Bose–Einstein condensate: Difference between revisions

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

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	=== Vortices ===
	{{refimprove section\|date=September 2011}}
	As in many other systems, ] 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 ]. These phenomena are allowed for by the non-linear <math>\|\psi(\vec{r})\|^2</math> term in the GPE.{{Disputed inline\|Talk page section\|date=April 2017\|reason=I do not believe the non-linear term is necessary; vortices are a simple consequence of the continuity equation the condensate wavefunction satisfies, and this equation is the same without the interaction term because the interaction term is real.}} As the vortices must have quantized ] the wavefunction may have the form <math>\psi(\vec{r})=\phi(\rho,z)e^{i\ell\theta}</math> where <math>\rho, z</math> and <math>\theta</math> are as in the ], and <math>\ell</math> 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 <math>\phi(\rho,z)</math>, the energy of <math>\psi(\vec{r})</math> must be minimized, according to the constraint <math>\psi(\vec{r})=\phi(\rho,z)e^{i\ell\theta}</math>. This is usually done computationally, however in a uniform medium the analytic form:

	:<math>\phi=\frac{nx}{\sqrt{2+x^2}}</math>, where:
	{\| cellspacing="0" cellpadding="0"
	\|-
	\| <math>\,n^2</math>
	\|  is
	\| density far from the vortex,
	\|-
	\| <math>\,x = \frac{\rho}{\ell\xi},</math>
	\|-
	\| <math>\,\xi</math>
	\|  is
	\| healing length of the condensate.
	\|}demonstrates the correct behavior, and is a good approximation.

	A singly charged vortex (<math>\ell=1</math>) is in the ground state, with its energy <math>\epsilon_v</math> given by

	:<math>\epsilon_v=\pi n
	\frac{\hbar^2}{m}\ln\left(1.464\frac{b}{\xi}\right)</math>

	where <math>\,b</math> is the farthest distance from the vortices considered.(To obtain an energy which is well defined it is necessary to include this boundary <math>b</math>.)

	For multiply charged vortices (<math>\ell >1</math>) the energy is approximated by

	:<math>\epsilon_v\approx \ell^2\pi n
	\frac{\hbar^2}{m}\ln\left(\frac{b}{\xi}\right)</math>

	which is greater than that of <math>\ell</math> 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 ]s 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.<ref name=Becker:2008/>

	=== Attractive interactions ===		=== Attractive interactions ===

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

Phases Phase transition QCP
States of matter Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttinger liquid Time crystal
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v t e

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

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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.

