"The Alternate View" columns of 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 360^{o} rotation. Therefore, all quantum systems
unaffected by a 360^{o} 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 360^{o}, but only when it is rotated by twice
360^{o} or 720^{o}. 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 360^{o}
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 360^{o} 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 ^{87}Rb (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 10^{17} 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.

*Magnetic Quadrupole Trapping:*W. Petrich, M. H. Anderson, J. R.
Ensher, E. A. Cornell, Phys. Rev. Lett.

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

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