## Bose-Einstein Condensates

Named for the theorists Satyendra Nath Bose and Albert Einstein who predicted its existence, a Bose-Einstein condensate is an unusual state of matter that arises because of quantum mechanical effects on a collection of entities called bosons.
Everything is either a boson or a fermion. The spin of an object determines whether it is a boson or a fermion. For more details, click here.
The reason why is important to differentiate between bosons and fermions is that they have vastly different quantum mechanical behavior. Identical fermions cannot occupy the same place. This is called the Pauli exclusion principle. For example, you cannot put two electrons spinning in the same direction on top of one other. It is forbidden and never happens in nature. Bosons behave in almost the opposite way. They like to overlap.
In quantum mechanics, the position of an object is uncertain. An object has a definite probability of being at any given point in space. This probability is encoded in what-is-called a wave function. It is like a "cloud" that tells you the probability that an object has a certain location. The object is more likely to be found in denser parts of the "cloud" and is less likely to be found in the less dense parts. If a region of space has no "cloud," then there is zero chance that the object is there.
If one concentrates a large number of identical bosons in a small region, then it is possible for their wave functions to overlap so much that the bosons loose their identity. If a dozen clouds are well separated in the sky, then it is easy to determine where each one is. But if you look up and the 12 clouds have already joined to form one large cloud, it is no longer possible to tell which part comes from the original 12 clouds. A collection of bosons can do the same thing. When this happens, a Bose-Einstein condensate forms. This exotic state of matter is only possible at low temperatures. At high temperatures, the individual bosons not only have small wave functions but they move rapidly and fly apart. In summary, in a Bose-Einstein condensate, the individual bosons become indistinguishable.
Two examples of materials containing Bose-Einstein condensates are superconductors and superfluids. Superconductors conduct electricity with virtually zero electrical resistance: Once a current is started, it flows indefinitely. The liquid in a superfluid also flows forever. In effect, there is no friction. The nucleons in a neutron star9 are believed to form a superfluid. Scientists have been able to make superfluids in the laboratory by cooling materials to very low temperatures. Helium-4 below a temperature of 2.17 Kelvins is an example.

### A Play to Illustrate Bose-Einstein Condensates

The scene takes place on a sidewalk on 5th Avenue in New York City. A man named Dr. Bose is sitting behind a card table. On the table are some cups, balls, tape, paper and a black felt-tipped pen.

[A tourist comes up to Dr. Bose's table.]

Dr. Bose: "My name is Satyendra Nath Bose. Would you like to play Monte?"

Tourist: "How do you play Monte?"

Dr. Bose: "Well, normally a ball is placed under one of three cups. Then I shuffle the cups quickly hoping to confuse you. You guess which cup contains the ball. If you are correct, I give you a dollar. If you are wrong, you give me a dollar. Sounds simple, no?"

Tourist: "I have keen eyesight. Let's play."

Dr. Bose: "Well, eyesight won't help you with my version of Monte. In my version of the game, numerical labels -- one, two and three -- are taped to three balls. You get to put the three balls under the cups. Then, you get to guess which number is under a particular cup. During this whole process, I don't touch anything -- not the balls, not the cups. Only you handle them. Sounds like an easy way to make a buck, doesn't it? Want to play?"

Tourist: "Are you a magician?"

Dr. Bose: "No, I am a physicist."

Tourist: "Well, in that case, let's play."

Dr. Bose: "Here are the balls, here is some tape, here are the labels and here are the cups."

[The tourist takes that three balls and attaches labels with the numbers one, two and three to the balls. He then places the number one ball under the left cup, the number two ball under the middle cup and the number three ball under the right cup.]

Tourist: "Now what?"

Dr. Bose: "Choose a cup."

Tourist: "The middle one."

Dr. Bose: "Tell me what number is under it?"

Tourist: "Two."

Dr. Bose: "O.K. Lift up the middle cup."

[The tourist lifts the middle cup and is astonished to find the ball with the label one under it.]

Tourist: "That's impossible. I'm sure that I put the number two ball under the middle cup."

[The tourist hands Dr. Bose a dollar.]

Tourist: "Let's play again."

Dr. Bose: "O.K. Put the number one ball back under the middle cup."

Tourist: "Done."

Dr. Bose: "Choose a cup."

Tourist: "The middle one."

Dr. Bose: "Tell me what number is under it?"

Tourist: "One."

Dr. Bose: "O.K. Lift up the middle cup."

[The tourist lifts the middle cup and indeed finds the ball with the label one is under it.]

Tourist: "Give me back my buck."

[Dr. Bose returns the dollar.]

Tourist: "I must have just made a silly mistake the first time."

[The tourist puts the number one ball back under the middle cup.]

Tourist: "I again choose the middle cup and ball number one will be under it."

[The tourist lifts up the middle cup only to find the number two ball under it.]

Tourist: "That's strange. The number two ball was the one I originally thought was under the middle cup."

[The tourist gives a dollar to Dr. Bose.]

Tourist: "Well, since we're back to the original situation. The number one ball is probably under the left cup."

[The tourist picks up the left cup, only to find that the number three ball is under it.]

Dr. Bose: "You loose again."

Tourist: "I thought you said that you were not a magician."

Dr. Bose: "I'm not."

Tourist: "Then how did you do this trick?"

Dr. Bose: "It is not a trick and I did not do it. It did it itself."

Tourist: "I don't' follow."

Dr. Bose: "These three balls are bosons and they are part of a Bose-Einstein condensate. Their individual wave functions do not exist. Instead, they have a collective wave function, which does not permit them to be distinguishable. Thus, when you lift a cup, it is equally probable that you will pick any numbered ball. That is why I do not have to touch the cups. The balls randomize themselves automatically."

Tourist: "I didn't understand a word you said. Hey, I know what you are. You're one of those . . . What's it called. . . . psychokinesists, aren't you."

[Dr. Bose just shook his head. At this point, a voice shouts out, "Hey, Isaac have you seen the statue of Atlas in Rockefeller Center?"]

Tourist: "No. Hey, wait for me."

[And the tourist runs off].

[curtain falls]

Moral of the play: Don't play Monte with physicists.

Postscript: Rumor has it that Mayor Giuliana is proposing a new ordinance to prohibit the playing of Bose-Einstein Monte in public places in New York City.

The above play perfectly illustrates a Bose-Einstein condensate. When a Bose-Einstein condensate of a million atoms is achieved, the identity of each one is lost. If labels were placed on each atom to try to keep track of them, a person would have just as much trouble picking a particular atom out of the sample as the tourist had in selecting a numbered ball under a cup. It would be as if all the atoms had cups over them, hiding their identity. Each time an atom in a particular position in the condensate is picked, a random atom of the sample is selected. The atoms have lost their individuality. Of course, one cannot implement a Bose-Einstein version of Monte: the temperature is too high and the objects are too big. A Bose-Einstein condensate needs to have a very low temperature to allow the bosons to "stick together" and the bosons must be microscopic so that quantum mechanical effects are important.

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