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Laser Cooling and Trapping
Nathan Wenk
PH 464 – Applied Optics
Prof. La Rosa
March 17, 2006
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Abstract: The terms “laser cooling” and “trapping” refer to the use of lasers to cool atoms
down to 1 μK and below and keep them in a relatively known location. The photons from
the laser light slow down the velocity of the atoms using the principle of conservation of
momentum. The lasers are also used to move the atoms to a central location and “trap”
them there. Employing the use of magnets allows the atoms to only be affected by light
coming from a specific direction. When multiple lasers are used, the net effect is to push
the atoms to the center of the apparatus where they are cooled and trapped. The use of
laser cooling has enabled scientists to create and observe a Bose-Einstein Condensate
(BEC), a phenomenon predicted in 1924 by Satyendra Nath Bose and Albert Einstein. This
paper discusses the theory behind laser cooling and trapping, how it is done, and how it is
measured.
Investigating the topic of laser cooling and trapping is fascinating because it allows
atoms to be cooled down to previously unheard of temperatures. Taking this single step
forward not only won Carl Wieman, Eric Cornell, and Wolfgang Ketterle a Nobel Prize in
2001, but confirmed the prediction made by Einstein and Bose over 70 years earlier. The
BEC is an area of research that is growing in a somewhat unknown direction. Researchers
are still in the process of what it all means, how to interpret the results, and where to go
from here.
Photons that are traveling from a laser source do not have mass; however, they do
carry momentum. The value of their momentum is equal to Planck’s constant divided by
the wavelength as shown in equation [1].
p
h

[1]
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The narrowest of spectrums possible is necessary in order to match with the energy which
is needed to excite an atom to the first energy level. The Doppler Effect is taken into
account when atoms moving toward the laser will see the light at a shorter wavelength. By
slightly increasing the wavelength of the light from one which equals that of a stationary
atom, the atoms moving toward the laser will “see” the light at the correct wavelength. An
atom moving away from the laser will see the light as too “red” and will not absorb the
photon. By allowing only the atoms moving toward the laser to see the light, only those
atoms will absorb the photon as well as its momentum. This explanation works well for
one dimension and more lasers are added in different configurations to accommodate the
slowing of atoms in all three dimensions.
Once the atom has absorbed the photon and its momentum, it slows down a little
bit and reemits a photon as it moves back to its ground state. The net effect is a reduction
in the atoms velocity since all of the photons will be hitting the atom from only one
direction, however, the direction the atom emits the photon will be random. The decrease
in velocity of the atom is on the order of less than a cm/s and the process has been
compared to bombarding a bowling ball with stream of ping pong balls (5). Each one has
very little effect individually, but collectively, the bowling ball is eventually moved. In the
case of the atom, it can be moved rather quickly since the scattering rate of photons has
reached 107 photons per second creating acceleration around 104 g (5).
One laser is used and is split into three separate beams. The three lasers are then
focused on the trap in such a way that they are all simultaneously orthogonal to the other
two. After the beams pass through the trap, they are then reflected back onto themselves,
where they again pass through the trap, but in the opposite direction. This configuration
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allows atoms to be slowed down by laser light from six different directions. Densities of
more than 1011 cm-3 have been observed. The traps that were originally created were about
0.001 mm3, but recent ones are on the order of 1.0 cm3. This volume is directly related to
the diameter of the laser beams. The beam diameter does have upper limits since it is
inhibited by the size of the mirrors from which it reflects.
Very low pressures are required to cool atoms using lasers. Pressures in the 10-6 to
10-7 Pa range are necessary to carry out the experiment for any appreciable length of time
(4). Low pressures remove most of the unwanted gases such as water, hydrogen, and
helium. These impurities not only add unnecessary energy to the system, but also block
and deflect laser light that is intended for the target atoms (4). Ion pumps are a common
way to obtain 10-7 Pa pressures, however some ion pumps do require prepumping before
they are effective.
