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Bose-Einstein Condensation, A New Form of Matter

by John G. Cramer

Alternate View Column AV-77
Keywords: boson fermion quantum statistics Bose-Einstein condensate rubidium laser trap
Published in the March-1996 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 8/30/95 and is copyrighted ©1995 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

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The fundamental particles of physics come in two distinct quantum personality types: the individualistic fermions and the group-oriented bosons. Fermions have half-integer spins and exhibit the territorial behavior described by the Pauli exclusion principle, with only one particle allowed in each quantum state. Bosons, on the other hand, have integer spins and tend to congregate together, piling up many particles in the same quantum state.

The "groupie" tendency of bosons has recently been demonstrated in a breakthrough experiment by Carl Wieman of the University of Colorado and Eric Cornell of the National Institute for Standards and Technology and their group. They were able to cool a gas of rubidium-87 atoms to a temperature so low that thousands of atoms coalesced into the same quantum state, forming a new state of matter called a Bose-Einstein condensate (BEC). This column is about that work.

To understand what Bose-Einstein condensation is, we need to discuss the quantum mechanics of spin. When a massive object spins like a top or orbits like a planet, it is described in physics as having angular momentum. Angular momentum is said to be conserved because it can only be gained or lost under the influence of external forces. For example, in our solar system it is angular momentum conservation that keeps the planets in their orbits, each orbit having a definite and nearly constant angular momentum.

In quantum mechanics the angular momentum of a system is encoded in the system's quantum wave function. Consider for example an atom that has a certain definite angular momentum and wave function. Now suppose that this atom is slowly rotated through 360 degrees and brought back to the same orientation. Common sense tells us that the rotated atom is indistinguishable from the original atom and its wave function after the 360 degree rotation should be the same as the original un-rotated wave function.

However, setting the rotated and unrotated wave function equal leads to a remarkable result: only atoms (and systems in general) having an angular momentum that is an integer multiple of h/2pi (Planck's constant h = 6.626 x 10-34 Joule seconds and pi = 3.14159...) will return to the same state after a 360o rotation. Therefore, all quantum systems unaffected by a 360o rotation must have angular momentum only in integer units of h/2pi. This is called the quantization of angular momentum, and it is one of the most fundamental results of quantum mechanics.

Angular momentum quantization, when it emerged from the first formulations of quantum mechanics in the mid-1920's, was a very satisfying result that went a long way toward convincing physicists of the validity of the quantum formalism. This was because a decade earlier angular momentum quantization had been an ad hoc assumption used by Neils Bohr in formulating what became the famous Bohr model of the atom. The new quantum mechanics revealed principles that were the underpinning for Bohr's assumption.

The satisfaction did not last long. In the 1930's it was discovered that electrons violated angular momentum quantization. Electrons were found to have an irreducible angular momentum, called spin, of 1/2 an h/2pi unit. The electron, behaving like a tiny top that cannot be stopped from spinning, is said to be a "spin 1/2 particle". This means that the wave function of an electron does not come back to the same quantum state when it is rotated by 360o, but only when it is rotated by twice 360o or 720o. The same is true for protons, neutrons, and other spin 1/2 particles.

In other words, the world you view after turning your body by 360o is not the same world as before your rotation. All spin 1/2 particles in the universe will have the algebraic signs of their wave functions reversed by your action. You have to make another 360o rotation to put the world back the way it was. There are few directly observable effects of this sign reversal, but it is nevertheless a bizarre and counter-intuitive result. We have no idea where these half integer spins come from or why most fundamental particles have them, yet they do.

Our world is made of particles, some with half integer spins and others with integer spins. Quarks and leptons, plus composite particles like protons, neutrons, and many nuclei and atoms all have half-integer spins. The integer spin particles include the force-producing exchange particles like photons, gluons, and the Z and W weakons, plus many composite particles such as mesons, nuclei, and atoms in which the half-integer spins of the components cancel or add to integer spins. The integer spin particles are called bosons because the statistics of their behavior in groups is governed by Bose-Einstein statistics, as first described by S. N. Bose and Albert Einstein. The half-integer spin particles are called fermions because the statistics of their behavior in groups is governed by Fermi-Dirac statistics, as first described by Enrico Fermi and Paul Dirac.

Fermions are highly territorial individualists. If one fermion is in a particular quantum state, then all other fermions are excluded from that state, resulting in the Pauli exclusion principle. In a universe where electrons were bosons rather than fermions, no life would be there to worry about it. Bosonic electrons around atoms, instead of forming into "shells" providing the outer valence electrons that make chemistry work, would pile up together in the most tightly bound inner atomic orbit, making chemistry and also life impossible. We owe our very existence to the Fermi-Dirac statistics of electrons.

Bosons, on the other hand, are gregarious groupies. If one boson is in a particular quantum state, all other bosons are "invited in" to share the same state. The more bosons that pile into the state, the stronger becomes the tendency for others to join them. In such a state, a very large number of particle will have a single quantum wave function. This is what is called a Bose-Einstein condensate. It is a new state of matter because, although predicted, it has never before been observed in an atomic system.

The grouping-tendencies of bosons are responsible for many interesting, important, and quite counter-intuitive phenomena. The laser, for example, operates because photons from atomic transitions "invite" other photons to join their state as they move past, triggering an avalanche of atomic transitions and forming a beam of coherent photons in the same quantum state through the Bose-Einstein process called stimulated emission. Superconductivity is possible because bosonic pairs of spin correlated electrons move through the superconductor, inviting other pairs of electrons to join their state. Liquid helium is a superfluid because helium atoms are bosons and their tendency to group in the same state produces unusual fluid properties. The Hanbury-Brown-Twiss effect, with which photons are used to measure the sizes of nearby stars and pi-mesons to measure the sizes of fireballs from ultra-relativistic heavy ion collisions (one of my areas of research), is based on the tendency of photons (spin = 1) and pi-mesons (spin = 0) to group together in the same momentum state.

