Editing Bose–Einstein condensate (section)

== Current research ==
{{unsolved|physics|How do we rigorously prove the existence of Bose–Einstein condensates for generally interacting systems?}}
Compared to more commonly encountered states of matter, Bose–Einstein condensates are extremely fragile.<ref>{{Cite web|url=http://physicsworld.com/cws/article/news/2013/nov/28/how-to-watch-a-bose-einstein-condensate-for-a-very-long-time|title=How to watch a Bose–Einstein condensate for a very long time - physicsworld.com|website=physicsworld.com|date=28 November 2013|language=en-GB|access-date=2018-01-22}}</ref> 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.<ref>{{cite journal|url=https://www.nist.gov/news-events/news/2001/10/bose-einstein-condensate-new-form-matter |title=Bose-Einstein Condensate: A New Form of Matter |journal=NIST |date=October 9, 2001 |access-date=January 17, 2022 |publisher=[[National Institute of Standards and Technology]]}}</ref>

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.

Bose–Einstein condensates composed of a wide range of [[isotope]]s have been produced; see below.<ref>{{cite web | url=http://physicsworld.com/cws/article/print/2005/jun/01/ten-of-the-best-for-bec| title=Ten of the best for BEC | publisher=Physicsweb.org | date=1 June 2005 }}</ref>

=== Fundamental research ===

Examples include experiments that have demonstrated [[Interference (wave propagation)|interference]] between condensates due to [[wave–particle duality]],<ref>{{cite web | author=Gorlitz, Axel | url=http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm | title=Interference of Condensates (BEC@MIT) | publisher=Cua.mit.edu | access-date=13 October 2009 | url-status=dead | archive-url=https://web.archive.org/web/20160304092631/http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm | archive-date=4 March 2016}}</ref> the study of [[superfluidity]] and quantized [[vortex|vortices]], the creation of bright matter wave [[soliton]]s from Bose condensates confined to one dimension, and the [[slow light|slowing of light]] pulses to very low speeds using [[electromagnetically induced transparency]].<ref>
{{cite journal
 |author1=Z. Dutton
 |author2=N. S. Ginsberg
 |author3=C. Slowe
 |author4=L. Vestergaard Hau |name-list-style=amp
 |year=2004
 |title=The art of taming light: ultra-slow and stopped light
 |journal=Europhysics News
 |volume=35 |issue=2 |pages=33–39
 |doi=10.1051/epn:2004201
 |bibcode=2004ENews..35...33D|doi-access=free
 }}
</ref> Vortices in Bose–Einstein condensates are also currently the subject of [[analogue gravity]] research, studying the possibility of modeling [[black hole]]s and their related phenomena in such environments in the laboratory.

Experimenters have also realized "[[optical lattice]]s", where the interference pattern from overlapping lasers provides a [[periodic potential]]. These are used to explore the transition between a superfluid and a [[Mott insulator]].<ref>{{cite web | url=http://qpt.physics.harvard.edu/qptsi.html | title=From Superfluid to Insulator: Bose–Einstein Condensate Undergoes a Quantum Phase Transition | publisher=Qpt.physics.harvard.edu | access-date=13 October 2009}}</ref>

They are also useful in studying Bose–Einstein condensation in fewer than three dimensions, for example the [[Lieb–Liniger model]] (an the limit of strong interactions, the [[Tonks–Girardeau gas]]) in 1D and the [[Berezinskii–Kosterlitz–Thouless transition]] in 2D. Indeed, a deep optical lattice allows the experimentalist to freeze the motion of the particles along one or two directions, effectively eliminating one or two dimension from the system.