Atoms above the critical velocity, vc, of between 15 and 20 m/s are moving too
quickly to be greatly affected by the trap (5). They may move through the trap and will
slow down, but are still traveling too fast when they reach the outer edge, thus they simply
keep on traveling. The atoms whose velocities are below vc are thus contained within the
trap and slowed down to the μK range. To obtain temperatures below the μK range, other
methods are required. This lower limit is called the “Doppler limit” velocity [2] and
requires sub-Doppler cooling techniques.
v
h
m
[2] (4)
Most of the experiments published so far included either rubidium or cesium atoms.
One experiment referenced the use of sodium and one theorized use of francium. Most of
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the published laser cooling experiments used 87Rb in their laser cooling experiments. For
87
Rb, the wavelength of 780 nm works best to excite the atom out of its ground state as the
atom moves toward the laser. Using equation [1], the photons of this wavelength have a
momentum in the order of 10-28 kg m/s. This number is about 104 times smaller than the
momentum of an 87Rb atom moving at the 20 m/s critical velocity. There are many
obstacles to overcome in order to get this frequency just right. All of the lasers must be
aligned so that they intersect all at right angles. If they become skewed, the atoms will
create a small orbit, as they are being accelerated unevenly (1). The lasers used are diode
lasers featuring the use of both optical and electronic feedback systems to get a consistent
wavelength of light (3). The beam emitted from the laser is reflected off an adjustable
diffraction grating in order to narrow the spectrum of light going into the trap.
Fluctuations in laser temperature, base plate temperature, room temperature and air
currents, as well as vibrations from the building systems all negatively impact the laser’s
performance. Therefore it is necessary to both isolate and stabilize the laser generating
system (2). After the light has been tuned and stabilized, it must be split into three beams
and redirected (by using mirrors) into the trap from three different sides. After they pass
through, they are reflected back through the trap to impact the atoms from all six sides.
The beams are not reflected back directly at the incoming source because doing so could
cause damage to the diode. Instead they are typically diverted to the side of the incoming
laser by 5 - 10 beam widths (5). It has been found that a beam with a diameter of 1.5 cm
works best. Any smaller and the trap becomes smaller. Any larger and the mirrors have
trouble reflecting all of the light consistently. The power of the laser should also be at
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least in the 5 to 10 mW range (5) (2). The more powerful the laser is the more photons
will be scattered per second.
Temperatures in the μK range have been obtained with the sole use of laser
cooling. When two symmetric magnetic field coils are added which have oppositely
directed current, the net effect is a zero magnetic field in the center, and a linear magnetic
gradient as you move out in all directions. These magnets will produce a dipole in the
neutral 87Rb atoms and will thus be attracted to the neutral center of the trap (5). If the
current direction is reversed, the dipole in the atom will be reversed, but will then be
attracted to the maximum magnetic field in the center of the trap (7). Therefore, the
magnets are therefore used to help contain all of the atoms not only in the trap, but in the
center of the trap. The technique called a Magneto-Optical Trap (MOT) was an important
step towards creating a BEC because the atoms must be grouped very closely together. A
longitudinal gradient of about 5.1 G/cm is necessary (3). The force applied to each atom is
now positionally dependent.
In addition to the atoms being magnetically attracted to the center of the trap, the
magnetic field also affects how much energy is required to excite the atom out of its
ground state. By using approximately circularly polarized light, the atom will only be
affected by the laser light that has yet to enter the trap and will therefore be pushed back
toward the center of the trap. The light reflected off the mirror heading back through the
trap will not affect an atom on the far side of the trap because the polarization is wrong for
the dipole created by the magnet. The magnetic field creating sensitivity to only one
direction of circularly polarized light is called the Zeeman shift. Therefore, this setup is
called the Zeeman shift optical trap (ZOT) (5).
