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An event mentioned in this article is a June 5 selected anniversary

Discussion

Bosonic statistics allows for many particles to have the same quantum numbers. However, at normal temperatures, the distribution of particles is shared over many energy levels. Bose condensation occurs when a macroscopic (from a thermodynamic point of view) number of particles are in the ground state. A superconductor can loosely be thought of as a bose condensed state of electrion pairs, but this is heuristic only. Superfluidity does not necessarily occur with bose condensation. The easiest way to see this is that in bose condensation the ground state is at zero momentum. Superfluidity is the absence of viscosity, where, if given an initial velocity, there is no mechanism for the degredation of this velocity. Landau realized that the extra ingredient needed was a minimum in the energy dispersion relation, where the particles could then exists at finite velocity in a macroscopically coherent state.

In the first paragraph, in the parenthetical statement about Fermi-Dirac Statistics, the word "pearl" is used. Is this a typo? Should it be "particles?"

-> yes i think so, i just made this change

"A Bose-Einstein condensate was not actually created in a lab until June 5, 1995,"

Isn't Helium II a Bose-Einstein condensate? This has been created much earlier. If anyone knows in what way a superfuid is not considered a BEC it would be a good idea to clarify this statement.

--> AFAIK the major difference is that BEC occurs without any interactions between the particles, and is due to a rather simple balance between entropy and single particle energies. In He II the interactions are crucial to the phase transition. It would be nice to have an explanation of the opiginal Bose-Einstein derivation of the transition temperature. I might try to write one up later on.

--> The theory of a BEC as described by the work of Bose and Einstein is for a gas of non-interacting bosons. The superfluid Helium of P.Kapitsa can only be seen as an (strongly) interacting analogon for BEC. In Helium there is something like a 10% of the particles that can become superfluid, while non-interacting Bose-gas BEC's have no depletion whatsoever and interacting Bose-gas BEC's have only a very small depletion. To make life complicated bare in mind is that an interacting bose-gas condensate has superfluid(N.N. Bogoliubov proved this in 1947 IIRC) properties, but this doesn't mean a superfluid is a BEC. A BEC is caused by the statistics and only influenced by the interactions.

The derivation of the transition temperature isn't that hard(in a uniform potential). In D-dimensions one finds for the amount of particles (N) allowed to live in excited states:

${\displaystyle N=({\frac {L^{2}2\pi mk_{B}T_{c}}{h^{2}}})^{D/2}\sum _{k=1}^{\infty }{\frac {1}{k^{D/2}}}}$

in 3D this gives a critical temperature

${\displaystyle T_{c}=({\frac {n}{\zeta ({\frac {3}{2}})}})^{2/3}{\frac {h^{2}}{2\pi mk_{B}}}}$

with n=particle density

h=planck's constant

${\displaystyle k_{B}}$=Boltzman constant

${\displaystyle \zeta }$= the Rieman zeta-function

Usually BEC is observed in modern experiments using dilute atomic gasses, where the atoms are confined to a harmonic potential. For the case of non-interacting atoms confined by a harmonic potential the critical temperature is

${\displaystyle k_{B}T_{c}=\hbar {\bar {\omega }}\left({\frac {N}{\zeta (3)}}\right)^{1/3}\approx 0.94\hbar {\bar {\omega }}N^{1/3}}$

where ${\displaystyle {\bar {\omega }}=(\omega _{x}\omega _{y}\omega _{z})^{1/3}}$ is the geometric average of the oscillator frequencies, and ${\displaystyle N}$ is the average number of atoms in the trap. I believe that this article should use this, more usefull, criticle temperature.

The moment I start the Dutch article about BEC, I'll add some things here.

Disagree. The BEC is a name for phenomenum when bose-particles get accumulated in the base state in macroscopic quantities (as written in Landau-Lifshitz, vol. V, paragraph 62). The wave function of the condensate is supefluid and parameter of order. I don't undestand why you think that BEC is something can happen only with noninteracting gas. OK, suppose BEC is for gases only - then how do you call accumulation of particles in the base state? --GS 02:57, 7 May 2005 (UTC)

(only second arrow is my opinion) Yes you are right when you say BEC is a phenomenon where a macroscopic amount of particles reside in the groundstate. And you are also right when you say that a BEC has the superfluid property...but I believe it is wrong to conclude the other way around: namely that a system that is superfluid is a BEC, this is not necessarily true.(something like saying: birds can fly => everything that can fly is a bird).