Further, the sensitivity of the pinning transition of strongly interacting bosons confined in a shallow one-dimensional optical lattice originally observed by Haller<ref>
{{cite journal
 |author1=Elmar Haller
 |author2=Russell Hart
 |author3=Manfred J. Mark
 |author4=Johann G. Danzl
 |author5=Lukas Reichsoellner
 |author6=Mattias Gustavsson
 |author7=Marcello Dalmonte
 |author8=Guido Pupillo
 |author9=Hanns-Christoph Naegerl
 |year=2010
 |title=Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
 |journal=Nature Letters
 |volume=466 |issue=7306
 |pages=597–600
 |doi=10.1038/nature09259|pmid=20671704
 |arxiv=1004.3168
 |bibcode=2010Natur.466..597H
 |s2cid=687095
 }}
</ref> has been explored via a tweaking of the primary optical lattice by a secondary weaker one.<ref>
{{cite journal
 |author1=Asaad R. Sakhel
 |year=2016
 |title=Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm- algorithm Monte Carlo study
 |journal=Physical Review A
 |volume=94 |issue=3
 |pages=033622
 |doi=10.1103/PhysRevA.94.033622|arxiv=1511.00745
 |bibcode=2016PhRvA..94c3622S
 |s2cid=55812834
 }}
</ref> Thus for a resulting weak bichromatic optical lattice, it has been found that the pinning transition is robust against the
introduction of the weaker secondary optical lattice.

Studies of vortices in nonuniform Bose–Einstein condensates<ref>
{{cite journal
 |author1=Roger R. Sakhel
 |author2=Asaad R. Sakhel
 |year=2016
 |title=Elements of Vortex-Dipole Dynamics in a Nonuniform Bose–Einstein Condensate
 |journal=Journal of Low Temperature Physics
 |volume=184 |issue=5–6
 |pages=1092–1113
 |doi=10.1007/s10909-016-1636-3|bibcode=2016JLTP..184.1092S
 |s2cid=124942094
 }}
</ref> as well as excitations of these systems by the application of moving repulsive or attractive obstacles, have also been undertaken.<ref>
{{cite journal
 |author1=Roger R. Sakhel
 |author2=Asaad R. Sakhel
 |author3=Humam B. Ghassib
 |year=2011
 |title=Self-interfering matter-wave patterns generated by a moving laser obstacle in a two-dimensional Bose–Einstein condensate inside a power trap cut off by box potential boundaries
 |journal=Physical Review A
 |volume=84 |issue=3
 |pages=033634
 |doi=10.1103/PhysRevA.84.033634|arxiv=1107.0369
 |bibcode=2011PhRvA..84c3634S
 |s2cid=119277418
 }}
</ref><ref>
{{cite journal
 |author1=Roger R. Sakhel
 |author2=Asaad R. Sakhel
 |author3=Humam B. Ghassib
 |year=2013
 |title=Nonequilibrium Dynamics of a Bose–Einstein Condensate Excited by a Red Laser Inside a Power-Law Trap with Hard Walls
 |journal=Journal of Low Temperature Physics
 |volume=173 |issue=3–4
 |pages=177–206
 |doi=10.1007/s10909-013-0894-6|bibcode=2013JLTP..173..177S
 |s2cid=122038877
 }}
</ref> Within this context, the conditions for order and chaos in the dynamics of a trapped Bose–Einstein condensate have been explored by the application of moving blue and red-[[Laser detuning|detuned]] laser beams (hitting frequencies slightly above and below the resonance frequency, respectively) via the time-dependent Gross-Pitaevskii equation.<ref>
{{cite journal
 |author1=Roger R. Sakhel
 |author2=Asaad R. Sakhel
 |author3=Humam B. Ghassib
 |author4=Antun Balaz
 |year=2016
 |title=Conditions for order and chaos in the dynamics of a trapped Bose–Einstein condensate in coordinate and energy space
 |journal=European Physical Journal D
 |volume=70 |issue=3
 |pages=66
 |doi=10.1140/epjd/e2016-60085-2|arxiv=1604.01349
 |bibcode=2016EPJD...70...66S
 |s2cid=119180702
 }}
</ref>

