Bose–Einstein condensate

A Bose–Einstein condensate (BEC) is a state of matter of bosons confined in an external potential and cooled to temperatures very near to absolute zero (val|0|u=K, val|-273.15|u=°C, or val|-459.67|u=°F ). Under such supercooled conditions, a large fraction of the atoms collapse into the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale.

This state of matter was first predicted by Satyendra Nath Bose in 1925. Bose submitted a paper to the "Zeitschrift für Physik" but was turned down by the peer review Fact|date=October 2008. Bose then took his work to Einstein who recognized its merit and had it published under the names Bose and Einstein, hence the hyphen.

Seventy years later, the first gaseous condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder NIST-JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvin (nK) [cite web | title = Bose-Einstein Condensation | work = World of Physics on Bose-Einstein Condensation | publisher = BookRags | date = 2005-01-05 | url = http://www.bookrags.com/Bose%E2%80%93Einstein_condensate | accessdate = 2008-01-26 ] (val|1.7|e=-7|u=K). Eric Cornell, Carl Wieman and Wolfgang Ketterle at MIT were awarded the 2001 Nobel Prize in Physics in Stockholm, Sweden [cite web | last = Levi | first = Barbara Goss | title = Cornell, Ketterle, and Wieman Share Nobel Prize for Bose-Einstein Condensates | work = Search & Discovery | publisher = Physics Today online | date = 2001 | url = http://www.physicstoday.org/pt/vol-54/iss-12/p14.html | accessdate = 2008-01-26 ] .

Introduction

"Condensates" are extremely low-temperature fluids which contain properties and exhibit behaviors that are currently not completely understood, such as spontaneously flowing out of their containers. The effect is the consequence of quantum mechanics, which states that since continuous spectral regions can typically be neglected, systems can almost always acquire energy only in discrete steps. If a system is at such a low temperature that it is in the lowest energy state, it is no longer possible for it to reduce its energy, not even by friction. Without friction, the fluid will easily overcome gravity because of adhesion between the fluid and the container wall, and it will take up the most favorable position, all around the container [This is the so-called "Onnes effect", named after Heike Kammerlingh Onnes in Leiden, NL.] .

Bose-Einstein condensation is an exotic quantum phenomenon that was observed in dilute atomic gases for the first time in 1995, and is now the subject of intense theoretical and experimental study Fact|date=October 2008 .

Theory

The slowing of atoms by use of cooling apparatuses produces a singular quantum state known as a Bose condensate or Bose–Einstein condensate. This phenomenon was predicted in 1925 by generalizing Satyendra Nath Bose's work on the statistical mechanics of (massless) photons to (massive) atoms. (The Einstein manuscript, believed to be lost, was found in a library at Leiden University in 2005. [http://www.livescience.com/history/ap_050822_einstein.html, http://www.lorentz.leidenuniv.nl/history/Einstein_archive/] ) The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose–Einstein statistics, which describes the statistical distribution of identical particles with integer spin, now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einsteindemonstrated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.

This transition occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:

:$T_c=left\left(frac\left\{n\right\}\left\{zeta\left(3/2\right)\right\} ight\right)^\left\{2/3\right\}frac\left\{h^2\right\}\left\{2pi m k_B\right\}$

where:

demonstrates the correct behavior, and is a good approximation.

A singly-charged vortex ($ell=1$) is in the groundstate, with its energy $epsilon_v$ given by

:$epsilon_v=pi nfrac\left\{hbar^2\right\}\left\{m\right\}lnleft\left(1.464frac\left\{b\right\}\left\{xi\right\} ight\right)$

where:

(to obtain an energy which is well defined it is necessary toinclude this boundary b)

For multiply-charged vortices ($ell >1$) the energy isapproximated by

:$epsilon_vapprox ell^2pi nfrac\left\{hbar^2\right\}\left\{m\right\}lnleft\left(frac\left\{b\right\}\left\{xi\right\} ight\right)$

which is greater than that of $ell$ singly-chargedvortices, indicating that these multiply-charged vortices areunstable to decay. Research has, however, indicated they aremetastable states, so may have relatively long lifetimes.