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In order to cool the atoms even further into the nK range, the range that is
necessary to observe a BEC, another method has been used. After all of the atoms are
condensed and slowed down as much as possible by the above techniques, the atoms with
greater velocities are then allowed to evaporate and exit the trap. By adjusting the
magnetic field and the light coming into the trap, the constraints on the atoms are gradually
reduced and the faster ones are no longer prohibited from leaving. By allowing the faster
atoms to evaporate, the average velocity (and therefore the average temperature) of the
remaining atoms is reduced. Using this technique, temperatures of 50 nK (fifty billionths
of a Kelvin!) have been reached.
Measuring a temperature this low certainly couldn’t be done with an ordinary
kitchen thermometer. Common sense would say that any attempt to measure the
temperature of atoms this cold will certainly affect the sample and give questionable
results. The method for measuring the temperature in two experiments is the procedure of
placing a 0.5 mm probe beam within 4 mm from the side of the cloud. The time-of-flight
(TOF) spectrum is then analyzed and compared to theoretical models which for the most
part confer (1) (3).
The laser cooling experiments most often referenced rubidium and cesium, and
one experiment mentioned francium. I am unclear as to why these particular atoms were
used. All are Group I elements, but I read nothing of why this is of particular importance.
Rubidium may have an advantage over cesium because it is heavier and therefore has a
smaller vrms for the same temperature. In addition, the 780 nm laser required for the
rubidium appeared to be in a common range and therefore more accessible at a reasonable
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price. Other elements may require a laser wavelength which is not as accessible, and
would add unnecessary cost to the experiment.
The setup for many of the published experiments used 6 laser beams
entering the trap all at right angles to each other. A second configuration has been
successfully tested whereby only four lasers enter the trap. Two orthogonal beams enter
the trap in the y,z plane, while two more orthogonal beams enter the trap from the opposite
direction in the x,z plane (figure 1) (9). This setup also used linearly instead of circularly
polarized light, but still recorded temperatures as low as 700 nK. The theory of using
photons to reduce velocity in atoms by way of conservation of momentum is used in this
experiment as well.
Figure 1
When doing these experiments, the basic goal was to determine the number of
trapped atoms as well as the time the atoms remained in the trap (4). More elaborate
experiments have been performed using lasers to cool and trap atoms. Other experiments
include creating a BEC as well as slowing down light to a crawl, actually stopping it, and
then restarting it at full speed (8). Some of the constants, such as the speed of light, are
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becoming less and less constant. The scientific advances and understanding created by
observing a BEC are continuously increasing. One never knows what one might find when
exploring, and presently, research suggests that perhaps scientists are content with
exploration in the field of laser cooling. After all, education is a very important part of the
scientific process.
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References:
1. D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous
force trap”, J. Opt. Soc. Am. B 8, 946 (1991).
2. K. B. MacAdam, A. Steinback, and Carl Wieman, “A narrow-band tunable diode laser
system with grating feedback and a saturated absorption spectrometer for Cs and Rb,” Am.
J. Phys. 60, 10098-1111 (1992).
3. D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional Losses
from a Light-Force Atom Trap”, Phys. Rev. Lett. 63, 961 (1989).
4. Carl Wieman, Gwenn Flowers, and Sarah Gilbert, “Inexpensive laser cooling and
trapping experiment for undergraduate laboratories”, Am J. Phys. 63, 317 (1995).
5. K. Wagner, “Laser Cooling and Trapping”,
http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf , accessed
March 19, 2006.
6. A. Steane, M. Chowdhury, and C. Foot, “Radiation force in the magneto-optical trap”,
J. Opt. Soc. Am. B 9, 2142 (1992).
7. Steven Chu, “Laser Trapping of Neutral Particles”, Sci. Am., 71-76, February (1992).
8. William J. Cromie, “Researcher now able to stop, restart light”,
http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html , Harvard University
Gazette, accessed March 19, 2006.
9. A. Kastberg, W. D. Phillips, S. L. Rolston, and R. J. C. Spreeuw, “Adiabatic Cooling of
Cesium to 700 nK in and Optical Lattice”, Phys. Rev. Lett. 74, 1542 (1995).