Download Vacuum Chamber Design for a Magneto

Vacuum Chamber Design for a Magneto-Optical Trap
Connor Fitzsimmons
Department of Physics, Middlebury College, Middlebury, Vermont 05753
Project report for PHYS0704
Abstract
To trap atoms, we will need a vacuum chamber pumped to a pressure 107 times below atmospheric, with laser beams converging on its center and a position-dependent magnetic field.
We need to model how the power and polarization of our laser beams will be affected by
the optical components we use to send light into the chamber. We must correct for any loss
of power or change of polarization due to the air/glass interface at the chamber’s windows.
When the laser beams enter the chamber at an angle, we will use quarter-wave plates to
offset the effects of the interface. As we are using chamber components from another lab,
we will have to adapt the configuration in which the laser beams enter the chamber. The
dimensions of our chamber will require us to use an orthogonal six-beam arrangement.
Signatures
Advisor:
A. Goodsell
2nd Reader:
N. Graham
Date accepted:
Contents
1 Laser Cooling
1.1 Cooling physics . .
1.2 Magnetic trapping
1.3 Optical systems . .
1.4 Project Goals . . .
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2 Polarization Through Windows
2.1 Polarization . . . . . . . . . . .
2.2 Window transmission . . . . . .
2.2.1 Fresnel equations . . . .
2.3 Controlling polarization . . . .
2.3.1 Polarizing beam-splitting
2.3.2 Quarter-wave plates . .
2.4 Test measurements . . . . . . .
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cubes
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3 Geometry of Laser Beams
3.1 General description . . . . . . . . . . .
3.2 Diagram . . . . . . . . . . . . . . . . .
3.3 Vacuum chamber specs/characteristics
3.4 Chamber constraints . . . . . . . . . .
3.5 Six-beam configuration . . . . . . . . .
3.6 Tetragonal beam configuration . . . . .
4 Future Efforts
4.1 Assembly of 6.0" Chamber . . . .
4.2 Pump workings . . . . . . . . . .
4.2.1 Ion pumps . . . . . . . . .
4.2.2 Turbomolecular pumps . .
4.3 Considerations for Later Designs .
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22
List of Figures
2.1
2.2
2.3
2.4
3.1
3.2
Transmission of light through a fused silica window. . . . . . . . . . . . . . .
Quarter-wave plate axes in comparison to external axes, with incident polarization indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Circularly polarized light passes through both the quarter-wave plate and
chamber window before being split into horizontal and vertical components
for measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
"Tower of Fresnel": rotating mount with angle measurements to hold the
chamber window in place. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
11
12
14
Schematic diagram of 6.0" Multi-CF Spherical Octagon [3] . . . . . . . . . . 16
Relevant chamber lengths in considering beam configurations for angled beams. 17
List of Tables
2.1
3.1
Power in vertically and horizontally polarized laser light after transmission
through a quarter-wave plate and a fused silica vacuum chamber window. . .
14
Relevant specs for Kimball Physics spherical octagon vacuum chamber. . . .
16
2
Chapter 1
Laser Cooling
The goal of our lab is to set up a magneto-optical trap using laser cooling targeting the
transition of 85 Rb with λ=780 nm. This trap wil be able to radically reduce the temperature
of the rubidium atoms, to less than one Kelvin, allowing us to measure their behavior in
response to small perturbations in the form of electric fields with high precision and minimal
background disturbances.
1.1
Cooling physics
Laser cooling works by reducing the speed of atoms, which also reduces their temperature.
It exploits the fact that atoms are able to absorb energy only in specific quantized amounts
determined by their internal structure. An atom that collides with a photon can only absorb
its energy and enter an excited state if the photon carries the same energy as the difference
in energy between the atom’s current state and the excited state. Laser light consists of
many coherent photons of the same phase and frequency. Since photons carry energy proportional to their frequency, this means that the photons emitted by a laser all have the
same energy as well. The ability to control the energy of the photons is crucial because it
means that we can bombard atoms with photons with specific energies corresponding to one
of the element’s transitions. Since photons also carry momentum, an atom that absorbs a
photon also absorbs the photon’s momentum, changing the atom’s speed.
