Bose–Einstein condensate

A Bose–Einstein condensate is a phase of matter formed by bosons cooled to temperatures very near to absolute zero. The first such condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder, 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, at which point quantum effects become apparent on a macroscopic scale.

Introduction

Condensates are extremely low temperature fluids with properties that are currently not completely understood, such as spontaneously flowing out of their container. The effect is the consequence of quantum mechanics, which states that systems can only acquire energy in discrete steps. Now, if a system is at such a low temperature that it is in the lowest energy state, it is no longer possible for it to reduce its energy, not even by friction. Therefore, without friction, the fluid will easily overcome gravity because of adhesion between the fluid and the container wall, and it will take up the most favorable position, i.e. all around the container.

Theory

The slowing of atoms by use of cooling aparati produces a singular quantum state known as a Bose condensate or Bose–Einstein condensate. This phenomenon was predicted in 1925 by Albert Einstein, by generalizing Satyendra Nath Bose's work on the statistical mechanics of (massless) photons to (massive) atoms. (The Einstein manuscript, believed to be lost, was found in a library at Leiden University in 2005.) The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose-Einstein statistics, which describes the statistical distribution of identical particles with integer spin, 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.

This transition occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:

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

where:

$T_c$	is	the critical temperature,
$n$		the particle density,
$m$		the mass per boson,
$h$		Planck's constant,
$k_B$		the Boltzmann constant, and
$\zeta$		the Riemann zeta function; $\zeta(3/2)$ ≈ 2.6124.

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 2.17 kelvins (K) (lambda point). Superfluid helium has many unusual properties, including zero viscosity (the ability to flow without dissipating energy) 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, Wieman and Ketterle (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 theory of Bose–Einstein condensation must be heavily modified in order to describe it.

The first "true" Bose–Einstein condensate was created by Eric Cornell, Carl 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 below 170 nK 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 Bose–Einstein condensation also applies to quasiparticles in solids. A magnon in an antiferromagnet carries spin 1 and thus obeys the Bose–Einstein statistics. The density of magnons is controlled by an external magnetic field, which plays the role of the magnon chemical potential. This technique provides access to a wide range of boson densities from the limit of a dilute Bose gas to that of a strongly interacting Bose liquid. A magnetic ordering observed at the point of condensation is the analog of superfluidity. In 1999 Bose condensation of magnons was demonstrated in the antiferromagnet TlCuCl3 by Oosawa et al. The condensation was observed at temperatures as large as 14 K. Such a high transition temperature (relative to that of atomic gases) is due to a greater density achievable with magnons and a smaller mass (roughly equal to the mass of an electron).

Unusual characteristics

Further experimentation by the JILA team in 2000 uncovered a hitherto unknown property of Bose–Einstein condensate. Cornell, Wieman, and their coworkers originally used rubidium-87, an isotope whose atoms naturally repel each other making a more stable condensate. The JILA team instrumentation now had better control over the condensate so experimentation was made on naturally attracting atoms of another rubidium isotope, rubidium-85 (having negative atom-atom scattering length). Through a process called Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, the JILA researchers lowered the characteristic, discrete energies at which the rubidium atoms bond into molecules making their Rb-85 atoms repulsive and creating a stable condensate. The reversible flip from attraction to repulsion stems from quantum interference among condensate atoms which behave as waves. When the scientists raised the magnetic field strength still further, the condensate suddenly reverted back to attraction, imploded and shrank beyond detection, and then exploded, blowing off about two-thirds of its 10,000 or so atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not being seen either in the cold remnant or the 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. Due to the fact that supernovae explosions are implosions, the explosion of a collapsing Bose–Einstein condensate was named "bosenova."

The atoms that seem to have disappeared are almost certainly still around in some form, just not in a form that could be detected in that current experiment. Two likely possibilities are that they have formed into molecules consisting of two bonded rubidium atoms, or they received enough energy from somewhere to fly away fast enough that they are out of the observation region before being observed.

Current research

Compared to more commonly-encountered states of matter, Bose–Einstein condensates are extremely fragile. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, forming a normal gas and losing their interesting properties. It is likely to be some time before any practical applications are developed.

Nevertheless, they have proved to be 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 explosion 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 slowing of light pulses to very low speeds using electromagnetically induced transparency ^*." target="_blank" >Experimentalists have also realized "optical lattices", where the interference pattern from overlapping lasers provides a periodic potential for the condensate. These have been used to explore the transition between a superfluid and a Mott insulator [http://qpt.physics.harvard.edu/qptsi.html, and may be useful in studying Bose–Einstein condensation in less than three dimensions, for example the Tonks-Girardeau gas.

Bose–Einstein condensates composed of a wide range of isotopes have been produced ^*.

Related experiments in cooling fermions rather than bosons to extremely low temperatures have created degenerate gases, where the atoms do not congregate in a single state due to the Pauli exclusion principle. To exhibit Bose–Einstein condensate, the fermions must "pair up" to form compound particles (e.g. molecules or Cooper pairs) that are bosons. The first molecular Bose–Einstein 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 ^*.

External links

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
The Bose–Einstein Condensate at Utrecht University, the Netherlands
Alkali Quantum Gases at MIT
Atom Optics at UQ
Einstein's manuscript on the Bose–Einstein condensate discovered at Leiden University
The revolution that has not stopped PhysicsWeb article from June 2005

References

S. N. Bose, Z. Phys. 26, 178 (1924)
A. Einstein, Sitz. Ber. Preuss. Akad. Wiss. (Berlin) 1, 3 (1925)
L.D. Landau, J. Phys. USSR 5, 71 (1941)
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C. J. Pethick and H. Smith, "Bose–Einstein Condensation in Dilute Gases", Cambridge University Press, Cambridge, 2001.
Lev P. Pitaevskii and S. Stringari, "Bose–Einstein Condensation", Clarendon Press, Oxford, 2003.
Mackie M, Suominen KA, Javanainen J., "Mean-field theory of Feshbach-resonant interactions in 85Rb condensates." Phys Rev Lett. 2002 Oct 28;89(18):180403.
Oxford Experimental BEC Group. http://www-matterwave.physics.ox.ac.uk/bec/bec.html

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