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== Experimental observation ==

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=== Gaseous ===

The first "pure" Bose–Einstein condensate was created by ], ], and co-workers at ] on 5 June 1995. They cooled a dilute vapor of approximately two thousand ] atoms to below 170 nK using a combination of ] (a technique that won its inventors ], ], and ] the 1997 ]) and ]. About four months later, an independent effort led by ] at ] condensed ]. Ketterle's condensate had a hundred times more atoms, allowing important results such as the observation of ] ] between two different condensates. Cornell, Wieman and Ketterle won the 2001 ] for their achievements.<ref name="nobel">{{cite web |url=http://nobelprize.org/nobel_prizes/physics/laureates/2001/cornellwieman-lecture.pdf |title=Eric A. Cornell and Carl E. Wieman&nbsp;— Nobel Lecture |format=PDF |publisher=nobelprize.org}}</ref>

A group led by Randall Hulet at Rice University announced a condensate of ] atoms only one month following the JILA work.<ref name=Bradley:1995/> Lithium has attractive interactions, causing the condensate to be unstable and collapse for all but a few atoms. Hulet's team subsequently showed the condensate could be stabilized by confinement quantum pressure for up to about 1000 atoms. Various isotopes have since been condensed.

==== Velocity-distribution data graph ====

In the image accompanying this article, the velocity-distribution data indicates the formation of a Bose–Einstein condensate out of a gas of ] atoms. The false colors indicate the number of atoms at each velocity, with red being the fewest and white being the most. The areas appearing white and light blue are at the lowest velocities. The peak is not infinitely narrow because of the ]: spatially confined atoms have a minimum width velocity distribution. This width is given by the curvature of the magnetic potential in the given direction. More tightly confined directions have bigger widths in the ballistic velocity distribution. This ] of the peak on the right is a purely quantum-mechanical effect and does not exist in the thermal distribution on the left. This graph served as the cover design for the 1999 textbook ''Thermal Physics'' by Ralph Baierlein.<ref>{{cite book |url=https://books.google.com/?id=fqUU71spbZYC&printsec=frontcover|title=Thermal Physics|author=Baierlein, Ralph |publisher=Cambridge University Press|year=1999|isbn=0-521-65838-1}}</ref>

=== Quasiparticles ===

{{Main|Bose–Einstein condensation of quasiparticles}}Bose–Einstein condensation also applies to ]s in solids. ]s, ], and ] have integer spin which means they are ] that can form condensates.

Magnons, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic ordering is the analog of superfluidity. In 1999 condensation was demonstrated in antiferromagnetic ]]]<sub>3</sub>,<ref name=Nikuni:1999/> at temperatures as large as 14 K. The high transition temperature (relative to atomic gases) is due to the magnons small mass (near an electron) and greater achievable density. In 2006, condensation in a ] yttrium-iron-garnet thin film was seen even at room temperature,<ref name=Demokritov:2006/><ref>. Website of the "Westfählische Wilhelms Universität Münster" Prof.Demokritov. Retrieved 25 June 2012.</ref> with optical pumping.

]s, electron-hole pairs, were predicted to condense at low temperature and high density by Boer et al. in 1961. Bilayer system experiments first demonstrated condensation in 2003, by Hall voltage disappearance. Fast optical exciton creation was used to form condensates in sub-kelvin Cu<sub>2</sub>O in 2005 on.

] was firstly detected for ] in a quantum well microcavity kept at 5 K.<ref name="ReferenceA">{{Cite journal|url = |title = Bose–Einstein condensation of exciton polaritons|date = 28 September 2006|journal = Nature|accessdate = |doi = 10.1038/nature05131|pmid = 17006506|volume=443 |issue = 7110|pages=409–414|bibcode = 2006Natur.443..409K |author=Kasprzak J, Richard M, Kundermann S, Baas A, Jeambrun P, Keeling JM, Marchetti FM, Szymańska MH, André R, Staehli JL, Savona V, Littlewood PB, Deveaud B, Dang}}</ref>


== Peculiar properties == == Peculiar properties ==

Revision as of 08:34, 21 December 2018

"Super atom" redirects here. For clusters of atoms that seem to exhibit some of the properties of elemental atoms, see Superatom.

Condensed matter physics
States of matter
Phase phenomena
Electronic phases
Electronic phenomena
Magnetic phases
Quasiparticles
Soft matter
Scientists
Schematic Bose–Einstein condensation versus temperature and the energy diagram

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (-273.15°C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to ultra-low temperatures.

This state was first predicted, generally, in 1924–1925 by Satyendra Nath Bose and Albert Einstein.

