Leonidovich Kapitsa and John F. Allen, Misener discovered the superfluid phase of matter in 1937....
. Superfluidity in helium-4, which occurs at temperatures below 2.17
kelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
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
liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
while the latter is condensed from a
gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
.
Fermionic superfluids
It is far more difficult to produce a fermionic superfluid than a bosonic one, because the
Pauli exclusion principleThe Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
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 transitionBCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
, discovered in 1957 by
John BardeenJohn Bardeen was an American physicist and electrical engineer, the only person to have won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a...
, Leon Cooper and
Robert SchriefferJohn Robert Schrieffer is an American physicist and, with John Bardeen and Leon N Cooper, recipient of the 1972 Nobel Prize for Physics for developing the BCS theory, the first successful microscopic theory of superconductivity.-Biography:...
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 pairIn condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
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-3Helium-3 is a light, non-radioactive isotope of helium with two protons and one neutron. It is rare on Earth, and is sought for use in nuclear fusion research...
atoms. These speculations were confirmed in 1971, when experiments performed by
Douglas D. OsheroffDouglas Dean Osheroff is an American physicist known for his work in experimental condensed matter physics, in particular for his co-discovery of superfluidity in Helium-3. For his contributions he shared the 1996 Nobel Prize in Physics along with David Lee and Robert C...
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 WiemanCarl Edwin Wieman is an American physicist at the University of British Columbia and recipient of the Nobel Prize in Physics for the production, in 1995 with Eric Allin Cornell, of the first true Bose–Einstein condensate.-Biography:...
produced a Bose–Einstein condensate from
rubidiumRubidium is a chemical element with the symbol Rb and atomic number 37. Rubidium is a soft, silvery-white metallic element of the alkali metal group. Its atomic mass is 85.4678. Elemental rubidium is highly reactive, with properties similar to those of other elements in group 1, such as very rapid...
atomThe atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
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 fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
.
In 2003, working on Holland's suggestion,
Deborah JinDeborah S. Jin is a physicist with the National Institute of Standards and Technology ; Professor Adjoint, Department of Physics at the University of Colorado; a fellow of the JILA, a NIST joint laboratory with the University of Colorado. In 2003, Dr. Jin's team at JILA made the first fermionic...
at JILA,
Rudolf GrimmRudolf Grimm is an experimental physicist from Austria. His work centres on ultracold atoms and quantum gases. He was the first scientist worldwide who, with his team, succeeded in realizing a Bose-Einstein condensation from molecules.-Career:Grimm graduated in physics from the University of...
at the University of Innsbruck, and
Wolfgang KetterleWolfgang Ketterle is a German physicist and professor of physics at the Massachusetts Institute of Technology . His research has focused on experiments that trap and cool atoms to temperatures close to absolute zero, and he led one of the first groups to realize Bose-Einstein condensation in these...
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 16th of the same year, Jin managed to produce a condensate out of fermionic atoms for the first time. The experiment involved 500,000
potassiumPotassium is the chemical element with the symbol K and atomic number 19. Elemental potassium is a soft silvery-white alkali metal that oxidizes rapidly in air and is very reactive with water, generating sufficient heat to ignite the hydrogen emitted in the reaction.Potassium and sodium are...
-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 LettersPhysical Review Letters , established in 1958, is a peer reviewed, scientific journal that is published 52 times per year by the American Physical Society...
on January 24, 2004.
BCS theory
The
BCS theoryBCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
of
superconductivitySuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
has a fermion condensate. A pair of
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in a
metalA metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
, with opposite spins can form a
scalarIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
bound stateIn physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
called a
Cooper pairIn condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
. Then, the bound states themselves form a condensate. Since the Cooper pair has
electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, this fermion condensate breaks the electromagnetic gauge symmetry of a superconductor, giving rise to the wonderful electromagnetic properties of such states.
QCD
In
quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
(QCD) the chiral condensate is also called the
quark condensate. This property of the
QCD vacuumThe QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...
is partly responsible for giving masses to hadrons (along with other condensates like the
gluon condensateIn Quantum chromodynamics , the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons.If the gluon field tensor is represented as Gμν, then...
).
In an approximate version of QCD, which has vanishing quark masses for
N quark
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
s, there is an exact chiral SU(
N)xSU(
N) symmetry of the theory. The
QCD vacuumThe QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...
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 theoryBCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
of superconductivity. The Cooper pairs are analogous to the
pseudoscalar mesonIn high energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity . Compare to scalar meson.Pseudoscalar mesons are commonly seen in proton-proton scattering and proton-antiproton annihilation...
s. However, the vacuum carries no charge. Hence all the gauge symmetries are unbroken. Corrections for the masses of the
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s can be incorporated using
chiral perturbation theoryChiral perturbation theory is an effective field theory constructed with a Lagrangian consistent with the chiral symmetry of quantum chromodynamics , as well as the other symmetries of parity and charge conjugation. ChPT is a theory which allows one to study the low-energy dynamics of QCD...
.
Helium-3 superfluid
A
helium-3Helium-3 is a light, non-radioactive isotope of helium with two protons and one neutron. It is rare on Earth, and is sought for use in nuclear fusion research...
atom is a
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
and at very low temperatures, they form two-atom Cooper pairs which are bosonic and condense into a
superfluidSuperfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
. These Cooper pairs are substantially larger than the interatomic separation
See also
- Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
and the BCS theoryBCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
.
- The QCD vacuum
The QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...
and the gluon condensateIn Quantum chromodynamics , the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons.If the gluon field tensor is represented as Gμν, then...
.
- Quark matter, diquark condensate and the pion condensate.
- The top quark condensate
In particle physics, the top quark condensate theory is an alternative to the Standard Model in which a fundamental scalar Higgs field is replaced by a composite field composed of the top quark and its antiquark. These are bound by a four-fermion interaction, analogous to Cooper pairs in a BCS...
and TechnicolorTechnicolor theories are models of physics beyond the standard model that address electroweak symmetry breaking, the mechanism through which elementary particles acquire masses...
models.
- Nambu-Jona-Lasinio model
In quantum field theory, the Nambu–Jona-Lasinio model is a theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry which parallels the construction of Cooper pairs from electrons in the BCS theory of superconductivity...
- Gross-Neveu model
The Gross-Neveu model is a quantum field theory model of Dirac fermions interacting via four fermion interactions in 1 spatial and 1 time dimension. It was introduced in 1974 by David Gross and André Neveu as a toy model for quantum chromodynamics, the theory of strong interactions.It consists of...
- gaugino condensate