3
To make sure that this results in a reduction in speed, we need some way to make sure
that the atom’s momentum is likely to be in a direction opposite that of the photons it
absorbs. Optical Doppler shifting causes photons’ frequency to appear different depending
on the atom’s motion relative to the photons’ source. Compared to the case where an atom
is at rest with respect to a photon source, the photons emitted will appear to have higher
frequency when the atom is travelling towards the source, and lower frequency when it is
traveling away. By deliberately detuning the laser frequency from the frequency that can
excite an atom at rest, we can increase the probably that the laser’s photons are preferentially
absorbed by atoms moving towards the source. With this effect, we ensure that atoms moving
away are unlikely to interact with the photons, while atoms moving towards the source are
slowed and cooled.
1.2
Magnetic trapping
The Doppler cooling effect of the laser beams slows the atoms, but does nothing to constrain
them to a particular location. To do this, it is necessary to set up a magnetic field that is
dependent on the distance from the center of the chamber using a a pair of anti-Helmholtz
coils. This field causes the energy levels in in the atoms to split due to the Zeeman effect,
which results from the interaction between the atoms’ magnetic moments and the external
field. The amount by which the energy levels are shifted is a function of position, which
can be exploited to provide a spatially dependent restoring force. This is aided by the fact
that the up-shifted and down-shifted energy levels preferentially absorb circularly polarized
light with different handedness. Another benefit of this technique is that it does not require
precise balancing of the laser beams [7].
4
1.3
Optical systems
Our experimental setup uses a 780 nm infrared laser, with two slave lasers matching its
frequency to increase the total power available. The laser frequency will be stabilized by a
circuit monitoring the rubidium spectrum and self-correcting the laser towards the resonant
frequency for the desired transition. We use acousto-optical deflection to modulate the
frequency to match the correct transition in rubidium. The deflection uses sound waves
travelling through crystal as an adjustable diffraction grating, splitting a single laser beam
into beams of several orders, each differing by a constant frequency shift. In the future we will
use a Fabry-Perot interferometer to measure such frequency shifts, which uses destructive
interference to create transmission peaks at regular frequency intervals. The rubidium will
be located within a vacuum chamber, with four to six separate laser beams converging on
the sample at its center.
1.4
Project Goals
My project investigates the challenges and constraints imposed on our setup by the vacuum
chamber. Its dimensions will affect the possible configuration of laser beams we can use in
the trap. I show that with our current chamber, we can only use a six-beam orthogonal
configuration. Additionally, I discovered that its windows will have an effect on the polarization of light that passes through them, which could jeopardize the restoring force that
maintains the trap. I propose a method for correcting for these effects using manipulations
of the existing optics that create the desired polarizations outside of the chamber. This
information will inform decisions on the necessary geometry of future chambers as well.
5
Chapter 2
Polarization Through Windows
2.1
Polarization
Light is composed of electromagnetic waves, which are transverse waves since the oscillations
of their electric and magnetic fields are perpendicular to the direction of their motion. We
define the polarization of light to be the direction of its electric field rather than of its magnetic field. Since there are two dimensions perpendicular to any given direction of travel,
there are two simple polarizations: one in the horizontal plane and one in the vertical plane
[5]. Polarization in any arbitrary direction can be decomposed into some superposition of
these two types of polarization.
In addition to superposing electromagnetic waves with polarizations in different directions from each other, we can also superpose waves that are out of phase with each other –
even though they might oscillate with the same frequency, they will not be at the same point
in their cycles simulatenously. Considering a superposition of two waves with horizontal and
vertical polarization respectively and with some phase shift relative to each other, we find
that the direction of their polarization vector traces out an ellipse in space as time passes.