Unusual characteristics

Further experimentation by the JILA team in 2000 uncovered a hitherto unknown property of Bose–Einstein condensates. Cornell, Wieman, and their coworkers originally used rubidium-87, an isotope whose atoms naturally repel each other, making a more stable condensate. The JILA team instrumentation now had better control over the condensate so experimentation was made on naturally "attracting" atoms of another rubidium isotope, rubidium-85 (having negative atom-atom scattering length). Through a process called Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, the JILA researchers lowered the characteristic, discrete energies at which the rubidium atoms bond into molecules making their Rb-85 atoms repulsive and creating a stable condensate. The reversible flip from attraction to repulsion stems from quantum interference among condensate atoms which behave as waves. When the scientists raised the magnetic field strength still further, the condensate suddenly reverted back to attraction, imploded and shrank beyond detection, and then exploded, blowing off about two-thirds of its 10,000 or so atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not being seen either in the cold remnant or the expanding gas cloud. [ [http://nobelprize.org/nobel_prizes/physics/laureates/2001/cornellwieman-lecture.pdf Eric A. Cornell and Carl E. Wieman - Nobel Lecture ] ] Carl Wieman explained that under current atomic theory this characteristic of Bose–Einstein condensate could not be explained because the energy state of an atom near absolute zero should not be enough to cause an implosion; however, subsequent mean-field theories have been proposed to explain it. Because supernova explosions are also preceded by an implosion, the explosion of a collapsing Bose–Einstein condensate was named "bosenova", a pun on the musical style bossa nova.

The atoms that seem to have disappeared almost certainly still exist in some form, just not in a form that could be detected in that experiment. Most likely they formed molecules consisting of two bonded rubidium atoms. The energy gained by making this transition imparts a velocity sufficient for them to leave the trap without being detected.

Current research

Compared to more commonly-encountered states of matter, Bose–Einstein condensates are extremely fragile. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, forming a normal gas and losing their interesting properties. It is likely to be some time before any practical applications are developed.

Nevertheless, they have proved to be useful in exploring a wide range of questions in fundamental physics, and the years since the initial discoveries by the JILA and MIT groups have seen an explosion in experimental and theoretical activity. Examples include experiments that have demonstrated interference between condensates due to wave-particle duality, [ [http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm Interference of Condensates (BEC@MIT) ] ] the study of superfluidity and quantized vortices, [ [http://www.aip.org/pt/vol-53/iss-8/p19.html Physics Today Online - Search & Discovery ] ] and the slowing of light pulses to very low speeds using electromagnetically induced transparency. [ [http://www.europhysicsnews.com/full/26/article1/article1.html The art of taming light: ultra-slow and stopped light ] ] Vortices in Bose-Einstein condensates are also currently the subject of analogue-gravityresearch, studying the possibility of modeling black holes and theirrelated phenomena in such environments in the lab.Experimentalists have also realized "optical lattices", where the interference pattern from overlapping lasers provides a periodic potential for the condensate. These have been used to explore the transition between a superfluid and a Mott insulator, [ [http://qpt.physics.harvard.edu/qptsi.html From Superfluid to Insulator: Bose-Einstein Condensate Undergoes a Quantum Phase Transition ] ] and may be useful in studying Bose–Einstein condensation in fewer than three dimensions, for example the Tonks-Girardeau gas.

Bose–Einstein condensates composed of a wide range of isotopes have been produced. [ [http://physicsweb.org/articles/world/18/6/1 Ten of the best for BEC - physicsworld.com ] ]

Related experiments in cooling fermions rather than bosons to extremely low temperatures have created degenerate gases, where the atoms do not congregate in a single state due to the Pauli exclusion principle. To exhibit Bose–Einstein condensation, the fermions must "pair up" to form compound particles (e.g. molecules or Cooper pairs) that are bosons. The first molecular Bose–Einstein condensates were created in November 2003 by the groups of Rudolf Grimm at the University of Innsbruck, Deborah S. Jin at the University of Colorado at Boulder and Wolfgang Ketterle at MIT. Jin quickly went on to create the first fermionic condensate composed of Cooper pairs. [ [http://physicsweb.org/articles/news/8/1/14/1 Fermionic condensate makes its debut - physicsworld.com ] ]

