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
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
is cooled to
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
s very close to
absolute zero (−273.15 °C or −459.67 °F). Under such conditions, a large fraction of bosons occupy the lowest
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 ...
, at which point microscopic
quantum mechanical phenomena, particularly
wavefunction interference, become apparent
macroscopically. A BEC is formed by cooling a gas of extremely low density (about 100,000 times less dense than
normal air) to ultra-low temperatures.
This state was first predicted, generally, in 1924–1925 by
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
following and crediting a pioneering paper by
Satyendra Nath Bose on the new field now known as
quantum statistics. In 1995, the Bose-Einstein condensate was created by
Eric Cornell and
Carl Wieman
Carl Edwin Wieman (born March 26, 1951) is an American physicist and educationist at Stanford University, and currently the A.D White Professor at Large at Cornell University. In 1995, while at the University of Colorado Boulder, he and Eric All ...
of the
University of Colorado at Boulder using
rubidium
Rubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher ...
atoms; later that year,
Wolfgang Ketterle of
MIT produced a BEC using
sodium
Sodium is a chemical element with the symbol Na (from Latin ''natrium'') and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable ...
atoms. In 2001 Cornell, Wieman and Ketterle shared the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
"for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates."
History
Bose first sent a paper to Einstein on the
quantum statistics of light quanta (now called
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s), in which he derived
Planck's quantum radiation law without any reference to classical physics. Einstein was impressed, translated the paper himself from English to German and submitted it for Bose to the ''
Zeitschrift für Physik
''Zeitschrift für Physik'' (English: ''Journal for Physics'') is a defunct series of German peer-reviewed physics journals established in 1920 by Springer Berlin Heidelberg. The series stopped publication in 1997, when it merged with other jour ...
'', which published it in 1924. (The Einstein manuscript, once believed to be lost, was found in a library at
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city o ...
in 2005.) Einstein then extended Bose's ideas to matter in two other papers. The result of their efforts is the concept of a
Bose gas, governed by
Bose–Einstein statistics, which describes the statistical distribution of
identical particles with
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
spin, now called
bosons. Bosons, particles that include the
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
as well as
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, a ...
s such as
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 cons ...
(), are allowed to share a quantum state. Einstein proposed that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible
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 ...
, resulting in a new form of matter.
In 1938,
Fritz London proposed the BEC as a mechanism for
superfluidity in and
superconductivity
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
.
[
The quest to produce a Bose–Einstein condensate in the laboratory was stimulated by a paper published in 1976 by two Program Directors at the National Science Foundation (William Stwalley and Lewis Nosanow). This led to the immediate pursuit of the idea by four independent research groups; these were led by Isaac Silvera (]University of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...
), Walter Hardy (University of British Columbia
The University of British Columbia (UBC) is a public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks among the top thr ...
), Thomas Greytak (Massachusetts Institute of Technology
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 th ...
) and David Lee (Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
).
On 5 June 1995, the first gaseous condensate was produced by Eric Cornell and Carl Wieman
Carl Edwin Wieman (born March 26, 1951) is an American physicist and educationist at Stanford University, and currently the A.D White Professor at Large at Cornell University. In 1995, while at the University of Colorado Boulder, he and Eric All ...
at the University of Colorado at Boulder NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
– JILA lab, in a gas of rubidium
Rubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher ...
atoms cooled to 170 nanokelvins (nK). Shortly thereafter, Wolfgang Ketterle at MIT produced a Bose–Einstein Condensate in a gas of sodium
Sodium is a chemical element with the symbol Na (from Latin ''natrium'') and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable ...
atoms. For their achievements Cornell, Wieman, and Ketterle received the 2001 Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
. These early studies founded the field of ultracold atoms, and hundreds of research groups around the world now routinely produce BECs of dilute atomic vapors in their labs.
Since 1995, many other atomic species have been condensed, and BECs have also been realized using molecules, quasi-particles, and photons.[
]
Critical temperature
This transition to BEC occurs below a critical temperature, which for a uniform three-dimensional
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called '' parameters'') are required to determine the position of an element (i.e., point). This is the inform ...
gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:
:
where:
:
Interactions shift the value and the corrections can be calculated by mean-field theory.
This formula is derived from finding the gas degeneracy in the Bose gas using Bose–Einstein statistics.
Derivation
Ideal Bose gas
For an ideal Bose gas we have the equation of state:
:
where is the per particle volume, the thermal wavelength, the fugacity
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas whic ...
and
:
It is noticeable that is a monotonically growing function of in