A fermionic condensate or Fermi–Dirac condensate is a
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
phase formed by
fermionic particles at low
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
s. It is closely related to the
Bose–Einstein condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.6 ...
, a superfluid phase formed by
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...
ic atoms under similar conditions. The earliest recognized fermionic condensate described the state of
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
s in a
superconductor; the physics of other examples including recent work with fermionic
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
s is analogous. The first atomic fermionic condensate was created by a team led by
Deborah S. Jin using
potassium
Potassium is the chemical element with the symbol K (from Neo-Latin ''kalium'') and atomic number19. Potassium is a silvery-white metal that is soft enough to be cut with a knife with little force. Potassium metal reacts rapidly with atmosph ...
-40 atoms at the
University of Colorado Boulder
The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado sy ...
in 2003.
Background
Superfluidity
Fermionic condensates are attained at lower temperatures than Bose–Einstein condensates. Fermionic condensates are a type of
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
. As the name suggests, a superfluid possesses fluid properties similar to those possessed by ordinary
liquids and
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
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
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
. At lower 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-4
Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
whose atoms are
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...
s, not fermions.
Fermionic superfluids
It is far more difficult to produce a fermionic superfluid than a bosonic one, because the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulat ...
prohibits fermions from occupying the same
quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution i ...
. However, there is a well-known mechanism by which a superfluid may be formed from fermions: That mechanism is the
BCS transition, discovered in 1957 by
J. Bardeen,
L.N. Cooper, and
R. 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
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
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
D.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.
Creation of the first fermionic condensates
When
Eric Cornell
Eric Allin Cornell (born December 19, 1961) is an American physicist who, along with Carl E. Wieman, was able to synthesize the first Bose–Einstein condensate in 1995. For their efforts, Cornell, Wieman, and Wolfgang Ketterle shared the Nobel ...
and
Carl Wieman produced a Bose–Einstein condensate from
rubidium atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
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
JILA, formerly known as the Joint Institute for Laboratory Astrophysics, is a physical science research institute in the United States. JILA is located on the University of Colorado Boulder campus. JILA was founded in 1962 as a joint institute ...
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
Rudolf Grimm (born 10 November 1961) 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 ...
at the
University of Innsbruck, and
Wolfgang Ketterle
Wolfgang Ketterle (; born 21 October 1957) is a German physicist and professor of physics at the Massachusetts Institute of Technology (MIT). His research has focused on experiments that trap and cool atoms to temperatures close to absolute ze ...
at
MIT
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...
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
potassium
Potassium is the chemical element with the symbol K (from Neo-Latin ''kalium'') and atomic number19. Potassium is a silvery-white metal that is soft enough to be cut with a knife with little force. Potassium metal reacts rapidly with atmosph ...
-40 atoms cooled to a temperature of 5×10
−8 K, subjected to a time-varying magnetic field.
Examples
Chiral condensate
A chiral condensate is an example of a fermionic condensate that appears in theories of massless fermions with
chiral symmetry
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, ...
breaking, such as the theory of quarks in
Quantum Chromodynamics.
BCS theory
The
BCS theory
BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of
superconductivity has a fermion condensate. A pair of
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
s in a
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
with opposite spins can form a
scalar bound state
Bound or bounds may refer to:
Mathematics
* Bound variable
* Upper and lower bounds, observed limits of mathematical functions
Physics
* Bound state, a particle that has a tendency to remain localized in one or more regions of space
Geography
* ...
called a
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
. The bound states themselves then form a condensate. Since the Cooper pair has
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
, 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
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...
is partly responsible for giving masses to hadrons (along with other condensates like the
gluon condensate
In quantum chromodynamics (QCD), the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to light mesons.
If the gluon field tensor is represented as Gμν, then the gluon condensat ...
).
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
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...
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
Quark matter or QCD matter (quantum chromodynamic) refers to any of a number of hypothetical phases of matter whose degrees of freedom include quarks and gluons, of which the prominent example is quark-gluon plasma. Several series of conferences ...
in this limit.
This is very similar to the
BCS theory
BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of superconductivity. The
Cooper pairs
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
are analogous to the
pseudoscalar meson
In high-energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity (usually notated as
Pseudoscalar mesons are commonly seen in proton-proton scattering and proton-antiproton annihilation, and include the pion (), ...
s. 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 pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
s which are bosonic and condense into a
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
. These Cooper pairs are substantially larger than the interatomic separation.
See also
*
Fermi gas
An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer sp ...
*
Bose gas
An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and abide by Bose–Einstein statistics. The statistical mechanics of bosons were deve ...
Footnotes
References
Sources
*
*
*
*
{{Phase of matter
American inventions
Condensed matter physics
Phases of matter
Quantum field theory
Exotic matter
Quantum phases
Superfluidity