A Brief Introduction to Bose-Einstein Condensation

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A Brief Introduction to Bose-Einstein
Condensation
??????????? ??? (July 29, 2003, NCTS)
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gas
solid
Phases of matter
liquid
The fifth phase?
BEC
The coldest and the most fragile matter ever
found in the universe
plasma
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The shape of the radiation spectrum of an ideal
blackbody (Planck, 1900)
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For any given temperature T, a black-body absorb
all the thermal radiation incident upon its
surface and emit thermal radiation with the same
spectrum at the same temperature.
An ideal black-body can be modeled by a cavity
inside a body connected by a small hole to the
outside. Thus the problem of black-body radiation
is equivalent to the problem of thermal radiation
in a cavity.
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discrete energy packet (quantum)
equi-partition of energy among cavity modes
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Bose-Einstein statistics (1924-1925)
In 1924, S.N. Bose rederived the Planck formula
by considering the cavity radiation as an ideal
photon gas. The photons are indistinguishable so
that the exchange of two photons in one energy
cell (see the following figure) does not lead to
a new state.
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Einstein generalized Bose statistics to the
systems containing fixed number of atoms and
claimed the existence of a macroscopically
occupied ground state (the so-called
Bose-Einstein condensation.)
Schematic diagram of the Bose-Einstein
distribution for a system of particles at a
temperature T.
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Some remarks on BEC (homogeneous)
1. condensation in momentum space
2. occurs even in the absence of inter-particle
interactions
3. phase coherence of the condensate (broken U(1)
symmetry)
4. critical phase-space density
5. no BEC in 1-D and 2-D
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??1/2
?????(spin angular momentum)
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Spin-statistics Theorem
All particles with integer spin are bosons (???),
and all particles with half-integer spin are
fermions (???).
field quantum photon, pion, graviton, gluon,...
bosons
composite boson 4He, 23Na, 87Rb,...
Total Spin Nucleon Spin Electron Spin ?All
atoms with an even number of neutrons are
bosons ?75 of the atoms in the periodic table
are bosons