Up to a few months ago, despite these well-studied phenomena which depend on the grouping tendencies of bosons, the goal of producing a true Bose-Einstein condensate in a gas had eluded experimental physicists. The laser involves photons, not atoms. Superconductivity involves a few pairs of electrons interacting at relatively large distances. Superfluidity involves very closely packed and strongly interacting helium atoms, with Bose-Einstein behavior and strong scattering interactions fighting for dominance. To produce a BEC, a gas of weakly interacting bosonic molecules must be cooled to an ultra-low temperature at which the deBroglie wavelength of the molecules becomes larger than their mean spacing. The problem has been reaching such a temperature. Since the deBroglie wavelength is inversely proportional to the square root of the temperature and molecule spacing grows with temperature, a BEC can only form at a temperature below 170 nano-Kelvin (or 1.7 x 10-7 K, 170 billionths of a Celsius degree above absolute zero).

Wieman and Cornell were able to produce a Bose-Einstein condensate of supercooled 87Rb (rubidium-87) atoms. Rubidium is an alkali metal from the first column of the periodic table, an atom that has a spin of 1/2 in its electron shell structure and is therefore not an obvious candidate for BEC production. However, when a gas of rubidium atoms is placed in a strong magnetic field, all spins line up and adjacent atoms combine to form spin 1 molecules that behave as integer-spin bosons.

To achieve the low temperatures needed, Wieman and Cornell used a combination of laboratory techniques: laser trapping and cooling, time-dependent magnetic trapping, and evaporative cooling. They optically trapped a gas of a few million rubidium atoms, holding them in place with an "optical molasses" of crossed laser beams. The laser frequencies were tuned to be just below the frequency of an atomic resonance for rubidium atoms. The frequency is too low for atoms at rest to absorb the laser light. Only the most rapidly moving atoms, when moving toward a laser beam, could be boosted by the Doppler shift to absorb the light. Thus the laser cooling technique selectively picks out the "hot" atoms and slows them down. This process was used to bring the gas of rubidium atoms down to a temperature of about 10-5 K. When this temperature was reached, a magnetic trap was switched on around the atoms and the trapping laser beams were switched off.

This magnetic trap, made with a pair of loop coils above and below the clustered atoms with oppositely directed currents, produced a "quadrupole" field that interacted with the aligned spins of the atoms to hold them in place. There is a fundamental problem, however, with a magnetic trap of this kind: it has a hole in the bottom. At the very center of the quadrupole field the magnetic field drops to zero, and there the coolest atoms can lose their spin alignment and leak out of the trap. Cornell solved this problem by adding additional coils that "stirred" the quadrupole field, moving the zero point away from the trap's center so that it circulated at the periphery of the cloud of trapped atoms in what the experimenters called "the orbit of death". As long as the atoms did not wander into the orbit of death, they remained trapped with no leaks.

Within the trap, the atoms cooled further by evaporation, with the hottest atoms escaping the trap while the cooler ones stayed behind. The cumulative effect of this process produced temperatures below 10-7 K, and the Bose-Einstein condensate formed. The problem then was to demonstrate that this had happened, since the BEC itself, because it is in a single quantum state, is too small to provide a direct optical image. Wieman and Cornell solved this problem by switching off the trap and watching the cloud of atoms as it expanded until it reached a size that could be imaged. They found that it expanded much slower than would any ensemble that was not in the same quantum state, and that the image was elliptical, characteristic of the orientation of the particular quantum state that had produced it. These observations provided overwhelming evidence for the first production of a Bose-Einstein condensate. One remarkable aspect of this work is the low cost of the "tabletop" apparatus used, only about $50,000 for an experiment that will probably earn its participants a Nobel Prize.

Finally, since this is a science fiction magazine, let's consider the SF aspects of this work. What is the story potential of this new technique for producing Bose-Einstein condensate? The BEC is interesting first because many atoms occupy precisely the same quantum state. This has implications for lasers, for energy storage and release, for many types of coherent behavior by a large ensemble of atoms.

Another aspect of the BEC is its small size. The size of a BEC of any number of atoms is the same as the size of one atom in the same state. This means that BEC has implications for producing ultra-compact matter. The BEC is a closet for storing atoms that is never full. In fact, the more atoms that have been stored in the BEC, the stronger is the tendency for more atoms to join them, and the strength of this "pull" increases as the factorial of the number of atoms in the condensate. The BEC is so compact and dense that, with sufficient atoms added, a mini-black hole of atomic size should form. Readers of David Brin's Earth and Larry Niven's "Hole Man" should be familiar with some of the implications of this.

The use of a BEC to produce a black hole in the laboratory is not likely in the near future, however. An isolated rubidium atom has an atomic radius of 3 x 10-10 meters, so a BEC of rubidium atoms should be about the same size. The mass of rubidium needed to form a black hole of this size would be 2 x 1017 kilograms, about 20 times the mass of Mars' largest moon Phobos. The BEC of Wieman and Cornell contained only a few thousand atoms of rubidium. The first BEC is a long way from any danger of black hole formation.

References:

Laser Trapping and Cooling:
C. Wieman and S. Chu, eds., J. Opt. Soc. Am. B 6, #11 (1989).

Magnetic Quadrupole Trapping:
W. Petrich, M. H. Anderson, J. R. Ensher, E. A. Cornell, Phys. Rev. Lett. 74 3352 (1995).

First Observation of a Bose-Einstein Condensate:
M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269 198 (1995).


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This page was created by John G. Cramer on 7/12/96.