I also didn't say a BEC is only something that can happen in a noninteracting gas. What I wrote was that the work of Bose and Einstein predicted BEC for a non-interacting gas. It is quite simple to show that this specific quantum phasetransition is caused purely by the used statistics, not the interactions. The interactions influence the transition by causing a depletion of the groundstate, but this depletion is very small(only a few % at most).

I only said that superfluid HeII isn't a BEC, this is because the transition happens at temperatures wich are much to high (eg order 1000x higher then expected), with hugh depletions(>90%) and in a strongly interacting system. The cause of the "condensation to the groundstate" is different that is why it shouldn't be called BEC.(Dutch article)--Shade² 12:23, 12 May 2005 (UTC)

There is no 'cause', there is only possibility to condensate. Temperature (in other words - energy per molecule) works against the tendency. Interaction... could work both directions depending on. The attraction between He atoms, most likely, is responsible for the critical temperature 'too high'. The depletion of 90% - I don't know what you mean, AFAIK density of superfluid in He goes to 0 as T goes to 0 (see google://"He superfluid normal component density").

You do agree with you that there is a "condensation to the groundstate" of the Bose-particles of He-4. --GS 18:14, 12 May 2005 (UTC)

Depletion of 90% means that at most 30% of the particles in He can become superfluid, while there are no restrictions(ie all particles condense) in the classical non-interacting theory and with interactions only a few percents remain in the excited states.

Is not in agreement with experiments. See, f.e. http://mxp.physics.umn.edu/s03/Projects/S03He/theory.htm --GS 17:36, 13 May 2005 (UTC)

Superfluid HeII isn't only in He-4(bosons) but also in He-3(fermions)...I do agree that there is a condensation to the groundstate but the underlying mechanism is different as far as I know. BEC=statistics, superfluid HeII=interactions. So, though the endresults look the same they might be considered different things.--Shade² 11:34, 13 May 2005 (UTC)

The second paragraph contains this statement: "the many overlapping atoms can be considered to be a single super-atom". I don't think this is a very precise way of describing it. The atoms are all in a single state, but they have not formed one particle ("super" or otherwise) in any way. Could someone come up with a better way of putting this?

Though there does not seem to be an entry in this encyclopedia for it, "Superatom" is used interchangably with "Bose-Einstein condensate" to mean the same thing, so i think "superatom" is a very appropriate term.

Temperature error

Why does the 50 pK temperature given in the second sentence in this article, and repeated later on, conflict with the 450 pK "lowest temperature ever" given in the 1 E-12 K article?

Especially when the value here is for the first activity in this field, back in 1995.

Is it just that somebody didn't know the difference between "one twenty-billionth of a Kelvin" (in that improperly capitalized name originally in this article) and "twenty billionths of a kelvin"? The former is 0.05 nK; the latter is 20 nK. I suspect that those two appearances in this article should read 20 nanokelvins. Gene Nygaard 03:20, 17 Dec 2004 (UTC)

Could the problem have been the ambiguous meaning of "billion"? (Different meanings in American and International English). We should use metric prefixes for everything....

Something is Missing!?

can anybody add what is meant by Tc and m, just to be precise. look at the formula. you will know what i mean. --212.202.37.226 23:49, 5 Jun 2005 (UTC)jan girke

ok, its fixed. PAR 01:27, 6 Jun 2005 (UTC)

Slowing light?

I think this section of the wiki should be removed, as it reflects the naivete of the author, and not modern physics. Claiming it's new science is not a great excuse for propagating wrong science. Photons never slow down. Ever. At the very least, clarification is necessary in this topic on the difference between an electromagnetic waveform and "light itself", or perhaps the distinction between phase velocity and group velocity. This is the same fallacy that leads people to believe that light can move faster than c (which is a universal constant, and the largest velocity it is physically possible to record). No respectable physicist would endorse the wording of this section as it stands.