In 1999, Danish physicist Lene Vestergaard Hau led a team from Harvard University who succeeded in slowing a beam of light to about 17 metres per second and, in 2001, was able to momentarily stop a beam. She was able to achieve this by using a superfluid.Hau and her associates at Harvard University have since successfully transformed light into matter and back into light using Bose-Einstein condensates: details of the experiment are discussed in an article in the journal "Nature", 8 February 2007 [ [http://www.nature.com/nature/journal/v445/n7128/index.html Table of contents : Nature ] ] .

ome subtleties

One should not overlook that the effect involves subtleties, which are not always mentioned. One may be already "used" to the prejudice that the effect really needs the mentioned ultralow temperatures of 10-7 K or below, and is mainly based on the "nuclear" properties of (typically) alkaline atoms, i.e. properties which fit to working with "traps". However, the situation is more complicated.

This it true, although, up to 2004, using the above-mentioned "ultralow temperatures" one hadfound Bose-Einstein condensation for a multitude of isotopes involving mainly alkaline and earth-alkaline atoms (7Li, 23Na, 41K, 52Cr, 85Rb, 87Rb, 133Cs and 174Yb). Not astonishingly, even with hydrogen condensation-research was finally successful, although with special methods. In contrast, the superfluid state of the bosonic 4He at temperatures below the "rather high" (many people would say "rather low"!) temperature of 2.17 K is "not" a good example for Bose-Einstein condensation, because the interaction between the 4He bosons is simply too strong, so that at zero temperature, in contrast to the Bose-Einstein theory, not 100%, but only 8% of the atoms are in the ground state. Even the fact that the mentioned alkaline gases show bosonic, and not fermionic, behaviour, as solid state physicists or chemists would expect, is based on a subtle interplay of electronic and nuclear spins: at the mentioned ultralow temperatures and corresponding excitation energies the (half-integer, in units of $hbar$) total spin of the electronic shell and the (also half-integer) total spin of the nucleus of the atom are "coupled" by the (very weak) hyperfine interaction to the (integer!) total spin of the atom. Only the fact that this last-mentioned total spin is integer, implies that, at the mentioned ultralow temperatures the behaviour of the atom is bosonic, whereas e.g. the "chemistry" of the systems at room temperature is determined by the electronic properties, i.e. essentially fermionic, since at room temperature thermal excitations have typical energies which are much higher than the hyperfine values. (Here one should remember the spin-statistics theorem of Wolfgang Pauli, which states that half-integer spins lead to fermionic behaviour (e.g., the Pauli exclusion principle, forbidding that more than two electrons possess the same energy), whereas integer spins lead to bosonic behaviour, e.g., condensation of identical bosonic particles in a common ground state).

In contrast to the above properties, the Bose-Einstein condensation is not necessarily restricted to ultralow temperatures: in 2006 physicists around S. Demokritov in Münster, Germany, [See e.g. Demokritov, S; Demidov, V; Dzyapko, O; Melkov, G.; Serga, A; Hillebrands, B; Slavin, A: Nature 443 (2006) 430-433] , have found Bose-Einstein condensation of magnons (i.e. quantized spinwaves) at room temperature, admittedly by the application of pump-processes.

