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# Bose-Einstein condensate

A Bose-Einstein condensate is a gaseous superfluid phase formed by atoms cooled to temperatures very near to absolute zero. The first such condensate was produced by Eric Cornell and Carl Wieman in 1995, using a gas of rubidium atoms cooled to 170 nanokelvins (nK). Under such conditions, a large fraction of the atoms collapse into the lowest quantum state, producing a superfluid.

Velocity-distribution data confirming the discovery of a new phase of matter, the Bose-Einstein condensate, out of a gas of rubidium atoms. The artificial 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. Left: just before the appearance of the Bose-Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate. The peak is not infinitely narrow because of the Heisenberg uncertainty principle: since the atoms are trapped in a particular region of space, their velocity distribution necessarily possesses a certain minimum width.
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## Theory

The collapse of the atoms into a single quantum state is known as Bose condensation or Bose-Einstein condensation. This phenomenon was predicted in the 1920s by Satyendra Nath Bose and Albert Einstein, based on Bose's work on the statistical mechanics of photons, which was then formalized and generalized by Einstein. The result of their efforts is the concept of a Bose gas, governed by the Bose-Einstein statistics, which describes the statistical distribution of certain types of identical particles now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einstein speculated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.

The critical temperature at which this happens can be derived to be:

$T_c=(\frac{n}{\zeta(\frac{3}{2})})^{2/3}\frac{h^2}{2\pi m k_B}$

Where:

n = particle density, h = Planck's constant, kB = Boltzmann constant, ζ = the Riemann zeta function

## Discovery

In 1938, Pyotr Kapitsa, John Allen and Don Misener discovered that helium-4 became a new kind of fluid, now known as a superfluid, at temperatures below 2.2 kelvins (K). Superfluid helium has many unusual properties, including the ability to flow without dissipating energy (i.e. zero viscosity) and the existence of quantized vortices . It was quickly realized that the superfluidity was due to Bose-Einstein condensation of the helium-4 atoms, which are bosons. In fact, many of the properties of superfluid helium also appear in the gaseous Bose-Einstein condensates created by Cornell and Wieman (see below). However, superfluid helium-4 is not commonly referred to as a "Bose-Einstein condensate" because it is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong. The original Bose-Einstein theory has to be heavily modified in order to describe it.

The first "true" Bose-Einstein condensate was created by Cornell, Wieman, and co-workers at JILA on June 5, 1995. They did this by cooling a dilute vapor consisting of approximately 2000 rubidium-87 atoms to 170 nK, the lowest temperature ever achieved at that time, using a combination of laser cooling (a technique that won its inventors Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips the 1997 Nobel Prize in Physics) and magnetic evaporative cooling. About four months later, an independent effort led by Wolfgang Ketterle at MIT created a condensate made of sodium-23. Ketterle's condensate had about a hundred times more atoms, allowing him to obtain several important results such as the observation of quantum mechanical interference between two different condensates. Cornell, Wieman and Ketterle won the 2001 Nobel Prize for their achievement.

The initial results by the JILA and MIT groups have led to an explosion of experimental activity. For instance, the first molecular Bose-Einstein condensates were created in 2003 by teams surrounding Rudolf Grimm at the University of Innsbruck and Deborah S. Jin at the University of Colorado at Boulder.

Bose-Einstein condensates are extremely fragile, compared to other states of matter more commonly encountered. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, causing them to break back down into individual atoms again; it will likely be some time before any practical applications are developed for them.

## Slowing light

However, several interesting properties have already been observed in experiments. Bose-Einstein condensates can be made to have an extremely high gradient in the optical densities. Normally, condensates do not have a particularly special refractive index, due to having an atomic density far less than normal solid materials. However, additional pump lasers can be used at frequencies designed to alter the state of atoms in the Bose-Einstein condensate, increasing drastically the index for a beam of a precise target frequency recorded at a probe point. This results in extremely low measured speed of light within it; some condensates have slowed beams of light down to mere meters per second, speeds which can be exceeded by a human on a bicycle. A rotating Bose-Einstein condensate could be used as a model black hole, allowing light to enter but not to escape. Condensates could also be used to "freeze" pulses of light, to be released again when the condensate breaks down. This is done by shutting off the pumping lasers with pulses still in transit and allowing the photons to be absorbed. Reapplying the pump lasers can then release the pulses of light, and due to the coherence of the Bose-Einstein condensate, there may be very little degradation. Research in this field is still young and ongoing.

## References

• S. N. Bose, Z. Phys. 26, 178 (1924)
• A. Einstein, Sitz. Ber. Preuss. Akad. Wiss. (Berlin) 22, 261 (1924)
• L.D. Landau, J. Phys. USSR 5, 71 (1941)
• L.D. Landau, Phys. Rev. 60, 356 (1941)
• M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, Science 269, 198 (1995).
• D.S. Jin, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, Phys. Rev. Lett. 77, 420 (1996).
• M.R. Matthews, B.P. Anderson,P.C. Haljan, D.S. Hall, C.E.Wieman, E.A. Cornell, Phys. Rev. Lett. 83, pp. 2498 (1999)
• S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, Science 302, 2101 (2003)
• M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003)
• C. J. Pethick and H. Smith, "Bose-Einstein Condensation in Dilute Gases", Cambridge University Press, Cambridge, 2004.

03-10-2013 05:06:04