The direction of rotation can be either counter-clockwise (right-handed) or clockwise (lefthanded) relative to the direction of propagation, depending on which linear component’s
phase is ahead of the other. For laser trapping and cooling, light with a circular polarization
6
is ideal. Circular polarization is a special case of elliptically polarized light whose horizontal
and vertical components are equal in magnitude and π/2 out of phase [6].
2.2
Window transmission
Some of the laser beams will not be entering our chamber perpendicular to its windows,
but instead at shallower angles of incidence. However, when light entering a new medium is
not normal to the plane of incidence, transmission and reflection are different for horizontally versus vertically polarized light. Since orthgonal polarizations are not affected equally,
the ratio of their magnitudes must change, potentially causing circularly polarized light to
become elliptical upon transmission.
2.2.1
Fresnel equations
The Fresnel equations deal with the reflection and transmission of of light polarized parallel
or perpendicular to the surface of an interface between two media. The ratio of the reflected
electric field’s amplitude to that of the incident field is called the coefficient of reflection,
and the analogous ratio for the transmitted field is known as the coefficient of transmission.
For light polarized parallel to the plane of incidence, the coefficients of transmission and
reflection are
tan(θi − θt )
tan(θi + θt )
(2.1)
2 sin(θt ) cos(θi )
;
sin(θi + θt ) cos(θi − θt )
(2.2)
r! =
t! =
for light polarized perpendicular to the plane of incidence they are
r⊥ = −
t⊥ =
sin(θi − θt )
sin(θi + θt )
2 sin(θt ) cos(θi )
sin(θi + θt )
7
(2.3)
(2.4)
[6]. θi represents the angle of incidence, while θt is the angle of transmission, determined by
the angle of incidence and the refractive indices of the two media according to Snell’s Law
ni sin(θi ) = nt sin(θt )
(2.5)
[6]. The actual percentages of light transmitted and reflected depend on the ratios of power
over the cross-sectional area of the beam, and so are
(2.6)
R! = r!2
T! =
nt cos(θt ) 2
t
ni cos(θi ) !
(2.7)
(2.8)
2
R⊥ = r⊥
T⊥ =
nt cos(θt ) 2
t
ni cos(θi ) ⊥
(2.9)
[6]. To gauge the consequence in our setup, we can consider light passing through a fused
silica window, as we use in lab. We must model the transmission of light from air to fused
silica and back again, using for the refractive index of air ni =1.0003 [10] and for fused silica
nt =1.45, as depicted in Figure 2.1.
Air
θi θr
First interface
θt
Fused silica
θi θr
Second interface
Air
θt
Figure 2.1: Transmission of light through a fused silica window.
8
If we aim a laser beam towards the glass at a 45◦ angle of incidence, then within the glass
its angle of transmission is approximately 29.2◦ (from Eq. 2.5), and upon exiting the glass
it leaves at a 45◦ angle once again. The cumulative fraction of transmitted light is T! =0.987
for the component with parallel polarization and T⊥ =0.846 for the component with parallel
polarization. If, before transmission through the glass, both polarization components had
the same magnitude, they must no longer be equal. Therefore, circularly polarized light
entering the chamber will become slightly elliptical.
2.3
Controlling polarization
Lasing creates coherent light, so the electromagnetic waves we are dealing with begin with
some unknown polarization but must be in phase with each other; ours emits light with linear
polarization. Manipulating the polarization of this light is not only necessary for conditions
within the vacuum chamber, it is also very useful for directing the beam path on our optical
table.