Use in popular science

A prominent example of the use of Bose-Einstein condensation in popular science is at the Physics 2000 [http://www.colorado.edu/physics/2000/cover.html web site] developed at the University of Colorado at Boulder. In the context of popularizations, atomic BEC is sometimes called a Super Atom. [ [http://www.colorado.edu/physics/2000/bec/what_is_it.html BEC - What is it and where did the idea come from? ] ]

ee also

*Atom laser
*Atomic coherence
*Bose gas
*Electromagnetically induced transparency
*Fermionic condensate
*Gas in a box
*Gross-Pitaevskii equation
*Slow light
*Superconductivity
*Superfluid
*superfluid film
*Supersolid
*Tachyon condensation
*Timeline of low-temperature technology
*Tonks-Girardeau gas
*Super-heavy atom
*
*Quantum vortex

References

*cite journal |last=Bose |first=S. N. |authorlink= |coauthors= |year=1924 |month= |title=Plancks Gesetz und Lichtquantenhypothese |journal=Zeitschrift für Physik |volume=26 |issue= |pages=178 |id= |url= |accessdate= |quote= |doi=10.1007/BF01327326
*cite journal |last=Einstein |first=A. |authorlink= |coauthors= |year=1925 |month= |title=Quantentheorie des einatomigen idealen Gases |journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften |volume=1 |issue= |pages=3 |id= |url= |accessdate= |quote= ,
*cite journal |last=Landau |first=L. D. |authorlink= |coauthors= |year=1941 |month= |title=The theory of Superfluity of Helium 111 |journal=J. Phys. USSR |volume=5 |issue= |pages=71&ndash;90 |id= |url= |accessdate= |quote=
*
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*cite journal | author= C. Barcelo, S. Liberati and M. Visser | title=Analogue gravity from Bose-Einstein condensates | journal=Classical and Quantum Gravity | year=2001 | volume=18 | pages=1137–1156 | doi=10.1088/0264-9381/18/6/312
*cite journal | author= P.G. Kevrekidis, R. Carretero-Gonzlaez, D.J. Frantzeskakis and I.G. Kevrekidis | title=Vortices in Bose-Einstein Condensates: Some Recent Developments | journal=Modern Physics Letters B | year=2006 | volume=5 | number=33|url=http://nlds.sdsu.edu/

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* C. J. Pethick and H. Smith, "Bose–Einstein Condensation in Dilute Gases", Cambridge University Press, Cambridge, 2001.
* Lev P. Pitaevskii and S. Stringari, "Bose–Einstein Condensation", Clarendon Press, Oxford, 2003.
* Amandine Aftalion, " Vortices in Bose–Einstein Condensates", PNLDE Vol.67, Birkhauser, 2006.
* Mackie M, Suominen KA, Javanainen J., "Mean-field theory of Feshbach-resonant interactions in 85Rb condensates." Phys Rev Lett. 2002 Oct 28;89(18):180403.

Notes

* [http://www.colorado.edu/physics/2000/bec/index.html BEC Homepage] General introduction to Bose–Einstein condensation
* [http://nobelprize.org/physics/laureates/2001/index.html Nobel Prize in Physics 2001] - for the achievement of Bose–Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates
* [http://www.physicstoday.org/pt/vol-54/iss-12/p14.html Physics Today: Cornell, Ketterle, and Wieman Share Nobel Prize for Bose–Einstein Condensates]
* [http://jilawww.colorado.edu/bec/ Bose–Einstein Condensates at JILA]
* [http://www.bec.phys.uu.nl/ The Bose–Einstein Condensate at Utrecht University, the Netherlands]
* [http://cua.mit.edu/ketterle_group/home.htm Alkali Quantum Gases at MIT]
* [http://www.physics.uq.edu.au/atomoptics/ Atom Optics at UQ]
* [http://www.lorentz.leidenuniv.nl/history/Einstein_archive/ Einstein's manuscript on the Bose–Einstein condensate discovered at Leiden University]
* [http://physicsweb.org/articles/world/18/6/8/1 The revolution that has not stopped] PhysicsWeb article from June 2005
* [http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=3&index1=6 Bose–Einstein condensate on arxiv.org]
* [http://www.vigyanprasar.gov.in/dream/jan2002/article1.htm Bosons - The Birds That Flock and Sing Together]
* [http://www-matterwave.physics.ox.ac.uk Oxford Experimental BEC Group.]
* [http://jilawww.colorado.edu/bec/BEC_for_everyone/ Easy BEC machine] - information on constructing a Bose-Einstein condensate machine.

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