References

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M. H. P. M. van Putten (2010). "Pair condensates produced in bosenovae". Phys. Lett. A. 374 (33): 3346–3347. Bibcode:2010PhLA..374.3346V. doi:10.1016/j.physleta.2010.06.020.
C. Sun; N. A. Sinitsyn (2016). "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". Phys. Rev. A. 94 (3): 033808. arXiv:1606.08430. Bibcode:2016PhRvA..94c3808S. doi:10.1103/PhysRevA.94.033808.
"How to watch a Bose–Einstein condensate for a very long time - physicsworld.com". physicsworld.com. Retrieved 22 January 2018.
Gorlitz, Axel. "Interference of Condensates (BEC@MIT)". Cua.mit.edu. Archived from the original on 4 March 2016. Retrieved 13 October 2009. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
Z. Dutton; N. S. Ginsberg; C. Slowe; L. Vestergaard Hau (2004). "The art of taming light: ultra-slow and stopped light". Europhysics News. 35 (2): 33–39. Bibcode:2004ENews..35...33D. doi:10.1051/epn:2004201. {{cite journal}}: Unknown parameter |lastauthoramp= ignored (|name-list-style= suggested) (help)
"From Superfluid to Insulator: Bose–Einstein Condensate Undergoes a Quantum Phase Transition". Qpt.physics.harvard.edu. Retrieved 13 October 2009.
"Ten of the best for BEC". Physicsweb.org. 1 June 2005.
"Fermionic condensate makes its debut". Physicsweb.org. 28 January 2004.
Cromie, William J. (18 February 1999). "Physicists Slow Speed of Light". The Harvard University Gazette. Retrieved 26 January 2008.
N. S. Ginsberg; S. R. Garner; L. V. Hau (2007). "Coherent control of optical information with matter wave dynamics". Nature. 445 (7128): 623–626. doi:10.1038/nature05493. PMID 17287804. {{cite journal}}: Unknown parameter |lastauthoramp= ignored (|name-list-style= suggested) (help)
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.
DLR. "MAIUS 1 – First Bose-Einstein condensate generated in space". DLR Portal. Retrieved 23 May 2017.
Laboratory, Jet Propulsion. "Cold Atom Laboratory". coldatomlab.jpl.nasa.gov. Retrieved 23 May 2017.
"2017 NASA Fundamental Physics Workshop | Planetary News". www.lpi.usra.edu. Retrieved 23 May 2017.
P. Weiss (12 February 2000). "Atomtronics may be the new electronics". Science News Online. 157 (7): 104. doi:10.2307/4012185. JSTOR 4012185. Retrieved 12 February 2011.
Tannenbaum, Emmanuel David (1970). "Gravimetric Radar: Gravity-based detection of a point-mass moving in a static background". arXiv:1208.2377 .
P. Sikivie, Q. Yang; Phys. Rev. Lett.,103:111103; 2009
Dale G. Fried; Thomas C. Killian; Lorenz Willmann; David Landhuis; Stephen C. Moss; Daniel Kleppner; Thomas J. Greytak (1998). "Bose–Einstein Condensation of Atomic Hydrogen". Phys. Rev. Lett. 81 (18): 3811. arXiv:physics/9809017. Bibcode:1998PhRvL..81.3811F. doi:10.1103/PhysRevLett.81.3811. {{cite journal}}: Unknown parameter |lastauthoramp= ignored (|name-list-style= suggested) (help)
"Bose–Einstein Condensation in Alkali Gases" (PDF). The Royal Swedish Academy of Sciences. 2001. Retrieved 17 April 2017.

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External links

Bose–Einstein Condensation 2009 Conference Bose–Einstein Condensation 2009 – Frontiers in Quantum Gases
BEC Homepage General introduction to Bose–Einstein condensation
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
Physics Today: Cornell, Ketterle, and Wieman Share Nobel Prize for Bose–Einstein Condensates
Bose–Einstein condensates at JILA
Atomcool at Rice University
Alkali Quantum Gases at MIT
Atom Optics at UQ
Einstein's manuscript on the Bose–Einstein condensate discovered at Leiden University
Bose–Einstein condensate on arxiv.org
Bosons – The Birds That Flock and Sing Together
Easy BEC machine – information on constructing a Bose–Einstein condensate machine.
Verging on absolute zero – Cosmos Online
Lecture by W Ketterle at MIT in 2001
Bose–Einstein Condensation at NIST – NIST resource on BEC

v t e States of matter (list)
State	Solid Liquid Gas / Vapor Supercritical fluid Plasma
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Other states	Colloid Crystal Liquid crystal Time crystal Quantum spin liquid Exotic matter Programmable matter Dark matter Antimatter Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String-net liquid Superglass
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Works	Annus mirabilis papers (1905) "Investigations on the Theory of Brownian Movement" (1905) Relativity: The Special and the General Theory (1916) The Meaning of Relativity (1922) The World as I See It (1934) The Evolution of Physics (1938) "Why Socialism?" (1949) Russell–Einstein Manifesto (1955)
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Prizes	Albert Einstein Award Albert Einstein Medal Kalinga Prize Albert Einstein Peace Prize Albert Einstein World Award of Science Einstein Prize for Laser Science Einstein Prize (APS)
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