=== Applications ===

In 1999, Danish physicist [[Lene Hau]] led a team from [[Harvard University]] which [[Slow light|slowed a beam of light]] to about 17 meters per second{{Clarify|date=January 2010|reason=group velocity and not actual velocity?}} using a superfluid.<ref>{{cite web | last = Cromie | first = William J. | title = Physicists Slow Speed of Light | website = The Harvard University Gazette | date = 18 February 1999 | url = http://news.harvard.edu/gazette/1999/02.18/light.html | access-date = 26 January 2008 }}</ref> 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.<ref name=Ginsberg:2007/>

Another current research interest is the creation of Bose–Einstein condensates in microgravity in order to use its properties for high precision [[Atom interferometer|atom interferometry]]. The first demonstration of a BEC in weightlessness was achieved in 2008 at a [[Fallturm Bremen|drop tower]] in Bremen, Germany by a consortium of researchers led by [[Ernst M. Rasel]] from [[Leibniz University Hannover]].<ref>{{Cite journal|last1=Zoest|first1=T. van|last2=Gaaloul|first2=N.|last3=Singh|first3=Y.|last4=Ahlers|first4=H.|last5=Herr|first5=W.|last6=Seidel|first6=S. T.|last7=Ertmer|first7=W.|last8=Rasel|first8=E.|last9=Eckart|first9=M.|date=2010-06-18|title=Bose–Einstein Condensation in Microgravity|journal=Science|language=en|volume=328|issue=5985|pages=1540–1543|doi=10.1126/science.1189164|pmid=20558713|bibcode=2010Sci...328.1540V|s2cid=15194813}}</ref> The same team demonstrated in 2017 the first creation of a Bose–Einstein condensate in space<ref>{{Cite news|url=http://www.dlr.de/dlr/en/desktopdefault.aspx/tabid-10081/151_read-20337/#/gallery/25194|title=MAIUS 1 – First Bose–Einstein condensate generated in space|last=DLR|work=DLR Portal|access-date=2017-05-23|language=en-GB}}</ref> and it is also the subject of two upcoming experiments on the [[International Space Station]].<ref>{{Cite web|url=https://coldatomlab.jpl.nasa.gov/|title=Cold Atom Laboratory|last=Laboratory|first=Jet Propulsion|website=coldatomlab.jpl.nasa.gov|access-date=2017-05-23}}</ref><ref>{{Cite web|url=http://www.lpi.usra.edu/planetary_news/2017/03/13/2017-nasa-fundamental-physics-workshop/|title=2017 NASA Fundamental Physics Workshop {{!}} Planetary News|website=www.lpi.usra.edu|language=en-US|access-date=2017-05-23}}</ref>

Researchers in the new field of [[atomtronics]] use the properties of Bose–Einstein condensates in the emerging quantum technology of matter-wave circuits.<ref>{{Cite journal |last1=Amico |first1=L. |last2=Boshier |first2=M. |last3=Birkl |first3=G. |last4=Minguzzi |first4=A.|author4-link=Anna Minguzzi |last5=Miniatura |first5=C. |last6=Kwek |first6=L.-C. |last7=Aghamalyan |first7=D. |last8=Ahufinger |first8=V. |last9=Anderson |first9=D. |last10=Andrei |first10=N. |last11=Arnold |first11=A. S. |last12=Baker |first12=M. |last13=Bell |first13=T. A. |last14=Bland |first14=T. |last15=Brantut |first15=J. P. |date=25 August 2021 |title=Roadmap on Atomtronics: State of the art and perspective |url=https://avs.scitation.org/doi/10.1116/5.0026178 |journal=AVS Quantum Science |language=en |volume=3 |issue=3 |pages=039201 |doi=10.1116/5.0026178 |arxiv=2008.04439 |bibcode=2021AVSQS...3c9201A |s2cid=235417597 |issn=2639-0213}}</ref><ref>
{{cite journal
 |author=P. Weiss
 |date=12 February 2000
 |title=Atomtronics may be the new electronics
 |journal=Science News Online
 |volume=157 |issue=7 |page=104
 |doi=10.2307/4012185
 |url=http://www.sciencenews.org/view/generic/id/69786
 |jstor=4012185}}
</ref>

