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Atlanta
(December 2, 2004) — Researchers at the Georgia Institute
of Technology have unveiled a fundamental change in
the properties of matter. The theoretical finding,
that bosons placed in two-dimensional harmonic traps
will crystallize when the strength of their repulsive
interactions is increased, appears in the December
3 issue of the journal Physical Review Letters (volume
93, article 230405, 2004).
One
of two categories of elementary particles, bosons
typically form cloudy aggregates called Bose-Einstein
condensates when cooled to temperatures near absolute
zero. In the condensate, the particles may be pictured
as sitting on top of one another, occupying the same
space.
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Uzi
Landman and colleagues propose that the elementary
particles known as bosons will act like their subatomic
counterparts and crystallize when placed in two-dimensional
traps.
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that’s only when their interactions are relatively weak,
said Uzi Landman, director of the Center for Computational
Materials Science, Regents’ professor and Callaway chair
of physics at Georgia Tech. "When
the repulsive interaction between the bosons is increased,
they separate and instead of forming a condensate
they crystallize, acting more like their counterpart
fermions. Experimentally, such behavior was shown
this year to happen in one-dimension, now we predicted
theoretically that it will happen in two-dimensions.
Furthermore, through a straightforward extension of
our method one could easily extend it to three-dimensions,”
he said.
In
quantum physics, all elementary particles such as
quarks, electrons and gluons are classified as either
fermions or bosons, depending on their spin. The spin
of bosons takes integer values and fermions have half-integer
values of their spin. Electrons and quarks –two examples
of fermions – are the basic building blocks of matter,
while bosons such as photons and gluons govern the
fundamental forces of nature such as electromagnetism.
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In
1960 it was theoretically predicted by Marvin Girardeau,
now at the University of Arizona, that in one-dimensional
space, bosons would act more like fermions and form
a lattice if their repulsion became sufficiently strong.
It took more than 40 years for experimental physicists
to test the theory, but recently two different groups
of scientists published articles in Science and Nature
verifying the theory, using experiments carried out
on trapped bosons.
Now,
Landman, his colleague Constantine Yannouleas, and
graduate student Igor Romanovsky, discovered, through
theoretical modeling involving computer-based simulations
of up to seven bosons in a harmonic two-dimensional
trap, that instead of clumping together to form Bose-Einstein
condensates, the bosons localize in space forming
polygonal crystals. For example, six bosons crystallize
into a two-dimensional pentagon-shaped crystal with
one boson in the center. “The forces between the bosons
are repulsive,” said Landman. “The trap is the only
thing holding them together. As soon as you release
the trap, the crystal goes away.”
Landman
and Yannouleas do not think that it will take another
40 years for experimental physicists to test the theoretical
prediction. “Now that people know how to make Bose-Einstein
condensates, use traps, and vary the strength of the
interactions, testing could be done faster,” Landman
explained.
As
for potential applications of this research, Landman
notes that “the main merit of this research is in
increasing our fundamental understanding of nature
and of the processes underlying physical behavior
under certain extreme conditions”. “Nevertheless,”
he adds, “out of such basic scientific contributions
other things may develop, for example in the area
of quantum computing – you just have to wait and see.”
In
the 1920s Indian physicist Satyendra Nath Bose and
Albert Einstein predicted that atoms cooled to temperatures
close to absolute zero would collapse to their lowest
quantum state, forming a state of matter that became
known as the Bose-Einstein condensate. It wasn’t until
1995 that physicists in Boulder, Colorado, and at
MIT were successful in creating the condensate. And
in 2001, Eric Cornell, Wolfgang Ketterle and Carl
Wieman were awarded the Nobel Prize in Physics for
this achievement.
Graph Captions
Theoretical simulations of six harmonically trapped
bosons. (a) The density of a Bose-Einstein condensate
formed for weak repulsive interactions. (b) The density
distribution of the symmetry-broken crystalline solution
that is predicted to form for stronger repulsive interactions.
(c) Density distribution of the symmetry-restored
state, showing overall circular symmetry. (d) Conditional
probability map, with the reference point located
on one of crystalline sites (marked by a black dot),
illustrating a predicted pentagonal lattice with one
boson at the center. Distances are in units of L0
which is determined by the characteristic harmonic
frequency of the trap, and the effective mass of the
bosons.
Related
Links
Uzi Landman
http://www.physics.gatech.edu/people/faculty/ulandman.html
Georgia
Tech School of Physics
http://www.physics.gatech.edu/
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