2.3.1
Polarizing beam-splitting cubes
We can use a polarizing beam-splitting cube to isolate horizontal and vertical polarizations
out of the superposition. A beam-splitting cube is made from two triangular prisms sealed
together with a dielectric coating along their inner diagonal faces. This coating takes advantage of a property of the Fresnel equations: there is an angle at which all of the light
polarized perpendicular to the plane of the interface between materials is transmitted. This
angle is known as Brewster’s angle and it can be calculated from the refractive indices of the
two materials
θB = tan−1 (
n2
)
n1
(2.10)
[9]. For polarizing beam-splitting cubes, both halves of the cube are made from the same
9
material and so Brewster’s angle is 45◦ . Putting a cube in the path of a laser beam with
unknown polarization results in two orthogonal beams, one with vertical polarization transmitted directly through it and one with horizontal polarization reflected at a 90◦ angle.
Linearly polarized light is useful because it can be easily screened from backreflecting by
using absorption polarizers, but it also allows the creation of circularly polarized light.
2.3.2
Quarter-wave plates
To create the circularly polarized light that will be used in the magneto-optical trap, we
need to use quarter-wave plates. Quarter-wave plates are created from materials that split
incident light into two waves with orthogonal linear polarizations, called the o-wave and the
e-wave. The e-wave’s polarization is parallel to the material’s optical axis while the o-wave’s
is perpendicular to it. A wave plate introduces a phase shift between these two new waves
of
δφ =
2π
d(no − ne )
λo
(2.11)
where λo is the vacuum wavelength of the light, d is the thickness of the plate, and no and
ne are the refractive indices for the o- and e-waves [6]. Quarter-wave plates are designed
for a specific frequency of light with a thickness such that they introduce a phase-shift of
π/2 between the o- and e-waves, creating elliptical polarization in the transmitted wave.
When the waveplate is properly aligned and the linear polarization of the incident wave
is at 45◦ to one of its principal axes, both o- and e-waves have equal magnitude and the
transmitted wave has circular polarization; for any other angle, an elliptically polarized wave
is transmitted.
Consider an electromagnetic wave with vertical polarization
& = Ey ei(kz−wt) ŷ
E
10
(2.12)
y
o
θ
e
P
θ
x
Figure 2.2: Quarter-wave plate axes in comparison to external axes, with incident polarization indicated.
passing through a quarter-wave plate at some angle θ relative to the o-axis. The e-wave
experiences a phase shift so that the total wave can be expressed (using ô and ê as a new set
of coordinate axes rotated by θ with regard to x̂ and ŷ as in Figure 2.2). The field is then
given by
& = Ey ei(kz−wt+π/2) sin(θ) · ê + Ey ei(kz−wt) cos(θ) · ô.
E
(2.13)
Returning to x and y after the wave is transmitted through the plate, we find the resulting
wave is expressable as
& =Ey [−ei(kz−wt) cos(θ) sin(θ) + ei(kz−wt+π/2) cos(θ) sin(θ)] · x̂
E
+ Ey [ei(kz−wt) cos2 (θ) + ei(kz−wt+π/2) sin2 (θ)] · ŷ.
=Ey e
i(kz−wt+π/2)
[cos(θ) sin(θ) + e
iπ/2
(2.14)
cos(θ) sin(θ)] · x̂
+ Ey ei(kz−wt) [cos2 (θ) + eiπ/2 sin2 (θ)] · ŷ
Applying Euler’s formula to recognize the factor of eiπ/2 =−i and discarding the resulting
imaginary components, we arrive at
& = Ey (ei(kz−wt+π/2) cos(θ) sin(θ) · x̂ + ei(kz−wt) cos2 (θ) · ŷ)
E
11
(2.15)
which represents a right-handed elliptically polarized wave whose x-component leads its ycomponent by π/2. Further, it is clear that at θ = 45◦ , the components will have equal
magnitude and the total polarization will be circular.
2.4
Test measurements
I acquired an isolated vacuum chamber window in order to test that polarization within the
chamber will not be undesirably affected during its entry. Using a quarter-wave plate to
convert linearly polarized light into circularly polarized light and a polarizing beamsplitting
cube to split it back into horizontal and vertical linear components, I tested the light’s transmission through the window at various angles of incidence.
Quarter-wave Plate
θi
Vacuum Window
(rotating mount)
Polarizing
Beamsplitting Cube
Figure 2.3: Circularly polarized light passes through both the quarter-wave plate and chamber window before being split into horizontal and vertical components for measurement.
The window does differentially reflect and transmit the light passing through it according
to whether its polarization is vertical or horizontal, with the effect of converting circularly
polarized light into an elliptical polarization; when the window is placed in the beam path
(even at normal incidence) and whenever a modification to the positioning of the window
is made, the balance between horizontal and vertically polarized light is lost. However, Eq.
12
2.15 implies that a deliberately misaligned quarter-wave plate will create slightly elliptical
polarization, allowing the effects of transmission to be counteracted. The effect of the window then is to correct the elliptically polarized light created by the quarter-wave plate into
circularly polarized light for use within the chamber. This is supported by the data; for any
angle of the window, I was able to find a position of the quarter-wave plate that resulted in
equal power readings for both horizontal and vertical polarizations. This experiment serves
as a proof of concept, demonstrating that we can use this correction technique to create light
that becomes circularly polarized once it has passed through the vacuum chamber’s windows.
Table 2.1 lists some relevant trials of this experiment. The angle represented by θi is the
angle of incidence, the angle of the quarter-wave plate θλ/4 was read off of its rotating mount
and is arbitrary except as a relative measurement. P|v> and P|h> are power measurements of
the two different components of transmitted light, separated by beamsplitter. Every evennumbered trial represents an adjustment to the window and shows that the uncorrected
effect is indeed elliptical polarization, although the difference in transmission between the
horizontally and vertically polarized components is not as great as predicted by the Fresnel
equations (Eq. 2.7 and Eq. 2.9). This may be due to the effects of the window’s antireflection coating. The odd-numbered tests show that an adjustment to the quarter-wave
plate after the window’s adjustment makes the final polarization circular again. Tests #4
and #5 are particularly important as they represent the most desirable angle in a tetragonal
configuration of laser beams, which we hope to utilize in the future.
13
Test # θi (◦ ) θλ/4 (◦ ) P|v> (mW) P|h> (mW) P|h> /P|v>
1
208
3.04
3.04
1.00
2
0
208
2.96
3.04
0.97
3
0
300
2.99
3.00
1.00
4
45
300
3.00
2.96
1.01
5
45
301
2.98
2.99
1.00
6
65
301
2.80
2.42
1.16
7
65
305
2.59
2.60
1.00
8
30
305
2.76
3.18
0.87
9
30
300
2.98
2.99
1.00
Final Polarization
circular
elliptical
circular
elliptical
circular
elliptical
circular
elliptical
circular
Table 2.1: Power in vertically and horizontally polarized laser light after transmission through
a quarter-wave plate and a fused silica vacuum chamber window.
Figure 2.4: "Tower of Fresnel": rotating mount with angle measurements to hold the chamber
window in place.
14
Chapter 3
Geometry of Laser Beams
3.1
General description
Our current chamber is a stainless-steel spherical octagon manufactured by Kimball Physics.
A spherical octagon is essentially a disk whose sides are fittings for 6.0" copper flanges ringed
by eight 2.75" copper flanges facing out of its perimeter. It is cut from a sphere, with the
intersections for its various flanges removed. Laser light will enter the chamber through
four of the small flanges via fiberoptic cables, as well as through the centers of the two large
flanges, which will have windows mounted in them. The remaining flange fittings will be used
for measurement instruments and to connect the pump, which will create vacuum conditions
within the chamber. We will use a Gamma TiTan ion pump to reduce the pressure within
the chamber to 10−9 Torr.
15
3.2
Diagram
Figure 3.1: Schematic diagram of 6.0" Multi-CF Spherical Octagon [3]
3.3
Vacuum chamber specs/characteristics
Material
Unitary Stainless Steel 316L
Internal Volume
77.1 in3
Width
2.780 in
Total Diameter
6.980 in
Window Diameter
4.28 in
Table 3.1: Relevant specs for Kimball Physics spherical octagon vacuum chamber.
3.4
Chamber constraints
The size and shape of our vacuum chamber constrains the possible arrangements for incoming laser beams. Our calculations show that we will be unable to use the ideal tetragonal
16
beam configuration due to the chamber’s geometry. We will have to develop workarounds to
use the chamber as it is, while still preparing to make the most of a new, larger chamber. Our
chamber’s 6.0" viewing ports, combined with the width required for its 2.75" side windows,
prevent us from using the angles of incidence that a tetragonal beam configuration would
require. Such an arrangement requires that incident beams at an angle of approximately
45◦ pass through the chamber’s center, which is precluded by the chamber’s high width in
In
cid
en
tB
ea
m
comparison to its main windows’ radii.
r
A
Atan(θ)
Chamber
θ
Btan(θ)
B
Window
θ
r/cos(θ)
θ
Center
R
Figure 3.2: Relevant chamber lengths in considering beam configurations for angled beams.
As Figure 3.2 shows, at a given angle θ the radius r of a beam passing through the center
of the chamber is limited by the width R and depth A of the chamber and the depth B of
the window flange’s edge, according to
r = R cos(θ) − (A + B) sin(θ).
(3.1)
For our current chamber, R=6.980 in, A=2.14 in, and B=0.79 in. At θ=45◦ , it is not possible
for even a beam with an infinitesimally small radius to pass through the chamber’s center.
For such a beam to even reach the center, it must have an angle of incidence less than 44.5◦ ;
17
for a practical beam radius of r=1 cm, the angle would have to be less than 25.38◦ . At such
an extreme angle the tetragonal configuration is not practical. Until a larger chamber is in
place, we will have to use a six-beam configuration.
3.5
Six-beam configuration
For our current chamber, we are planning to make a magneto-optical trap with six beams.
The standard six-beam configuration uses three mutually orthogonal pairs of counterpropagating laser beams converging as its optical trap. Each pair acts independently to confince
atomic motion along a single axis of movement, with the combination of all three pairs cooling atoms that move out of the trap in any direction [1]. Because only three separate beams
are used, the remaining counterpropagating beams must be created by reflection back along
the beam path (with quarter-wave plates used to preserve the chirality of circular polarization). Although the reflections have less power than the incoming beams due to the atomic
absorption encountered before they reflect, the restoring force created by the Zeeman effect
is not particularly sensitive to such a power difference [7].
We want to allow the possibility of dropping the atoms, with movement constrained in
two dimensions and free in the third. In order to do this while maintaining a stable trap
with this configuration, we will need to position the chamber and incoming beams so that
none of the x-, y-, and z-axis are in line with the vertical on our table. Furthermore, this
configuration will require more quarter-wave plates than the alternative, because in addition
to generating circularly polarized light for the three entering beams, we must also reverse
the handedness of the polarization in the retroflected beams.
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3.6
Tetragonal beam configuration
In the future, we hope to use a more versatile beam configuration with a larger chamber. The
use of a tetragonal arrangement of four incoming beams will allow us to move the cooled
atoms by altering the relative force along any opposing directions. Two beams introduce
opposing forces in the ± x̂ directions and identical forces in the −ẑ direction, while the other
two beams create forces in the ±ŷ and +ẑ directions. Depending on the angles of the beams
relative to each other, this can form differently shaped traps. When the angle between the
paired beams is near 90◦ , it is essentially a two-dimensional version of the six-beam configuration (as the opposing contributions in the ẑ direction are minimal); near a 45◦ angle, there
is an efficient cooling effect in the all three dimensions. For such a configuration, fluctuations in relative phase between the laser beams translate the system rather than introducing
heating [2], increasing the stability of the optical trap.
The frequency detuning of the beams in this configuration is simpler than for the sixbeam configuration. Doppler detuning need only be considered in the x̂ and ŷ directions,
since the z-axis is the axis along which we will be moving the atoms. To move atoms using
this configuration, we will detune the beams descending from above the chamber separately
from those ascending from below. By setting the frequency of one beam pair further from
the targeted atomic transition, we decrease the number of photon collision an atom is likely
to undergo. This resulting force imbalance will push the atoms along the z-axis without
having to worrying about the horizontal plane.
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Chapter 4
Future Efforts
4.1
Assembly of 6.0" Chamber
The next step for our lab is to integrate the 6.0" chamber with the rest of the optics already
in place, and to begin testing the pumping process. An ion pump must be attached to the
chamber, with some modifications of the flanges used to leave the large windows available for
use by the lasers. This will likely necessitate finding a way to hold the vacuum chamber in
place above the table with the pump underneath it. When adding or substituting components
for a vacuum chamber, it is important to maintain an evenly distributed pressure across all
of the bolts, unscrewing each one slightly and then proceeding rather than removing them
one at a time. Once the system is connected and secured, we will bake the chamber to
remove particles from its inner surfaces, and begin to troubleshoot the pumping process.
We will eventually add a turbomolecular pump as well, and for the chamber assembly to be
complete and ready for laser cooling, we will need to get the anti-Helmholtz coils in place
to generate the trapping magnetic field and align the lasers for cooling. This alignment
will require both directional alignment, using mirrors and fiberoptic cables to aim the laser
beams in the six-beam configuration, as well as polarizational alignment, using quarter-wave
plate to adjust all the beams to have the correct handedness of circular polarization within
the chamber.
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4.2
Pump workings
We will reduce the chamber to vacuum pressures for future experiments by pumping the
gases out of it. The two kinds of pumps we will be using are ion pumps and turbomolecular
pumps, which will both need sealed connections to the chamber. This will be a major
consideration in the placement of the chamber on the table, as well as in the optics we need
to direct laser light into the chamber. The two pump types function in different ways as
outlined below.
4.2.1
Ion pumps
Ion pumps use the tendency of ions to react with surfaces to embed them in the walls of the
pump. Ion pumps are composed of Penning cells, which trap electrons in a small potential
well created by an anode between two cathodes, and use magnetic fields to drive them
into spherical orbits [8]. The net effect is to maximize the time before the electron reaches
the anode and thus increase the chance that it ionizes a neutral atom on its way. Different
mechanisms resulting from this same process allow it to pump various types of gases. Organic
gases can be pumped after being dissociated by the electrons, while other active gases are
pumped by reacting with titanium. Noble gases and hydrogen are pumped mainly through
ion burial. Ion pumps suffer somewhat because while pumping begins rapidly, it eventually
reaches a steady-state with the reemission of the gases [8].
4.2.2
Turbomolecular pumps
Turbmolecular pumps compress gas with a series of rotating blades interspersed with nonrotating barriers. The blades transfer momentum to gas particles when striking them and
the barriers make it likely for particles to be transported during this process. Each blade
and barrier pair can contribute only a small amount of pressure, so to overcome this they
are used as a cascade [8].
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4.3
Considerations for Later Designs
One of the principal components necessary to create a magneto-optical trap is a vacuum
chamber to isolate the trap from external disturbances. This project investigated the constraints we need to consider when choosing our own vacuum chamber. We do not need to
choose a chamber and flanges such that all of the laser beams enter at normal incidence;
although other angles of incidence will alter the polarization of the transmitted light, we can
correct for this effect using quarter-wave plates. If the wave plates are used to create slightly
elliptically polarized light instead of circularly polarized light, then transmission through
the window will cause the light within the chamber to have the desired perfectly circular
polarization. We do need to consider the dimensions of the chamber as they constrain the
angles at which laser beams can pass through the center and therefore also constrain the
possible beam configurations that we will use. A chamber with a greater radius in relation
to its thickness will allow us to use the tetragonal configuration.
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