In 1970, BECs were proposed by [[Emmanuel David Tannenbaum]] for anti-[[stealth technology]].<ref>{{cite arXiv | last=Tannenbaum| first=Emmanuel David | title=Gravimetric Radar: Gravity-based detection of a point-mass moving in a static background| year=1970| eprint=1208.2377| class=physics.ins-det}}</ref>

=== Isotopes ===
Bose-Einstein condensation has mainly been observed on alkaline atoms, some of which have collisional properties particularly suitable for evaporative cooling in traps, and which were the first to be laser-cooled. As of 2021, using ultra-low temperatures of {{val|e=-7|u=K}} or below, Bose–Einstein condensates had been obtained for a multitude of isotopes with more or less ease, mainly of [[alkali metal]], [[alkaline earth metal]], and [[lanthanide]] atoms ({{SimpleNuclide|lithium|7|link=yes}}, {{SimpleNuclide|sodium|23|link=yes}}, {{SimpleNuclide|potassium|39|link=yes}}, {{SimpleNuclide|potassium|41|link=yes}}, {{SimpleNuclide|rubidium|85|link=yes}}, {{SimpleNuclide|Rubidium|87|link=yes}}, {{SimpleNuclide|caesium|133|link=yes}}, {{SimpleNuclide|chromium|52|link=yes}}, {{SimpleNuclide|calcium|40|link=yes}}, {{SimpleNuclide|strontium|84|link=yes}}, {{SimpleNuclide|strontium|86|link=yes}}, {{SimpleNuclide|strontium|88|link=yes}}, {{SimpleNuclide|ytterbium|170|link=yes}}, {{SimpleNuclide|ytterbium|174|link=yes}}, {{SimpleNuclide|ytterbium|176|link=yes}}, {{SimpleNuclide|dysprosium|164|link=yes}}, {{SimpleNuclide|erbium|168|link=yes}}, {{SimpleNuclide|thulium|169|link=yes}}, and metastable {{SimpleNuclide|helium|4|link=yes}} (orthohelium)).<ref>{{cite journal | last1=Schreck | first1=Florian | last2=Druten | first2=Klaasjan van | title=Laser cooling for quantum gases | journal=Nature Physics | volume=17 | issue=12 | date=2021 | issn=1745-2473 | doi=10.1038/s41567-021-01379-w | pages=1296–1304| arxiv=2209.01026 }}</ref><ref>{{cite thesis |last=Stellmer |first=Simon |date=2013 |title=Degenerate quantum gases of strontium |degree=PhD |publisher=University of Innsbruck|url=http://www.ultracold.at/theses/2013-stellmer.pdf}}</ref> Research was finally successful in atomic hydrogen with the aid of the newly developed method of 'evaporative cooling'.<ref>
{{cite journal
 |author1=Dale G. Fried
 |author2=Thomas C. Killian
 |author3=Lorenz Willmann
 |author4=David Landhuis
 |author5=Stephen C. Moss
 |author6=Daniel Kleppner
 |author7=Thomas J. Greytak |name-list-style=amp
 |year=1998
 |title=Bose–Einstein Condensation of Atomic Hydrogen
 |journal=Phys. Rev. Lett.
 |volume=81 |issue=18 |pages=3811
 |doi=10.1103/PhysRevLett.81.3811 |bibcode=1998PhRvL..81.3811F|arxiv = physics/9809017 |s2cid=3174641
 }}
</ref>

In contrast, the superfluid state of {{SimpleNuclide|Helium|4|link=yes}} below {{val|2.17|u=K}} is differs significantly from dilute degenerate atomic gases because the interaction between the atoms is strong. Only 8% of atoms are in the condensed fraction near absolute zero, rather than near 100% of a weakly interacting BEC.<ref>{{cite web | url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2001/advanced-physicsprize2001.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.nobelprize.org/nobel_prizes/physics/laureates/2001/advanced-physicsprize2001.pdf |archive-date=2022-10-09 |url-status=live| title=Bose–Einstein Condensation in Alkali Gases | publisher=The Royal Swedish Academy of Sciences | date=2001 | access-date = 17 April 2017 }}</ref>

