22. MACROSCOPIC QUANTUM SYSTEMS
Although unfamiliar to most people, the laws of Quantum Mechanics – Schrödinger's
Equation expecially – have important consequences for us all. they describe,
for instance, why all atoms do not simply self-destruct. Important indeed! Nevertheless,
when these atoms are clumped together into large mass, their motion is seemingly
governed by the simpler rules of Newton. DeBroglie wavelength are so incredibly
small that the probabilistic nature of position and velocity measurements is
unnoticable. After all, the reason the laws of quantum mechanics seem so strange
to us is they are unnoticable in our everyday lives.
There are several situations, however, wherein quantum behavior is evident at
the macroscopic level. They are, in the order of their discovery, superconductivity,
superfluidity, and the Bose-Einstein condensate. They occurs in conditions which
are far from "everyday", but they are interesting nonetheless, for
what they tell us about the nature of matter. And superconductivity, especially,
does hold promise of future important inductrial and technological applications.
(a) SUPERCONDUCTIVITY
History, promise, and theory. Demo.
(b) SUPERFLUIDITY
(c) BOSE-EINSTEIN CONDENSATE
You have no doubt heard something about the various states of matter in some
science class or other. A given material may exist as a solid, a liquid, a
gas or a plasma, depending in the temperature. Recall that temperature is really
just a measure of the average kinetic energy of the atoms of a material. If
those atoms are moving so fast that, when they bash into each other, electrons
are knocked free, that is a plasma. A hot mixture of positive ions and free
electrons, plasmas exhibit interesting behavior when they encounter a magnetic
field., because the magnetic field exerts Lorentz forces on the moving charged
particles of the plasma. The Sun is a ball of plasma, 5800 K at the surface,
15,000,000 K at the center. The solar wind (mostly ionized hydrogen, that is,
protons and electrons) flowing outward from the Sun is also a plasma; when
it encounters Earth's magnetic field, it is funnelled towards the polar regions,
forming the aurora borealis and aurora austalis when the charged particles
collide with the atmosphere and cause air molecules to radiate light. Although
hot and similar in appearance to a plasma, an ordinary fire from a gas stove
burner, candle, or match is not a plasma. ???
At lower temperatures, the atoms are moving about vigorously, but less so.
When they collide the attraction between positive nucleus and negative electrons
is sufficient to keep the electrons bound to the atom. This is a simple gas.
At cooler temperatures, the atoms condense into a liquid. At even colder temperatures,
forces beween the atoms are sufficiently strong to hold them in place relative
to each other – the material solidifies, becomes a solid. The atoms line
up in a regularly repeating matrix structure, called its crystal structure.
For most materials, the transition from gas to liquid occurs at a very specific
temperature, called the boiling point. For water, this is of course 100.0°C
(at standard atmospheric pressure); but it is different for other materials:
-269°C for helium, -196°C for nitrogen, 2750°C for iron. The transitions
from plasma to gas, and liquid to solid also occur at very specific temperatures.
A change from one state to another is called a phase transition, and this property
of occuring at a precise temperature is characteristic of phase transitions.
An example of a different kind of phase transition is the Curie point of magnetic
materials. Magnets maintain their magnetization only at low temperatures. When
heated, they lose their magnetization at a particular temperature, which depends
on the exact material the magnet is made of.
The "melting" of glass is not a phase transition. As you heat glass,
it gets softer and softer gradually, not at any particular temperature. This
is because glass at room temperature is not a solid at all, but rather a liquid
of very high viscosity. Heating lowers its viscosity, just like pancake syrup,
which flows more easily when hot than when cold.
In 1924 Albert Einstein, continuing work begun by Satyenda Nath Bose, predicted
that at extremly low temperatures certain atoms would "condense",
forming a new state of matter. (Be careful here: the word 'condense' in this
context has nothing to do with the phase transition between gas and liquid – the
word was reapplied to this new situation by analogy.) The certain atoms concerned
are any with integer spin – that is, with spin quantum number of 0 or
1 or 2... Any particle with integer spin is called a boson; particles with
half-integer spin (e.g. ) are called fermions. Protons and neutrons are bosons,
with spin 1; the nucleus of any atom will always, therefore, have integer spin.
A whole atom, though, might not – electrons are fermions with spin .
If there is an unpaired electron somewhere in the cloud surrounding the nucleus,
the atom as a whole will be a fermion. Einstein's prediction applies only to
those atoms for which this is not the case.
Einstein's prediction was based on the following chain of reasoning: as a group
of atoms is cooled, they slow down. As a result, their deBroglie wavelengths
h/p get longer, because the momentum p is less. If the wavelengths spread to
be longer than the average separation between the atoms, that means they are
overlapping and subject to inteference like all waves. Those waves out-of-phase
with each other destructively intefere; those in-phase constructively interfere
and become, essentially, a single wavefunction. This is much like what happens
with light waves in the resonant cavity of a laser. The atoms lose their individual
identity. Instead of many atoms, there is only one 'particle' with mass equal
to the total mass of the atoms that blurred together to form it.
This Bose-Einstein Condensate (BEC), as it came to be called, remained only
a theoretical curiosity until 1980 or so, because the temperatures needed to
create a BEC were fractions of a microkelvin. Temperatures this close to absolute
zero were simply unreachable until then. Several teams began working on the
goal around the same time. Success came first, on 5 June 1995, to a group lead
by Eric Cornell and Carl Wieman at the National Institute of Standards and
Technology and the University of Colorado, in Boulder .
They combined just about every cooling technique available, and invented one
new one to achieve a record temperature of 20 nK with a sample of several thousand
atoms. they used Rubidium-87 as their sample (electron shell structure ) ???
There's a lot of interesting physics in the cooling techniques they used, so
it's worth looking at them in a little detail:
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