Elements of Modern Physics
230
principle prevents the electrons from having overlapping wave functions. As a
consequence, the force between these atoms is mostly repulsive and the atoms
do not bind. The experiments show that atomic hydrogen with parallel electron
spins, remains a gas at temperatures as low as 0.08 K. One may therefore be
able to observe Bose-Einstein condensation in atomic hydrogen. The critical
temperature at which the condensation takes place depends on the density and
is given by Eq. (7.78). For example, at ρ = 10
24
m
–3
, the predicted critical
temperature is 0.016 K. While the densities of atomic hydrogen achieved in the
laboratory, are as yet not sufficiently high to observe the condensation, they are
only one or two orders of magnitude lower than those at which Bose-Einstein
condensation is predicted to occur. An observation of Bose-Einstein condensation
in atomic hydrogen would be an exciting, unambiguous demonstration of
quantum properties of a collection of bosons.
Superfluidity in neutron stars: There are interesting speculations that
superfluidity may be occurring in neutron stars. Neutron stars are thought to be
the end products of stars whose masses are between 4 M s and 20 M s , M s being
the mass of the sun. They are very dense with an average density of about
10
14
– 10
15
g/cm
3
, have a radius of about 10 km, and are primarily made up of
neutrons. Under suitable conditions two neutrons, which are fermions, may
form weakly-bound states. The bound system which is a boson, may undergo
Bose condensation to become a superfluid. It may be expected that since the
densities of the neutron stars are so large, the transition temperature there would
also be very high.
Bose-Einstein Condensation
In the gas phase, the Bose-Einstein condensate (BEC) remained an unverified
theoretical prediction for many years. In 1995 the research groups of Eric Cornell
and Carl Weiman of JILA, at the University of Colorado at Boulder, produced
the first such condensate experimentally.
Condensation happens when several gas molecules come together and form
a liquid. It all happens because of loss of energy. Gases are really excited atoms.
When they lose energy, they slow down and begin to collect. They can collect
into one drop. Water condenses on the lid of a pot when water is boiled. It cools
on the metal and becomes a liquid again. One would then have a condensate.
If a sufficiently dense gas of cold atoms can be produced without
condensation into liquid state, the matter wavelengths of the particles will be of
the same order of magnitude as the distance between them. It is at that point
that the different waves of matter can ‘sense’ one another and co-ordinate their
230
principle prevents the electrons from having overlapping wave functions. As a
consequence, the force between these atoms is mostly repulsive and the atoms
do not bind. The experiments show that atomic hydrogen with parallel electron
spins, remains a gas at temperatures as low as 0.08 K. One may therefore be
able to observe Bose-Einstein condensation in atomic hydrogen. The critical
temperature at which the condensation takes place depends on the density and
is given by Eq. (7.78). For example, at ρ = 10
24
m
–3
, the predicted critical
temperature is 0.016 K. While the densities of atomic hydrogen achieved in the
laboratory, are as yet not sufficiently high to observe the condensation, they are
only one or two orders of magnitude lower than those at which Bose-Einstein
condensation is predicted to occur. An observation of Bose-Einstein condensation
in atomic hydrogen would be an exciting, unambiguous demonstration of
quantum properties of a collection of bosons.
Superfluidity in neutron stars: There are interesting speculations that
superfluidity may be occurring in neutron stars. Neutron stars are thought to be
the end products of stars whose masses are between 4 M s and 20 M s , M s being
the mass of the sun. They are very dense with an average density of about
10
14
– 10
15
g/cm
3
, have a radius of about 10 km, and are primarily made up of
neutrons. Under suitable conditions two neutrons, which are fermions, may
form weakly-bound states. The bound system which is a boson, may undergo
Bose condensation to become a superfluid. It may be expected that since the
densities of the neutron stars are so large, the transition temperature there would
also be very high.
Bose-Einstein Condensation
In the gas phase, the Bose-Einstein condensate (BEC) remained an unverified
theoretical prediction for many years. In 1995 the research groups of Eric Cornell
and Carl Weiman of JILA, at the University of Colorado at Boulder, produced
the first such condensate experimentally.
Condensation happens when several gas molecules come together and form
a liquid. It all happens because of loss of energy. Gases are really excited atoms.
When they lose energy, they slow down and begin to collect. They can collect
into one drop. Water condenses on the lid of a pot when water is boiled. It cools
on the metal and becomes a liquid again. One would then have a condensate.
If a sufficiently dense gas of cold atoms can be produced without
condensation into liquid state, the matter wavelengths of the particles will be of
the same order of magnitude as the distance between them. It is at that point
that the different waves of matter can ‘sense’ one another and co-ordinate their