The [[boson]]ic behavior of some of these alkaline gases appears odd at first sight, because their nuclei have half-integer total spin. It arises from the interplay of electronic and nuclear spins: at ultra-low temperatures and corresponding excitation energies, the half-integer total spin of the electronic shell (one outer electron) and half-integer total spin of the nucleus are coupled by a very weak [[hyperfine structure|hyperfine interaction]].<ref name="f953">{{cite book | last=Dunlap | first=Richard A. | title=Lasers and Their Application to the Observation of Bose-Einstein Condensates | publisher=Iop Concise Physics | date=2019-09-04 | isbn=978-1-64327-693-9 | page=}}</ref> The total spin of the atom, arising from this coupling, is an integer value.<ref>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.</ref> Conversely, alkali isotopes which have an integer nuclear spin (such as {{SimpleNuclide|lithium|6|link=yes}} and {{SimpleNuclide|potassium|40|link=yes}}) are fermions and can form degenerate [[Fermi gas]]es, also called "Fermi condensates".<ref>{{cite conference | last=Greiner | first=Markus | title=AIP Conference Proceedings | chapter=Fermionic Condensates | publisher=AIP | volume=770 | date=2005 | doi=10.1063/1.1928855 | pages=209–217| arxiv=cond-mat/0502539 }}</ref>

Cooling [[fermion]]s to extremely low temperatures has created [[degenerate matter|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. [[molecule]]s or [[BCS theory|Cooper pairs]]). The first [[molecule|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 [[Massachusetts Institute of Technology|MIT]]. Jin quickly went on to create the first [[fermionic condensate]], working with the same system but outside the molecular regime.<ref>{{cite web | url=http://physicsworld.com/cws/article/news/2004/jan/28/fermionic-condensate-makes-its-debut|title=Fermionic condensate makes its debut| publisher=Physicsweb.org | date=28 January 2004 }}</ref>

=== Continuous Bose–Einstein condensation ===
Limitations of evaporative cooling have restricted atomic BECs to "pulsed" operation, involving a highly inefficient duty cycle that discards more than 99% of atoms to reach BEC. Achieving continuous BEC has been a major open problem of experimental BEC research, driven by the same motivations as continuous optical laser development: high flux, high coherence matter waves produced continuously would enable new sensing applications.

Continuous BEC was achieved for the first time in 2022 with {{SimpleNuclide|strontium|84|link=yes}}.<ref>
{{cite journal
 |author1=Chun-Chia Chen
 |author2=Rodrigo González Escudero
 |author3=Jiří Minář
 |author4=Benjamin Pasquiou
 |author5=Shayne Bennetts
 |author6=Florian Schreck
 |year=2022
 |title=Continuous Bose–Einstein Condensation
 |journal=[[Nature (journal)|Nature]]
 |volume=606
 |issue=7915
 |pages=683–687
 |doi=10.1038/s41586-022-04731-z|pmid=35676487
 |pmc=9217748
 |bibcode=2022Natur.606..683C
 |s2cid=237532099
 }}</ref>

