BOSE EINSTEIN CONDENSATE

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BOSE EINSTEIN CONDENSATE Submitted by
Brijesh Bhayana

• Contents
• What is a BE condensate
• Formation of the condensate magnetic trapping
  and laser cooling
• Statistical mechanics of BE condensate

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What is BE condensate?
At normal temperatures, atoms are in many
different energy states, However, at very low
temperatures, according to Einsteins equations,
many atoms go the the lowest quantum energy
state. Atoms being non distinguishable, form
collapse to form a giant Wave function.
Cold atoms
BE Condensate
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The first BE condensate was realized in 1995 for
dilute alkali atom gases at MIT. A typical BE
condensate is composed of neutral alkali gas
atoms with total number, N , of atoms ranging
from few hundred to about 1010. Their
densities range from 1011/cm3 to 1015/cm3 and
their temperature ranges from 10-9 Kelvin to
10-6 K. At these low temperatures and
densities, normally the atoms would solidify,
but solidification is a 3 body interaction
process, that are rare, and the condensate can
exist for from few seconds to few minutes before
solidification.
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Laser cooling and magnetic trapping
Laser cooling pioneered by Cohen - Tannoudji and
Chu and instrumental in achieving BE condensate.
The basic principle of laser cooling is quite
simple atoms loose momentum on
interacting photons hitting them from the
opposite side. The hard part is to get
the photons of right frequency because of the
Doppler shift seen by moving atoms.
Laser
atoms absorb photon in s-gtp transition and loose
momentum.
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Magnetic Trapping
Helmholtz coils are used to create a harmonic
oscillator type magnetic potential.The atoms,
due to their spins, are confined to the local
minimum of the magnetic field.
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Trapping and cooling
The experimental setup consists of Helmholtz
coils and opposing laser beams. The atoms are
first cooled by interaction with the
laser followed by evaporative cooling. In
evaporative cooling, the height Of the magnetic
trap is decreased so that the atoms with
highest energy escape.
high energy atoms
Low energy atoms
Before evaporative cooling
After evaporation
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Statistical Consderation
At temperature T, the mean number n of the
particles in Energy eigenstate i has the formula
(Chemical potential is fixed by the summation)
The chemical potential is very large and negative
for high T. BEC is realized at a temperature
below Tc, when µ ?0
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The transition temperature Tc can be
exactly Calculated as a function of N. For a 3D
anisotropic trap potential, it has been derived
to be
For a non interacting gas in any geometry in
which BEC Occurs, the the condensate number
increases smoothly as Temperature falls to 0. For
a 3D trap one finds
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In addition to the effect of statistics, there is
also an energetic effect In dilute Bose gas with
weakly repulsive interactions, the
interactions Tend to reinforce the effects of
statistics in forming the BEC. Greater the
interactions, bigger the tendency to form the
condensate.
Some characteristic energies (in temp units) of a
BEC condensate
Energy of ns-gtnp transition
104 K Zero field hyperfine splitting
0.3 K Charateristic 2 body
energy 0.3
mK Transition temperature (KT)
500 nK Mean field energy (nUo)
100 nK Zero point energy
in harmonic well 5 nK
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• Conclusions
• BE condensate was achieved for alkali (Na, Rb)
  atoms
• as they have spin 1.
• 2) The number of atoms in the condensate was in
• agreement with the value predicted by the Bose
  Einstein
• statistics.
• 3) The temperature of the condensate was of the
  order of
• nano Kelvin.
• 4) The condensate was stable upto few minutes.
• 5) The condensate had a Gaussian density
  distribution.
• 6) The momentum of the condensate was not zero
  was confirmed
• by expansion experiment.

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REFERENCES
3) Fetter, A. L., 1999, in Bose-Einstein
Condensation in Atomic Gases, International
School of Physics "Enrico Fermi" Course 140,
edited by M. Inguscio, S. Stringari, and C. E.
Wieman (IOS Press, Amsterdam). 4)
Huang, K., 1987, Statistical Mechanics, 2nd
edition (Wiley, New York).