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Peculiar properties

Vortices

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As in many other systems, vortices can exist in BECs. These can be created, for example, by 'stirring' the condensate with lasers, or rotating the confining trap. The vortex created will be a quantum vortex. These phenomena are allowed for by the non-linear | ψ ( r → ) | 2 {\displaystyle |\psi ({\vec {r}})|^{2}} term in the GPE. As the vortices must have quantized angular momentum the wavefunction may have the form ψ ( r → ) = ϕ ( ρ , z ) e i ℓ θ {\displaystyle \psi ({\vec {r}})=\phi (\rho ,z)e^{i\ell \theta }} where ρ , z {\displaystyle \rho ,z} and θ {\displaystyle \theta } are as in the cylindrical coordinate system, and ℓ {\displaystyle \ell } is the angular number. This is particularly likely for an axially symmetric (for instance, harmonic) confining potential, which is commonly used. The notion is easily generalized. To determine ϕ ( ρ , z ) {\displaystyle \phi (\rho ,z)} , the energy of ψ ( r → ) {\displaystyle \psi ({\vec {r}})} must be minimized, according to the constraint ψ ( r → ) = ϕ ( ρ , z ) e i ℓ θ {\displaystyle \psi ({\vec {r}})=\phi (\rho ,z)e^{i\ell \theta }} . This is usually done computationally, however in a uniform medium the analytic form:

ϕ = n x 2 + x 2 {\displaystyle \phi ={\frac {nx}{\sqrt {2+x^{2}}}}} , where:
n 2 {\displaystyle \,n^{2}}  is  density far from the vortex,
x = ρ ℓ ξ , {\displaystyle \,x={\frac {\rho }{\ell \xi }},}
ξ {\displaystyle \,\xi }  is  healing length of the condensate.

demonstrates the correct behavior, and is a good approximation.

A singly charged vortex ( ℓ = 1 {\displaystyle \ell =1} ) is in the ground state, with its energy ϵ v {\displaystyle \epsilon _{v}} given by

ϵ v = π n ℏ 2 m ln ⁡ ( 1.464 b ξ ) {\displaystyle \epsilon _{v}=\pi n{\frac {\hbar ^{2}}{m}}\ln \left(1.464{\frac {b}{\xi }}\right)}

where b {\displaystyle \,b}  is the farthest distance from the vortices considered.(To obtain an energy which is well defined it is necessary to include this boundary b {\displaystyle b} .)

For multiply charged vortices ( ℓ > 1 {\displaystyle \ell >1} ) the energy is approximated by

ϵ v ≈ ℓ 2 π n ℏ 2 m ln ⁡ ( b ξ ) {\displaystyle \epsilon _{v}\approx \ell ^{2}\pi n{\frac {\hbar ^{2}}{m}}\ln \left({\frac {b}{\xi }}\right)}

which is greater than that of ℓ {\displaystyle \ell } singly charged vortices, indicating that these multiply charged vortices are unstable to decay. Research has, however, indicated they are metastable states, so may have relatively long lifetimes.

Closely related to the creation of vortices in BECs is the generation of so-called dark solitons in one-dimensional BECs. These topological objects feature a phase gradient across their nodal plane, which stabilizes their shape even in propagation and interaction. Although solitons carry no charge and are thus prone to decay, relatively long-lived dark solitons have been produced and studied extensively.

Attractive interactions

Experiments led by Randall Hulet at Rice University from 1995 through 2000 showed that lithium condensates with attractive interactions could stably exist up to a critical atom number. Quench cooling the gas, they observed the condensate to grow, then subsequently collapse as the attraction overwhelmed the zero-point energy of the confining potential, in a burst reminiscent of a supernova, with an explosion preceded by an implosion.

Further work on attractive condensates was performed in 2000 by the JILA team, of Cornell, Wieman and coworkers. Their instrumentation now had better control so they used naturally attracting atoms of rubidium-85 (having negative atom–atom scattering length). Through Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, they lowered the characteristic, discrete energies at which rubidium bonds, making their Rb-85 atoms repulsive and creating a stable condensate. The reversible flip from attraction to repulsion stems from quantum interference among wave-like condensate atoms.

When the JILA team raised the magnetic field strength further, the condensate suddenly reverted to attraction, imploded and shrank beyond detection, then exploded, expelling about two-thirds of its 10,000 atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not seen in the cold remnant or expanding gas cloud. 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. Most likely they formed molecules of two rubidium atoms; energy gained by this bond imparts velocity sufficient to leave the trap without being detected.

