Transcript Bose-Einstein Condensation

Bose-Einstein Condensation
PHYS 4315
R. S. Rubins, Fall 2009
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About BEC
• In 1924, Einstein applied Satyendra Bose’s explanation of
blackbody radiation to matter, predicting the phenomenon
known as Bose-Einstein condensation (BEC).
• BEC is a quantum mechanical phase-transition, thought to be
responsible for superfluidity in liquid helium.
• Not until 1995 was it observed in isolated atoms, in 87Rb
(NIST), 23Na (MIT) and 7Li (Rice U.). Since then, BEC has
been observed around the world, and 1H (MIT) and 4He
France.
• Samples typically contain of the order of 105 - 106 atoms, in
which several thousand form the condensate, with transition
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temperatures in the range 300 – 600 nK.
BEC: Scientific Entanglements
BEC belongs to atomic
physics, condensed matter
physics and stat. mech.
It could not have been
produced without the tools
of optics and laser physics,
the manipulation of
magnetism and fluid
dynamics, and the use of
new techniques in low
temperature physics.
BEC is a deep entanglement
of fields, giving rise to a
totally new field of physics.
See Physics Today,
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December 2006
Bosons and Fermions
• Identical particles follow either Bose-Einstein or Fermi-Dirac
statistics.
• Bosons have integer angular momentum quantum numbers
(e.g. photons, atoms with an even no. of neutrons.).
• They have symmetrical wavefunctions;
i.e.; if two particles (1 and 2) are in the states a and b, then
Ψsym = ψa(1) ψb(2) + ψa(2) ψb(1)  ψa(1) ψa(2) if a = b.
• Fermions have half-integer angular momentum quantum nos.
(e.g. electrons, nucleons, atoms with an odd no. of neutrons.).
• They have antisymmetrical wavefunctions;
i.e.; if two particles (1 and 2) are in the states a and b, then
Ψanti = ψa(1) ψb(2) – ψa(2) ψb(1)  0 if a = b.
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Boson and Fermion Gases Below 1 mK
In these Rice University
images of atomic clouds,
those of 7Li (a boson with
4 neutrons) continue to
collapse as the
temperature is lowered.
Since identical fermions
cannot occupy the
same space (the Pauli
exclusion principle), the
atomic cloud of 6Li (a
fermion with 3 neutrons)
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shows a smaller collapse.
BEC Photo from Rice University
• Cloud of about 70,000 7Li atoms, with about 1200 in the BEC peak at
the center, at about 600 nK.
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BEC: a Phase Transition in an Ideal Gas
• Like the ferromagnetic transition at the Curie point of iron
(1043 K), BEC is a phase transition, but unlike the
ferromagnetic transition, which occurs because of the
strong interaction between iron atoms, BEC occurs in an
ideal gas, for which interatomic forces are negligible.
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BEC Atoms: Each in the Same Wave Function
The de Broglie
wavelength λdB = h/mv,
becomes for a quantum
gas
λdB = h/(2πmkT)1/2.
Thus λdB increases as
T is lowered, and a
phase transition to
a BEC state occurs
when λdB reaches the
atomic separation.8
Interference Between BEC Waves
• Like the interference
patterns that may be
produced by the coherent
light from lasers, BEC
waves show interference
phenomena.
• However, unlike laser
beams, which are in nonequilibrium states, a BEC
wave is an equilibrium
state.
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Loading a Magnet Trap for Li7 (Rice U.)
• The apparatus is contained in an ultra-high vacuum at room temperature.
• Hot Li7 atoms, emitted from an oven at 800 K, form an atomic beam.
• The atomic beam is slowed by an oppositely directed laser beam, and
deflected by a second laser beam towards a magnetic and optical trap.
• Another laser beam collimates the deflected atomic beam, and optically
pumps it, so that each atom is in the same magnetic state.
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• Once in the trap, the atomic beam is contained by a set of six laser beams.
Magnetic Trap (Rice U.)
• If the magnetic moment of an atom is parallel to the magnetic field, it will be
attracted to a local minimum of the field, which occurs at the center of the
magnet distribution.
• If the direction of the magnetic moment is reversed, the center of the
distribution becomes a local maximum, which causes that atom to leave.
• The magnetic field at the minimum must not be zero, otherwise the atomic
moments may spontaneously reverse their directions.
• In practice, the field at the minimum was 0.1 T.
• Atoms in the trap may be lost by collisions in which the moment direction
is
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reversed.
Laser Cooling 1
• Laser cooling is achieved by using the Doppler effect to reduce vrms.
• Two opposing laser beams of equal intensity are each tuned to the low
frequency side of an optical transition.
• The beam opposing the atom’s motion is blue-shifted to higher frequencies,
so that the force on it is increased.
• The beam in the same direction as the atom’s motion is red-shifted to12lower
frequencies, so that the force on it is decreased.
Laser Cooling 2
• The net effect of the two opposing laser beams is to reduce
the magnitude of the velocity component of each atom along
the axis of the two beams.
• Three orthogonal pairs of lasers are used to slow the
motions of atoms moving in all directions.
• Using laser cooling for Rb87, the NIST group in Boulder,
achieved temperatures of 10 μK, which are still ten to a
hundred times too high for observing BEC.
• The effect of reducing vrms on the temperature of the sample
may be calculated using the equipartition theorem; i.e.
½ mvrms2 = (3/2)kT.
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Evaporative Cooling 1
• This method is analogous to the cooling of a hot liquid by evaporation.
• The fastest moving atoms move furthest from the minimum, to a position of
highest energy (see the upper atom shown in the figure).
• Magnetic resonance is used to reverse the moments of the most energetic
atoms, causing them to leave the trap, which is now an energy maximum.
• Slowly reducing the radio frequency removes progressively cooler atoms.
• At the end, only about 1% of the atoms remain in the trap, and the
temperature is reduced by a factor of about 100, giving a temperature14of the
order of 100 nK.
Photographing the Condensate (NIST) 1
False color images show the velocity distribution just before the appearance of
BEC (right), just after it (center), and for a nearly pure condensate (right).
To increase the sample size, the magnetic trap is turned off.
The excited- state (thermal) atoms move out faster, leaving the condensate
near the center of the trap.
These photographs were taken after the atoms had moved for about 0.05 s.
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The thermal cloud is almost circular, while the condensate cloud is elliptical.
Photographing the Condensate (NIST) 2
• The right frame has a horizontal dimension of 40 – 50 μm, equivalent to
about 1500 atoms forming a single wave.
• The shape of the peak is related to the elliptical shape of the trap, giving a
vivid demonstration of the uncertainty principle pxx  ħ.
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• The temperature within the condensate may be of the order of 1 nK.