PRINCIPLES OF TRAPPING.
A magneto-optical
trap creates a cloud of cold atoms that is spatially confined. Six
intersecting laser beams decelerate rubidium atoms in a three-dimensional
region of space. The beam intersection is overlapped with the minimum
of an inhomogeneous magnetic field, and the combination of magnetic and
optical forces confines the atoms. The purpose of my research this year
has been to optimize and characterize our magneto-optical trap in preparation
for future experiments on the cold atoms. We measured a trap population
of 1 million atoms confined in a cloud. Our traps had an average
diameter of 0.6mm, with an average density of 6 billion atoms per cubic
centimeter.
DAMPING FORCE
* Light exerts force
on atoms in the
direction that the beam travels.
* Three pairs of counter-propagating
beams provide force from all directions.
* Damping force is
not spatially-dependent,
so the atoms are cooled but not confined.
RESTORING FORCE
* Magnetic field creates
a spatially-dependent trapping force.
* Atoms interact with
the magnetic field such that they shift
into resonance with the trapping beams if they move away
from the center of the trap.
DIODE LASER AND
MOUNT.
The laser diode is
mounted in the tube on the far right, with red and black wires for the
current control and the back. Temperature is controlled by the white-and-silver
heater beneath the small platform. The beam diffracts off the rectangular
grating in the center. The position of the grating is adjusted by
controlling the green piezo-electric transducer (PZT) on the far left.
DIODE LASERS
* Commercial semiconductor
diode lasers
operate near the wavelength
l=780nm
resonant for rubidium.
* Energy of the emitted
light is controlled
using current, temperature, and cavity length.
FEEDBACK CIRCUITS
Our active feedback
circuits are designed to stabilize the laser
energy at the appropriate
energy by modulating the electronic
circuits that operate
the laser. In practical situations, the laser
will come unlocked
if energy changes too quickly or by a large
amount. In order
to minimize the affects of rapid perturbations
or large disturbances,
we use two feedback circuits. The first
is a slow-response
feedback circuit that changes the potential
across the PZT.
The second is a fast-response circuit that
modulates the current
across the laser diode.
To
produce the most stable laser operation, large
changes
are made with the PZT feedback circuit, and small
refinements
can be achieved by controlling the laser current.
The
combination
of slow and fast response circuits
provides
the
most stable locking system for the laser energy.
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TRAP CHARACTERIZATION
* Use camera image
to measure size.
* Computer software
provides intensity profile.
* Calibrate scale
of profile.
* Find population
of trap by measuring
the amount of light emitted.
TRAP PHOTOGRAPH
AND INTENSITY PROFILE.
The image from the
camera shows the light emitted by the
trap and the light
from the laser beams that scatters off the
surface of the wires
in the chamber. The cross-sectional
intensity profile
on the right shows the relative diameter of
the wires and the
trap.
TRAP WIDTH.
The intensity profiles
may be calibrated such that width of the trap measured in number of bins
corresponds to a distance in meters.  Wires
are 1/16 inches in diameter = 39 bins. Each bin represents 0.042mm.
Each data sample is fit with a Gaussian curve and the width (at one-fourth
of the maximum amplitude) is measured in terms of the parameter s.
Looking at intensity peak corresponding to trap, traps have average diameter
of 0.6mm, up to 1.0mm at the widest point of traps that are not perfectly
symmetrical.
POPULATION AND DENSITY.
The trap size can
be used to calculate the density of the cold-atom cloud, if we know how
many atoms are trapped. The process of relaxation, when atoms transition
from the excited state to the ground state, results in the emission of
light from the atoms. The total power will be equal to the power
emitted by a single atom multiplied by the number of atoms.
We use a photodetector to measure the amount of light, convert that to
a power, and then calculate the number of atoms.
MEASURING TRAP POWER.
Light emitted by the trapped atoms is collected by a lens and imaged onto
a photodetector. The detector signal is linearly related to the power
of light from the atoms.
The
combination of size and population measurements allows
for
the calculation of trap density. The measurements on three traps
of different sizes yielded trap densities
that ranged from about
5x109
to 7x109 atoms
per cubic centimeter.
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