The process of creation of molecular Bose condensate during the sweep of the magnetic field throughout the Feshbach resonance, as well as the reverse process, are described by the exactly solvable model that can explain many experimental observations.

Current research

Unsolved problem in physics: How do we rigorously prove the existence of Bose–Einstein condensates for general interacting systems? (more unsolved problems in physics)

Compared to more commonly encountered states of matter, Bose–Einstein condensates are extremely fragile. The slightest interaction with the external environment can be enough to warm them past the condensation threshold, eliminating their interesting properties and forming a normal gas.

Nevertheless, they have proven 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 increase in experimental and theoretical activity. Examples include experiments that have demonstrated interference between condensates due to wave–particle duality, the study of superfluidity and quantized vortices, the creation of bright matter wave solitons from Bose condensates confined to one dimension, and the slowing of light pulses to very low speeds using electromagnetically induced transparency. Vortices in Bose–Einstein condensates are also currently the subject of analogue gravity research, studying the possibility of modeling black holes and their related phenomena in such environments in the laboratory. Experimenters have also realized "optical lattices", where the interference pattern from overlapping lasers provides a periodic potential. These have been used to explore the transition between a superfluid and a Mott insulator, 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.

Cooling fermions to extremely low temperatures has created degenerate gases, subject to the Pauli exclusion principle. To exhibit Bose–Einstein condensation, the fermions must "pair up" to form bosonic compound particles (e.g. molecules or Cooper pairs). The first molecular 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.

In 1999, Danish physicist Lene Hau led a team from Harvard University which slowed a beam of light to about 17 meters per second, using a superfluid. Hau and her associates have since made a group of condensate atoms recoil from a light pulse such that they recorded the light's phase and amplitude, recovered by a second nearby condensate, in what they term "slow-light-mediated atomic matter-wave amplification" using Bose–Einstein condensates: details are discussed in Nature.

Another current research interest is the creation of Bose–Einstein condensates in microgravity in order to use its properties for high precision atom interferometry. The first demonstration of a BEC in weightlessness was achieved in 2008 at a drop tower in Bremen, Germany by a consortium of researchers led by Ernst M. Rasel from Leibniz University of Hanover. The same team demonstrated in 2017 the first creation of a Bose–Einstein condensate in space and it is also the subject of two upcoming experiments on the International Space Station.

Researchers in the new field of atomtronics use the properties of Bose–Einstein condensates when manipulating groups of identical cold atoms using lasers.

In 1970, BECs were proposed by Emmanuel David Tannenbaum for anti-stealth technology.

Dark matter

P. Sikivie and Q. Yang showed that cold dark matter axions form a Bose-Einstein condensate by thermalisation because of gravitational self-interactions. Axions have not yet been confirmed to exist. However the important search for them has been greatly enhanced with the completion of upgrades to the Axion Dark Matter Experiment(ADMX) at the University of Washington in early 2018.

Isotopes

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The effect has mainly been observed on alkaline atoms which have nuclear properties particularly suitable for working with traps. As of 2012, using ultra-low temperatures of 10 K or below, Bose–Einstein condensates had been obtained for a multitude of isotopes, mainly of alkali metal, alkaline earth metal, and lanthanide atoms (Li, Na, K, K, Rb, Rb, Cs, Cr, Ca, Sr, Sr, Sr, Yb, Dy, and Er). Research was finally successful in hydrogen with the aid of the newly developed method of 'evaporative cooling'. In contrast, the superfluid state of He below 2.17 K is not a good example, because the interaction between the atoms is too strong. Only 8% of atoms are in the ground state near absolute zero, rather than the 100% of a true condensate.

The bosonic behavior of some of these alkaline gases appears odd at first sight, because their nuclei have half-integer total spin. It arises from a subtle interplay of electronic and nuclear spins: at ultra-low temperatures and corresponding excitation energies, the half-integer total spin of the electronic shell and half-integer total spin of the nucleus are coupled by a very weak hyperfine interaction. The total spin of the atom, arising from this coupling, is an integer lower value. The chemistry of systems at room temperature is determined by the electronic properties, which is essentially fermionic, since room temperature thermal excitations have typical energies much higher than the hyperfine values.

See also

References

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  13. Zoest, T. van; Gaaloul, N.; Singh, Y.; Ahlers, H.; Herr, W.; Seidel, S. T.; Ertmer, W.; Rasel, E.; Eckart, M. (18 June 2010). "Bose-Einstein Condensation in Microgravity". Science. 328 (5985): 1540–1543. Bibcode:2010Sci...328.1540V. doi:10.1126/science.1189164. ISSN 0036-8075. PMID 20558713.
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