In general, I find wikipedia's science pages to be inaccurate, mutually contradictory, and (like everything else on this God damned website) constantly in a battle of revision between two equally wrong versions of different slants. This website proves once again that the collective intelligence of humanity -- even internet-going humanity -- is significantly lower than "average". Which is exactly why important projects that need to be accurate to be useful (like, oh, a fucking encyclopedia) cannot be community-edited. All Of Us is far dumber than Some Of Us.

And where in the article, pray, does it state that photons are slowing down? -- CYD

Understandible statement but years and years ago we also used to teach that light couldent bend, and that pluto was a planet. Many new sciences are not believeable but that dosen't mean that they are impossible. We as humans are not even near the peak of understanding the universe and that why people gather together to discover new things. If you dislike this website, and how the pages contradict themselves you do not need to include yourself in the processing of the information given.

5th State of Matter

The caption says "...new phase of matter..." so wouldn't the BEC be the 5th, after Solid, Liquid, Gas, and Plasma?

More like the 50th... (see phase) -- CYD

Restored some text from vandalism

Some text was removed during the vandalism that happened on 24/10/05, so I put it back. Tcb Beany 21:54, 20 November 2005 (UTC)

Removed "slowing light" section

I've made some changes to the article, the main one being that I removed the "slowing light" section. This was for a number of reasons:

1) It took up a disportionate amount of space, which made it seem that this was a big part of the research into Bose-Einstein condensation. While the experiments are very nice and have received a lot of media attention, this isn't really true. IMHO other topics have been more important.

2) The phenomenon isn't confined to Bose condensates- it has been observed in non-Bose condensed gases too.

3) I thought it was a bit confusing as it was written. This can be a confusing topic for many people (not least because it relies on knowing the distinction between phase velocity and group velocity) so I felt that this needed to be explained more carefully and in more detail in order to be useful and not to propagate this confusion.

I have mentioned it briefly in a new section titled "Current research" which discusses a few other things. If it's kept, I will add some external links and references a little later when I have more time.Brian Jackson 14:17, 15 December 2005 (UTC)

Note added: I've just noticed that there is an article on EIT, so I have linked to that instead.Brian Jackson 14:33, 15 December 2005 (UTC)

rewrite is erroneous

Bosenovas are not current research but the property of BECs, are an unexplained characteristic of BECs. Rewrite is erroneous and sounds uneducated. My link to Gravastars was also taken out even though Los Alamos National Laboratories is searching for them: --Voyajer 04:46, 2 January 2006 (UTC)

Bose condensation of magnons

I have added a brief mention of the Bose condensation of magnons in antiferromagnets. From the viewpoint of statistical mechanics this is the same phenomenon as condensation of atomic bosons. Historically, the first successful observation of magnon condensation predates the experiment of Cornell and Wieman. Oleg Tchernyshyov 03:46, 26 January 2006 (UTC)

The introduction...

- "with properties that are currently not completely understood"

Is this true? Especially since it goes on to give an explanation... Simply put that viscosity drops to zero. Does it have other, magical properties? Apocryphite 01:34, 28 April 2006 (UTC)

Apparently not. Superfluidity in an interacting Bose gas has been understood for half a century. Oleg Tchernyshyov 10:54, 28 April 2006 (UTC)

Boulder Group is not the only one!

Although among the first 2 or 3, Boulder Group is not absolutely the first to obtain BEC. More than one research teams obtained it in 1995. Enough credit should be given to others too. (Check Science 269, 198 (1995); Phys. Rev. Lett. 75, 1687 (1995) and Phys. Rev. Lett. 75 3969(1995).)

Dash in title?

Why is there an en-dash in the title? Wouldn't a hyphen be fine (and more grammatically correct) here? — 75.35.38.237 04:11, 30 September 2006 (UTC)

I agree with you, but I don't particularly feel like potentially getting involved in a revert war right now. Someone else want to make the change? Anonymous 57 05:25, 30 September 2006 (UTC)

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