Bose Einstein Condensation is the name for the behavior of bosons
as they reach very low temperatures and begin to occupy the lowest
quantum states; such behavior is impossible for fermions (note the
Pauli exclusion principle!). To observe the 'quantum clustering' of
bosons (a term I coined and felt descriptive of the cooling process),
they must be cooled. One method for achieving temperatures low enough
is called laser cooling.
Laser cooling utilizes laser beams to
lower the temperature of a dilute atomic gas. Because the temperature
of any material is a measure of the average kinetic energy of the
atoms, we know from chemistry that
KE
(average) = 1/2 m v 2 = 3/2 K T
To cool
the gas, a velocity -dependent force must be applied to the
atoms. Light can supply this force to the atoms in the form of photons
for absorption. However, this can happen only if the photons carry a
quanta of energy that corresponds exactly to an electron transition in
the atoms; namely,
E = h f
When photons are
absorbed, the energy of the atom is raised from the ground state to an
excited state. When the atom decays back down to its ground state, it
releases a photon. By the conservation of momentum, the atom will feel
a force equal in magnitude and opposite in direction to that of the
released photon (much like how the radiation pressure/refractile
properties for optical tweezers!). According to literature, "the net
force on a group of atoms will average to zero because the direction
in which the photon is released in random." This seems like a highly
Heisenburg-esque statement - how do you equate randomness with net
position change? Heisenburg is the only explanation I can think
of...but getting back to the velocity-dependent force - the candidate
is the Doppler Effect, mathematically represented as: f' = fo (1 + v/c)
From this equation,
it's clear that an atom moving towards a laser will see the light
blue-shifted (higher frequency). Because the energy of a photon is
related directly to frequency, the atom will -allegedly- feel a
greater force from the laser and be decelerated. Thus, the laser must
be 'red-detuned' to the atom's energy transition. This is perfect for
the idea of a velocity dependent force: atoms with very little
velocity will not 'feel' the Doppler force, while atoms with high
velocities will 'see' the light closer to the energy transition, and
have a higher probability of absorbing the photon (and later decaying
and releasing a photon, thus effectively decreasing the average
kinetic energy of the collection of atoms). A region of atoms
that are confined and cooled by six laser beans in three dimensions is
commonly known as optical molasses. Once the atoms are cooled,
they must by trapped so that they will not wander out of the vicinity
of the cell due to the random collisions (I hear a call for optical
tweezers!). Trapping requires a position-dependent (or restoring)
force, and Zeeman splitting with polarized light is the phenomenon
that allows for trapping of cooled atoms. Zeeman splitting states that
when an atom is under a magnetic field B, the quantum energy levels of
its electrons split:
Δ E = u m B,
where
u
= Bohr Magneton
m = 1, 0, -1 (magnetic quantum number)
B =
magnetic field
Because a circularly polarized photon has angular
momentum, LH or RH polarization dictate the specific transition that
it can make (either m = 1 or m = -1). Thus, if a magnetic field varies
lineraly as a function of distance from the center of the cell, x,
then
B = A x
This tells us that an atom far from
the center of the cell will have a large magnetic field imposed on it,
and consequently, there will be a significant splitting of its energy
transitions. One energy transition will be closer to the energy of the
laser photons (keeping in mind that the laser is "red-detuned"). Next,
the atom will be a calculated polarization of light in order to
slected which of the split energy transitions to utilize and
experience a force towards the center of the cell. Meanwhile, an atom
near the center of the cell will experience a small magnetic field,
causing little splitting of energy levels. Because the laser is
"red-detuned," it will feel no force due to the laser. Thus, this is a
successful plan for confinement of cooled atoms without warming them.
Before trapping two isotopes of Rubidium, it is evaporated from a
source into a trapping cell. The appratus is in a vaccuum (on the
order of 10-9 Torr) because higher pressures allow for
background gas. Background gas is unwanted because it presents an
opportunity for collision increase of the cooled vapor. Additionally,
some sources note that the collision rate between the background gas
and the cooled gas is actually higher than the trapping rate.
CERN COURIER
Diagram of of Helmholtz Coils:
Goal Sheet
- Saturated Spectroscopy
- design and construction of a MOT
- vaccuum chamber: to buy or not to buy (and suffer the design and construction - AGAIN)
- the BOSE EINSTEIN CONDENSATE
-
Components:
- The Diode Laser: this diode laser
must be frequency (or equivalently, wavelength) stabilized. The actual
experimental implementation of the optical feedback loop is done by a
diffraction grating that ensures the wavelength stays at 780.0nm (the
specific match for the D2 transition in rubidium atoms). This
frequency locking is achieved by deriving a feedback signal from the
interaction of a portion of the laser beam with a cell containing
rubidium vapor.
- Magneto Optical Traps:
