Download Spin-Polarizing Sodium Atoms

Spin-Polarizing Sodium Atoms
Anke Kuijk
5-10-2005
Bachelor Thesis
Supervisors:
Ir. K.M.R. van der Stam
Prof. Dr. P. van der Straten
Faculteit Btawetenschappen/Departement Natuur- en Sterrenkunde
Atom Optics & Ultrafast Dynamics
Contents
1 Introduction
1
2 Bose-Einstein condensation
2.1 What is a BEC? . . . . . . . . . . .
2.2 Making a BEC . . . . . . . . . . . .
2.2.1 Laser cooling . . . . . . . . .
2.2.2 Evaporative cooling . . . . .
2.2.3 Imaging . . . . . . . . . . . .
2.2.4 Stability of the magnetic field
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3
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5
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3 Spin-polarization
3.1 Theory . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Fine and hyperfine structure of sodium
3.1.2 Selection rules . . . . . . . . . . . . . .
3.1.3 From MOT to MT . . . . . . . . . . . .
3.1.4 Spin-polarizing sodium atoms . . . . . .
3.1.5 Simulation . . . . . . . . . . . . . . . .
3.2 Experimental setup . . . . . . . . . . . . . . . .
3.2.1 Frequency and intensity . . . . . . . . .
3.2.2 Polarization . . . . . . . . . . . . . . . .
3.2.3 Magnetic Field . . . . . . . . . . . . . .
3.2.4 Procedure . . . . . . . . . . . . . . . . .
3.3 Results . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Polarization . . . . . . . . . . . . . . . .
3.3.2 Intensity . . . . . . . . . . . . . . . . . .
3.3.3 Probe time . . . . . . . . . . . . . . . .
3.3.4 Magnetic Field . . . . . . . . . . . . . .
3.3.5 Frequency . . . . . . . . . . . . . . . . .
3.3.6 BEC . . . . . . . . . . . . . . . . . . . .
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4 Conclusion
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21
i
ii
Chapter 1
Introduction
In the 1920s Bose and Einstein predicted that for sufficiently low temperature and high density, a gas of atoms undergoes a phase transition that
is called Bose-Einstein condensation. In 1995 a Bose-Einstein condensate
(BEC) was observed for the first time [1, 2, 3]. The first sodium BEC of
this university’s group was observed in August 2004 [4]. The achievement of
a BEC is an important step towards the study of atoms in optical lattices.
For this study a high density of atoms is necessary. This criterion is fulfilled
in a BEC. In an optical lattice the density of sites is n ≈ (2/λ)3 = 1014
sites/cm3 . A BEC has a density of n ≈ 1014 atoms/cm3 , which is enough
to fill the lattice with one atom per site. An important parameter for the
formation of an optical lattice out of a BEC is the number of atoms that
is present in the BEC. A larger amount of atoms will increase the signal to
noise ratio. Also initial parameters become less critical when more atoms
are available to form a BEC. Altogether a larger amount of atoms will make
BEC experiments easier. An increase of atoms can be reached in different
ways. In the first place the number of atoms in the magneto-optical trap
(MOT) could be increased, for example by increasing the loading rate from
the Zeeman slower. Also the trapping frequencies of the magnetic trap (MT)
could be adjusted. Third, the number of atoms transferred from the MOT
to the MT could be increased by spin-polarizing the atoms. This last way
of reaching a larger amount of atoms will have the largest effect and is the
easiest to do. Therefore spin-polarization has been used in this research
project to increase the number of atoms in the BEC.
First discussed in this report is Bose-Einstein condensation. There will be
explained what a BEC is and the production of a BEC is briefly described.
Second, the transfer from the magneto optical trap to the magnetic trap is
discussed to show the reason of loss of atoms and how spin-polarization could
decrease this loss. Third, spin-polarization is discussed. This includes a
description of theory, experimental setup, simulations and results. Finally a
1
BEC was produced with and without spin-polarization to prove the positive
effect of spin-polarization on the number of particles in the BEC.
2
Chapter 2
Bose-Einstein condensation
2.1
What is a BEC?
Atoms at a finite temperature in a magnetic trap occupy several singleparticle states. For a Bose gas the average occupation number for a state
with energy εk is given by the Bose-distribution:
1
,
(2.1)
−1
with µ the chemical potential and T the temperature of the system. At zero
temperature all bosons occupy only the lowest energy state, this is called
Bose-Einstein condensation. Fermions obey the Pauli exclusion principle
and can therefore not form a BEC. The formation of a BEC is a secondorder phase transition, which means that there is no associated latent heat.
The transition occurs when the mean inter-particle distance is of the same
order as the thermal deBroglie wavelength. More specific, the phase space
density ρ has to be:
ρ ≡ nλ3deB ∼
(2.2)
= 2.612,
√
where n is the density of the gas and λ3deB = h/ 3M kB T the deBroglie
wavelength. The temperature at which this transition occurs is of the order
of 100 nK. In a vapor at room temperature the phase space density is ρ ∼
3 · 10−17 . In order to reach ρ ≈ 2.612 the atoms need to be cooled and
compressed. This is done by trapping atoms with magnetic fields and laser
light inside vacuum chambers. The vacuum is necessary to thermally isolate
the atoms from all material walls.
hεk i =
2.2
2.2.1
e(εk −µ)/kB T
Making a BEC
Laser cooling
In an oven a dilute gas of atoms is created at a temperature of 590 K.
The atomic beam coming out of the oven is slowed down by using laser
3
Figure 2.1: Principle of laser cooling; A) An atom travelling right meets a
photon travelling left. B) Absorption of the photon by the atom. C) Emission
of photons by the atom.
cooling. Laser cooling works by directing a laser beam in the opposite
direction of the atomic beam (Fig. 2.1A). When an atom absorps one photon
from this laser beam, its momentum p decreases with h̄k (Fig. 2.1B). After
absorption the excited atom emits a photon in a random direction, resulting
in a nett change of momentum of zero (Fig. 2.1C)[5, 6]. The technique of
laser cooling is used in the setup shown in Fig. 2.2. When laser cooling is
used, the atoms slow down and are no longer in resonance with the laser
light. To overcome this problem, a Zeeman slower is used [7]. This device
produces an inhomogeneous magnetic field to compensate for the Doppler
shift in frequency of the incoming laser beam by degenerating the energy
levels of the atoms. When the atoms leave the Zeeman slower they have
been slowed down to 40 m/s. Now they can be trapped in a magnetooptical trap (MOT)[8]. A MOT works with a magnetic field and six counterpropagating laser beams. The laser beams slow the atoms further down,
while the magnetic field in combination with the laser beams drives the
atoms to the center of the trap. When trapped in the MOT the temperature
of the atoms has reached about 100 µK and ρ ∼ 10−6 . The effect of laser
cooling is limited due to the recoil energy the atoms obtain by scattering
photons. To cool and compress the atoms towards BEC evaporative cooling
is used [9].
4
Figure 2.2: Overview of the experimental setup; 1) Oven, 2) Zeeman slower,
3) MOT.
2.2.2
Evaporative cooling
After they have been trapped in the MOT, the atoms are transferred into
a magnetic trap (MT). In this trap the atoms are caught in a magnetic
field, which creates a potential U = µ|B|. Close to the center of the trap
this potential can be approximated by an harmonic potential [4]. Atoms
that have a magnetic dipole that is anti-aligned with the magnetic field
direction, ‘low field seekers’, are trapped at the minimum of the magnetic
field in the center of the trap. When they are in the MT, the atoms are
further cooled by evaporative cooling [10]. Evaporative cooling works by
the removal of atoms with an energy higher than a threshold energy. Atoms
with a high potential energy can reach higher magnetic fields than atoms
with a low potential energy. This means that for high energy atoms the
atom levels are further apart due to the Zeeman-effect. The height of the
threshold energy is controlled by radio frequency radiation. By introducing
a relatively high radio-frequency, only high energy atoms are excited and
their magnetic quantum number M changes (see Fig. 2.3). Due to this
spin-flip these atoms cannot be hold in the MT anymore. This process is
repeated for lower frequencies until only cold atoms remain. This way the
phase space density and temperature for BEC are reached.
2.2.3
Imaging
When BEC has been reached, the atoms are imaged by fluorescence imaging.
First the magnetic field is turned off, which allows the atoms to expand
freely. After some time (the time of flight, usually 20 ms) the atoms are
probed by a laser pulse, which pumps them into an excited state. When
5
mF =-1
ω RF
F=1
mF =0
E
B
mF =1
B
position
Figure 2.3: Principle of evaporative cooling; On the left a schematic overview
of atoms in a magnetic trap, on the right the energy needed to change M F ,
E = h̄ωRF
they fall back into a ground state, the emitted photons are detected by a
CCD-camera. The intensity of scattered light is a measure for the density,
the width of the picture is a measure for temperature.
2.2.4
Stability of the magnetic field
In the production process of a BEC, it is important to know the stability of
the minimum magnetic field of the MT. This determines the final temperature of the atoms after evaporative cooling. Fluctuations in the magnetic
field effect the rf-frequency needed for evaporative cooling. To determine
to what extend the rf-frequency can be tuned, the stability of the magnetic
field has been determined. This has been done by measuring the temperature of the BEC by the ’time of flight’ method described in section 2.2.3.
The temperature for kB T µB0 can be deduced from:
T =
ωρ2
mrx2
(
),
2kB 1 + ωρ2 t2tof
(2.3)
where m is the mass of sodium, rx the half-width of the thermal cloud, ωρ
the trapping frequency and ttof is the time of flight. In this experiment the
time of flight was 30 ms, and ωρ is 90.7 · 2π s−1 . The temperature of the
BEC depends on the final rf-frequency used for evaporative cooling.
6
rf-Frequency [MHz]
Temperature [nK]
2.61
166 ± 44
2.615
82 ± 44
2.62
72 ± 27
The measured values lead to the conclusion that on a scale of 0.01 MHz there
is a significant difference in temperature. On a smaller scale (0.005 MHz)
the difference in temperature cannot be measured. Tuning on a smaller scale
than 0.01 MHz is therefor not useful.
7
Chapter 3
Spin-polarization
3.1
Theory
In this section several topics important for spin-polarization are discussed.
First the level structure of sodium atoms is explained, then the process of
optical pumping, including selection rules. Next the transfer of atoms from
MOT to MT is discussed and finally the simulations that have been done.
3.1.1
Fine and hyperfine structure of sodium
The ground state of sodium atoms consists of a closed shell with one valence
electron. The core does not contribute to the orbital angular momentum of
the atom. The state of the atom depends only on the state of the valence
electron. This state is determined by its orbital angular momentum L and
spin angular momentum S. Together they form the total angular momentum J of the electron: |L − S| ≤ J ≤ L + S. Different values of J lead to
~ · S,
~
different energies of the states, since the spin-orbit interaction, V ∼ L
~ with respect to L.
~ This splitting of states
depends on the orientation of S
by spin-orbit interaction is called the fine structure of the atom.
The addition of the nuclear spin I~ with the total angular momentum of the
~ Different values
electron J~ gives the total angular momentum: F~ = I~ + J.
~
~
~
of F for the same values of I and J are split by an interaction proportional
~ The resulting energy structure is called the hyperfine structure,
to I~ · J.
shown in Fig. 3.1.
For sodium the nuclear spin is I = 3/2. In the process of spin-polarization
the atoms are excited from the 2 S1/2 ground state to the 2 P3/2 excited state
(D2 line). In this case the angular momentum (L = 1) couples with the
total spin (S = 1/2) to form Je = 3/2. The ground state (Jg = 1/2) can be
split in 8 Zeeman sublevels, the excited state (Je = 3/2) in 16 sublevels as
shown in Fig. 3.1.
8
-3
-2
-1
0
+1
+2
Fe=3
62 MHz
2
Fe=2 3 P 3/ 2
Fe =1
Fe=0
36 MHz
16 MHz
1772 MHz
+3
-2
-1
0
+1 +2
Fg=2
32S1/ 2
Fg=1
Figure 3.1: Hyperfine structure of sodium. Shown are the different F levels,
which consist of several MF sublevels.
9
3.1.2
Selection rules
Light is required to drive the transitions between ground and excited sublevels. When light is used, selection rules have to be obeyed, which are
different for different polarizations of light. These rules limit the number
of transitions between the sublevels by setting constraints on quantumnumbers. Selection rules can be calculated from commutation relations [11]. The
~ for
selection rules for the projection of the angular momentum M along B
circularly polarized light are ∆MF = 1 for right-handed and ∆MF = −1
for left-handed circular polarization. Linearly polarized light can couple two
states only if ∆MF = 0. This could be understood as described in [11]: a
photon carries spin 1, and its value of M is 1, 0, or −1 (since the direction of
propagation of the photon need not be along the polar axis). Conservation
of angular momentum requires that the atom gives up whatever the photon
takes away. When the excited atom falls back by spontaneous emission, only
states with ∆MF = 0, 1 can be reached. For the total angular momentum
F the selection rule is ∆F = 0, ±1. This result is also interpreted in [11]:
the photon carries spin 1, so the rules for addition of angular momentum
would allow F 0 = F + 1, F 0 = F , or F 0 = F − 1. The spontaneous decay
after light driven excitation follows the same selection rules: ∆F and ∆MF
is 0, ±1.
3.1.3
From MOT to MT
The laser light used in the MOT pumps the atoms from the Fg = 2 state
to the Fe = 3 state [4]. Because this light is detuned also Fg = 2 → Fe = 2
transitions are possible. When the atoms fall back, there is a possibility that
atoms end up in the Fg = 1 ground state, where they are lost for further
cooling. To get them back in the cooling-process, a second laser (the repump
laser) is locked close to the Fg = 1 → Fe = 2 transition. In this experiment
a dark-spot MOT is used to increase the density of trapped atoms. This
means that there is no repump light in the center of the trap. Therefore
most atoms captured in the center are in the Fg = 1 ground state. For
further cooling these atoms must be transferred to the MT.
The atoms in the MT have a potential energy of:
~
U (~r) = µ
~ · B(r),
(3.1)
~
where µ
~ is the magnetic dipole moment of the atom and B(r)
is the magnetic
field. In terms of MF equation (3.1) becomes:
U = gF µB MF B,
(3.2)
here MF corresponds to the projection of the total angular momentum F
~ and gF is the Lande g-factor. To determine in which
in the direction of B
10
direction the atoms will move, the force applied by the magnetic field on the
atoms is important:
~
dB
.
(3.3)
F~ = −gF µB MF
d~r
~
Since dd~Br is positive, only atoms with gF MF > 0 are trapped at the minimum of the magnetic field. The polarization of the atoms in the F = 1
ground state in the MOT is homogeneously distributed over three magnetic
sublevels, MF = 1, 0 and −1. Since gF = −1/2 only MF = −1 meets the
criterium gF MF > 0. This means that the maximum transferred fraction
of atoms from the MOT to the MT is 1/3. To increase this fraction it is
possible to spin-polarize the atoms before transferring them to the MT.
3.1.4
Spin-polarizing sodium atoms
Since we want to pump atoms that are homogeneously distributed over the
three MF states of the F = 1 ground state to the F = 1, MF = −1 state,
linearly and σ + polarized light cannot be used because of the selection rules.
Only by using σ − polarized light, atoms in the MF = 0 and MF = 1 ground
state can be optically pumped to a lower MF state, in order to finally reach
MF = −1. However, during the process atoms can also end up in a F = 2
state. When this happens they can no longer be pumped by the spinpolarization light. To overcome this problem light of a different frequency
(depump light) will be necessary to pump the atoms back from F = 2 to
F = 1. To get atoms from the F = 2, MF = −2 state back in the process
the depump light needs to be σ + polarized.
3.1.5
Simulation
Beside the actual measurement, a theoretical simulation of the spin-polarizing
process has been made. In this model the scattering rates (γp ) for σ − polarized light of all possible excitations from a ground state to an excited
state and all decays back to a ground state are determined and combined
in a matrix. These scattering rates determine the coupling of ground states
and excited states. By multiplying this matrix with a vector that represents the population of the ground states, the gain and loss for each state
are calculated. Repeated multiplication leads eventually to an equilibrium
population. The free parameters for this simulation are the intensity and
frequency of the spin-polarization and depump light, the applied magnetic
field and the time of spin-polarization and depumping. The simulation gives
information about the dependence of effectivity of the spin-polarization process on these parameters. Since the simulation is based on the presence of
only one atom, effects of and interaction with other atoms that occur in
practice are not integrated in the model. The results of the simulations are
shown with the experimental data in section 3.3.
11
3.2
3.2.1
Experimental setup
Frequency and intensity
The first need for spin-polarization is light to pump the atoms to the F =
1, MF = −1 state. This light, the spin-polarization beam, is split off from
the repump light of the MOT and has a detuning of 14 MHz below the Fg =
1 → Fe = 2 transition. To decrease the loss of atoms that are pumped into
a F = 2 state, a second laser-beam is needed which pumps the atoms back
to a F = 1 state. For this depump-process the laser-beams of the MOT are
used, which are detuned 15 MHz below the Fg = 2 → Fe = 3 transition. The
intensity of the light is expressed in the on-resonance saturation parameter
s0 :
s0 ≡ I/Is ,
(3.4)
where Is is the saturation intensity, in this case Is = 6.0 mW/cm. The saturation parameter of the spin-polarization beam needs to be approximately
0.1 to 0.5. The saturation parameter of the depump light is s0 ≈ 10.
3.2.2
Polarization
As explained in section 3.1.4 the polarization of the spin-polarization beam
needs to be σ − . This polarization is obtained by leading the light coming
from the laser first through a polarizer which only lets linearly polarized
light through. Behind the polarizer a λ/4-plate is placed which turns the
linearly polarized light into circularly polarized light.
3.2.3
Magnetic Field
The last thing necessary to spin-polarize is a magnetic field to provide a
quantization axis. To apply this field the pinch and bias coils of the MT are
used (figure 3.2). These coils produce a homogeneous magnetic field in the
z-direction, which leads to a coupling of states with different F and same
MF values. In this case different MF values stay separated and the selection
rule for σ − polarized light stays valid. A second effect of the magnetic field
is that the different Zeeman sublevels split up. This changes the resonances
between different ground and excited states, which helps keeping the atoms
in the F = 1, MF = −1 state.
3.2.4
Procedure
The procedure of spin-polarization is as follows. When the atoms have been
trapped in the MOT, the MOT is turned off. Then a magnetic field is
applied and after a few milliseconds, when the field is relatively stable, a
2 ms pulse of spin-polarization and depump light is released on the atoms.
Then the spin-polarization beam is turned off and the depump beam stays
12
Figure 3.2: Clover leaf trap, showing pinch and bias coils used to apply the
magnetic field necessary for spin-polarization.
on for another millisecond to pump the last atoms back from a Fg = 2 to a
Fg = 1 state. After this the MT is turned on to capture the atoms in the
F = 1, MF = −1 state. Finally a picture of the atoms is made as described
in section 2.2.3.
13
Transferred fraction
1
0.8
0.6
0.4
0.2
25
75
50
100
125
150
Position ː4 @degreesD
175
Figure 3.3: Fraction of atoms transferred to the MT, depending on polarization of the light. The line represents the simulation, the dots the experimental data. The used parameters are: δspinpol = 181 Γ, δdepump = 9.6
Γ, s0,spinpol = 0.1, s0,depump = 10, B = 80 G, tspinpol = 2 ms and
tdepump = 1 ms. The detuning of the lasers is given in comparison with
the Fg = 2 → Fe = 0 transition.
3.3
Results
The effect of spin-polarization depends on several factors. It is important
to know the optimal values of these parameters. The dependence on polarization, intensity and length of the spin-polarization pulse are measured
as well as dependence on the applied magnetic field. To prove the positive
effect of spin-polarization on the number of atoms in the BEC, a BEC with
and without spin-polarization has been made.
3.3.1
Polarization
The polarization of the spin-polarization pulse is controlled by a λ/4-plate.
By changing the orientation of this plate, the polarization changes. A turn
over 900 means a change from σ − to σ + light. Figure 3.3 shows the fraction
of atoms transferred to the MT, depending on the polarization of the light.
The extremes of the simulated line correspond to σ − and σ + light. The
period of the plot is about 1800 , as expected. As can be seen in Fig 3.3, the
simulated and measured values correspond well with each other. Figure 3.3
shows that the right polarization (a position of the λ/4-plate around 0 0 or
1800 ) leads to a maximum transfer fraction of about 75 percent.
14
Temperature HΜKL
220
200
180
160
140
120
0.05 0.1
0.5 1
Saturation parameterHs0L
5
10
Figure 3.4: Temperature of the atoms in the MT versus the intensity of the
spin-polarization pulse, expressed by the saturation parameter (s0 ).The used
parameters are: δspinpol = 181 Γ, δdepump = 9.6 Γ, s0,depump = 10, B = 80
G, tspinpol = 2 ms and tdepump = 1 ms.
3.3.2
Intensity
The effect of spin-polarization also depends on the intensity of the spinpolarization pulse. A too low intensity has little effect, a too high intensity causes heating, which is negative for the subsequent cooling process.
Therefore the intensity-dependence of spin-polarization has been measured.
Figure 3.4 shows that the needed saturation parameter lies between 0.1 and
1. In our case of a 0.4 cm2 beam, this means an intensity between 0.25
and 2.5 mW. A s0 higher than 2 causes heating, expressed in Fig. 3.4 by a
distinct increase of temperature. This heating occurs when too many photons are scattered by the atoms. When photons are scattered by an atom
repeatedly, there is a transfer of momentum and energy which causes the
atoms to move randomly. More motion (and thus a higher kinetic energy)
means a higher temperature.
3.3.3
Probe time
In the measurements of intensity and polarization long pulse lengths, in
the order of milliseconds, were needed to spin-polarize the atoms. Because
this is very long for atoms to be optically pumped, the dependence of spinpolarization on probe time is measured. In Fig. 3.5 and Fig. 3.6. the
temperature and transfer of atoms versus the length of the pulse are shown.
Figure 3.5 shows a slow increase of temperature for t up to 20 ms. A longer
15
Velocity @msD
0.5
0.4
0.3
0.2
0.1
5
10
15
20
Pulse@msD
25
30
Figure 3.5: Velocity increase at longer pulse lengths. Measured by δ spinpol =
181 Γ, δdepump = 9.6 Γ, s0,spinpol = 0.1, s0,depump = 10, B = 80 G and
tdepump = 1 ms.
Transferred fraction
1
0.8
0.6
0.4
0.2
2
4
6
Pulse @msD
8
10
Figure 3.6: Fraction of atoms transferred into the MT versus the length of
the spin-polarization pulse. Measured by δspinpol = 181 Γ, δdepump = 9.6 Γ,
s0,spinpol = 0.1, s0,depump = 10, B = 80 G and tdepump = 1 ms.
16
pulse causes heating for the same reasons as in the case of a higher intensity.
The temperature of the atoms can be calculated from Fig. 3.5 by:
mv 2 = kB T,
(3.5)
where m is the mass of sodium, v the velocity and kB the Boltzmann
constant. Figure 3.6 shows a loss of particles from t = 2 ms. This loss
can be explained by the atoms that are pumped into other states than
F = 1, MF = −1, which prevents them from being transferred to the MT.
At short pulse lengths not all atoms are pumped to the F = 1, MF = −1
state, which explains the low transfer fractions there. From Fig. 3.6 can be
concluded that a pulse length of 1 to 2 ms is optimal.
From Fig. 3.5 the diffusion (D) and saturation parameter (s) can be calculated as described below. The change in temperature, dependent on probe
time is:
2D
mh(∆v)2 i = kB T =
t + k B T0 .
(3.6)
m
Figure 3.5 shows that ∆v is 0.06 m/s in 20 ms. This means 2D/m2 in Eq.
(3.6) is 3 (m/s)2 /s. In combination with the relation for diffusion,
1
D = (h̄k)2 Γs = 1.6 · 10−49 s,
2
(3.7)
where h̄ is the Plack constant, k is the wave number and Γ is the line width
of sodium, this leads to the results of s = 0.013 and D = 2 · 10−51 J·kg/s.
The saturation parameter can also be calculated in the simulation. By
summation of the total loss or gain of one vector-matrix multiplication the
scatter rate (γp ) of the process of optical pumping can be calculated. The
calculated γp is in relation with the detuning (δ) of the laser:
γp =
s0 Γ/2
,
1 + s0 + (2δ/Γ)2
(3.8)
where s0 is the saturation parameter at resonance. Using γp the saturation
parameter s can be calculated:
s=
γp
s0
≈
= 0.02.
2
1 + (2δ/Γ)
(Γ/2)
(3.9)
This means that the experimental results are in good agreement with the
theoretical simulated values.
3.3.4
Magnetic Field
In the previous measurements a high magnetic field was used. Because
usually low magnetic fields are used to spin-polarize atoms, the dependence
17
Transferred fraction
1
0.8
0.6
0.4
0.2
20
40
60
Magnetic field @GD
80
100
Figure 3.7: Simulation (line) and data (dots) of spin-polarization depending
on the applied magnetic field. The simulation parameters are: δspin = 181
Γ, δdepump = 9.6 Γ, s0,spin = 0.1, s0,depump = 10, tspinpol = 2.5 ms and
tdepump = 1 ms.
of spin-polarization on the magnetic field is also measured and shown in Fig.
3.7. The simulation of the magnetic field dependency in Fig. 3.7 shows two
minima. These occur at resonance with a transition from one of the ground
states to one of the excited states. The measured data show the same trend
as the simulation, but the values are shifted down. These lower results can
be explained by several factors. It might be a less than perfect overlap of the
MOT and MT. Also the depumping might be less effective than expected,
which leads to less atoms in the F = 1, MF = −1 state. Most probably the
optical density of the atoms is the problem.
3.3.5
Frequency
Since the magnetic field is linked to the frequency needed to spin-polarize,
the frequency dependence of spin-polarization is also measured. Figure 3.8
shows the fraction of atoms transferred into the MT depending on the frequency of the spin-polarization light. The simulation in Fig. 3.8 shows that
the transferred fraction depends strongly on the frequency of the light. The
experimental data show also a strong dependence, but do not correspond
well to the simulation. The shape of the measured curve is in agreement
with the shape of the simulation, but the position of the measured values
is shifted up 10 Γ. What causes this shift is unclear. The frequency of the
used light has been checked and is indeed what it was thought to be. Fur-
18
Transferred fraction
1
0.8
0.6
0.4
0.2
165
175
170
180
Detuning @GD
185
Figure 3.8: Frequency of the spin polarization beam dependence of spinpolarization. The line represents the simulation, the dots experimental data,
measured by δdepump = 9.6 Γ, s0,spin = 0.1, s0,depump = 10, B = 100 G,
tspinpol = 1 ms and tdepump = 1 ms.
thermore the stability of the lasers is 1 Γ, so this cannot explain the shift
either. It might be explained by a not perfect circular polarization of the
spin-polarization light, but this has not been checked yet.
3.3.6
BEC
The final purpose of spin-polarizing atoms is creating a BEC. This would
finally prove that the atoms are in the F = 1, MF = −1 state. Atoms in
other states that could be captured in the MT will be lost during evaporative cooling due to inelastic collisions. After evaporative cooling only atoms
in the F = 1, MF = −1 state will be left in the BEC. Fig. 3.9 shows a
picture of the atoms after evaporative cooling. Clearly spin-polarizing the
atoms causes a significant increase of atoms in the BEC.
19
Figure 3.9: Atoms left after evaporative cooling, with (left) and without
(right) spin-polarization
20
Chapter 4
Conclusion
In this report the positive effect of spin-polarization on the number of particles in the BEC is shown. Using spin-polarization a maximal fraction of
0.8 of the atoms is transferred from the MOT to the MT, compared to a
fraction of 0.3 without spin-polarization.
To determine the critical parameters for spin-polarization a simulation of the
process was made. The dependence of spin-polarization on these parameters
was also measured experimentally. The experimental data proved to be quite
consistent with the simulation, except for the measurement of the frequency
of the spin-polarization beam dependence. The small discrepancies between
simulation and experimental data can be explained by the large amount of
parameters the spin-polarization process depends on and the optical density
of the atoms in the MOT. The shift in frequency has not been explained
yet.
Using the technique of spin-polarization a BEC was made. In comparison
with a BEC without the use of spin-polarization the number of atoms in a
spin-polarized BEC is increased by a factor of 10.
21
22
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