=== In solid state physics ===

In 2020, researchers reported the development of [[superconductivity|superconducting]] BEC and that there appears to be a "smooth transition between" BEC and [[BCS theory|Bardeen–Cooper–Shrieffer]] regimes.<ref>{{cite news |title=Researchers demonstrate a superconductor previously thought impossible |url=https://phys.org/news/2020-11-superconductor-previously-thought-impossible.html |access-date=8 December 2020 |work=phys.org |language=en}}</ref><ref>{{cite journal |last1=Hashimoto |first1=Takahiro |last2=Ota |first2=Yuichi |last3=Tsuzuki |first3=Akihiro |last4=Nagashima |first4=Tsubaki |last5=Fukushima |first5=Akiko |last6=Kasahara |first6=Shigeru |last7=Matsuda |first7=Yuji |last8=Matsuura |first8=Kohei |last9=Mizukami |first9=Yuta |last10=Shibauchi |first10=Takasada |last11=Shin |first11=Shik |last12=Okazaki |first12=Kozo |title=Bose–Einstein condensation superconductivity induced by disappearance of the nematic state |journal=Science Advances |date=1 November 2020 |volume=6 |issue=45 |pages=eabb9052 |doi=10.1126/sciadv.abb9052 |pmid=33158862 |pmc=7673702 |bibcode=2020SciA....6.9052H |url=|language=en |issn=2375-2548}}</ref>

=== Dark matter ===
P. Sikivie and Q. Yang showed that [[cold dark matter]] [[axions]] would form a Bose–Einstein condensate by [[thermalisation]] because of gravitational self-interactions.<ref>P. Sikivie, Q. Yang; Physical Review Letters,103:111103; 2009</ref> 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.

In 2014, a potential dibaryon was detected at the [[Forschungszentrum Jülich|Jülich Research Center]] at about 2380 MeV. The center claimed that the measurements confirm results from 2011, via a more replicable method.<ref>{{cite web
|url=https://www.fz-juelich.de/SharedDocs/Pressemitteilungen/UK/EN/2014/14-05-23exotisches-teilchen.html
|title=Forschungszentrum Jülich press release
}}</ref><ref>{{cite web
|url=https://www.theregister.co.uk/AMP/2014/06/10/massive_news_in_the_microworld_a_hexaquark_particle/
|title=Massive news in the micro-world: a hexaquark particle
|website=[[The Register]]
}}</ref> The particle existed for 10<sup>−23</sup> seconds and was named d*(2380).<ref>
{{cite journal
 |author=P. Adlarson|year=2014
 |title=Evidence for a New Resonance from Polarized Neutron-Proton Scattering
 |journal=[[Physical Review Letters]]
 |volume=112 |issue=2 |pages=202301
 |arxiv=1402.6844
 |bibcode=2014PhRvL.112t2301A
 |doi=10.1103/PhysRevLett.112.202301
|s2cid=2280323
 |display-authors=etal}}</ref> This particle is hypothesized to consist of three [[Up quark|up]] and three [[down quark]]s.<ref>
{{cite journal
 |author=M. Bashkanov
 |year=2020
 |title=A new possibility for light-quark dark matter
 |journal=[[Journal of Physics G]]
 |volume=47 |issue=3 |pages=03LT01
 |bibcode=2020JPhG...47cLT01B
 |doi=10.1088/1361-6471/ab67e8
|arxiv=2001.08654
 |s2cid=210861179
 |doi-access=free
 }}</ref> It is theorized that groups of d* (d-stars) could form Bose–Einstein condensates due to prevailing low temperatures in the early universe, and that BECs made of such [[hexaquark]]s with trapped electrons could behave like [[dark matter]].<ref>{{cite web
|url=https://www.livescience.com/hexaquarks-could-explain-dark-matter.html
|title=Did German physicists accidentally discover dark matter in 2014?
|website=[[Live Science]]
|date=9 March 2020
}}</ref><ref>{{cite news
|url=https://www.sciencealert.com/d-star-hexaquark-particles-could-be-responsible-for-creating-dark-matter
|title=Physicists Think We Might Have a New, Exciting Dark Matter Candidate
|newspaper=Sciencealert
|date=4 March 2020
|last1=Starr
|first1=Michelle
}}</ref><ref>{{cite web
|url=https://www.space.com/hexaquarks-big-bang-form-universe-dark-matter.html
|title=Did this newfound particle form the universe's dark matter?
|website=[[Space.com]]
|date=5 March 2020
}}</ref>