Experiments to Control Atom Number and Phase-Space Density in ...

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center of the MOT. As an example it is shown how the CO2 laser beam moves within the cloud of atoms when the lens is moved along the y-axis (labeled (1)-(3)). The axes are defined as shown in figure 8.8. Figure 8.10 (b) - (d) shows the signal due to the imbalance caused by the pulsed CO2 laser as a function of position. The signal of the lock-in amplifier is recorded with a time constant of 1 s and a sensitivity of 2 mV. The focus of the beam is moved by translating the CO2 laser focusing lens using an X-Y-Z-translation stage. As long as the laser beam hits the lens with normal incidence the translation of the lens will correspond to a 1:1 movement of the focus inside the vacuum chamber. The lens moves along one axis, leaving the other two dimensions constant. The numerical values of the fixed dimensions are shown in the top left corner of each graph. The error bars indicate statistical uncertainties. Figure 8.10 (b) shows the position dependence along the x-axis. The position of the focus along the y-axis is at y = −0.8 mm, 0.8 mm away from the center of the MOT. This implies that the laser beam is focused predominantely into the lower half of the MOT. As the laser focus is scanned from x = −1.0 mm to x = 0 mm an increase in the signal is seen. At x = 0 mm the signal is maximum. Here the focus is aligned to the center of the MOT along the x-axis and therefore the laser beam affects the largest number of atoms, leading to the largest imbalance signal. If the focus is scanned further (x > 0 mm) the signal decreases again, as the number of affected atoms decreases. If the CO2 laser focus was aligned to the center of the MOT along the vertical dimension (y = 0 mm), the imbalance caused by the laser beam would be expected to be the same in both halves of the MOT. This would mean that the average signal would be zero. In figure 8.10 (c) the CO2 laser beam is translated along the y-axis. This is the dimension along which the fluorescence image is split in the image plane of the lens L1. The effect on the imbalance of the laser beam is therefore expected to be different than for the scan along the x-axis. At y = 0 mm both halves of the MOT will experience the same disturbance due to the laser beam, leading to a vanishing overall signal. As the laser focus is moved into the upper half of the MOT (y > 0 mm), the disturbance caused by the CO2 laser is no longer balanced and a signal is observed. If the focus is moved 159
(a) (c) y . x z X=0.0mm Z=2.5mm 1) 2) 3) (b) (d) Y=-0.8mm Z=2.5mm X=0.0mm Y=-0.5mm Figure 8.10: (a) Geometry of the split image and laser alignment. The horizontal black line symbolizes where the D-shaped mirror M2 splits the image into two halves. The two halves of the image are then detected with the two APDs. The coordinate system indicates how the coordinates at the CO2 laser focusing lens translate at the MOT image plane. z is the propagation axis of the laser beam and passes through the center of the MOT. x (y) is the horizontal (vertical) axis at the lens position. The three focused laser beams (1-3) show the location of the CO2 focus within the cloud for three differnet positions along the y-axis. The green beam (2) corresponds to the focus being aligned to the center of the MOT along the y-dimension, where the overall signal vanishes (see (c)) (b)-(d)Signal due to the imbalance caused by the pulsed CO2 laser as a function of position. The focus of the laser beam is moved along one dimension, while the other two are held constant. (b) The focus of the laser beam is moved along the x-axis. (c) The focus of the laser beam is moved along the y-axis. (d) The focus of the laser beam is moved along the z-axis (along the beam propagation axis). Error bars indicate statistical uncertainties. The inset in the upper left corner indicates the alignment in the other two dimensions. 160
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Copyright by Kirsten Viering 2012
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Experiments to Control Atom Number
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Acknowledgments First of all, I wou
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Experiments to Control Atom Number
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Table of Contents Acknowledgments v
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Chapter 7. Lithium Apparatus 92 7.1
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List of Tables 2.1 Physical propert
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4.1 Vacuum chamber . . . . . . . .
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7.39 Future vertical axis optics .
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The development of techniques to la
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Ptorr 10 5 10 6 10 7 10 8 10 9 260
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Property Symbol Value Reference Ato
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2.3.2 Hyperfine Structure So far th
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The Wigner-Eckhart theorem can be u
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The total magnetic moment of an ato
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interaction. The shift in the energ
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(a) (b) scattering length a 0 Energ
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a laser field with frequency ω. Th
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Here ω0 is the resonance frequency
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Optical molasses do not provide a s
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J=1 J=0 -1 Δ σ + σ - σ - 0 +1 -
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phase-space density is defined as
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which maintains a constant η = U/k
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2.12.1 Saturated Absorption Spectro
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Figure 2.22: Saturation absorption
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Signal 0 Signal (a) (b) Signal Freq
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(a) (b) (c) (d) Figure 2.24: Absorp
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y more complex energy level structu
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ight side of the box. An irreversib
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time (a) (b) (c) Figure 3.3: Single
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them to move from B to A, but close
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Figure 4.1: Vacuum chamber. Photogr
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( ( Figure 4.3: Helicoflex seal. (a
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88 mm 4.2.3 Auxiliary Coils 62 mm Q
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5 2 P 3/2 5 2 S 1/2 384. 230 484 46
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distribution of the MOT master lase
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shifts. First a frequency shift of
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transition. However, the laser freq
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4.3.1.4 Upper MOT Horizontal Slave
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provides the beam for the upper MOT
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demon beam λ λ horizontal MOT bea
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scholar, Florian Schreck. It is wri
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Atoms are then optically pumped to
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ferred into the |F = 1,mF = 0〉 or
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5.2 Branching Ratios and Population
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effect of the reflected beam at zer
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y the repulsive trough beams, gaini
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Figure 5.9: Atom number as a functi
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Figure 5.10: Radius of the magnetic
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on the collision rate of atoms insi
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ferred via the single-photon coolin
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By comparison an atomic Fock state
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of atoms in the two hyperfine groun
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difference in the lifetimes is dete
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Chapter 7 Lithium Apparatus Creatin
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angle valve rotary feedthrough ion
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an ion gauge controller (Granville
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viewports (MDC, 450002) are attache
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not trapped by the MOT impinge on t
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Should contamination of the vacuum
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Figure 7.12: The assembled Zeeman s
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7.2.2 MOT Coils A second set of coi
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Page 127 and 128: are required to create the high mag
Page 129 and 130: The coils are then checked for shor
Page 131 and 132: + B A Figure 7.23: Feshbach coil H-
Page 133 and 134: ensure that no particulates build u
Page 135 and 136: 118 Figure 7.26: Optical layout of
Page 137 and 138: The error signal shows three lines,
Page 139 and 140: into the CO2 laser. The optical lay
Page 141 and 142: Thorlabs PDA10A Coupler ZDC-10-1 to
Page 143 and 144: Imaging ber Imaging ber from Imagin
Page 145 and 146: Table 7.4 summarizes the beam power
Page 147 and 148: CO2 laser 40 MHz AOM f=2 in f=2 in
Page 149 and 150: 132 Figure 7.38: Optical layout aro
Page 151 and 152: Feshbach coil objective lenses atom
Page 153 and 154: MOT beams are no longer traveling a
Page 155 and 156: The second card (NI6733) offers eig
Page 157 and 158: Averaging over the magnetic subleve
Page 159 and 160: 2 2 P 3/2 D 2=670.977nm 2 2 S 1/2 m
Page 161 and 162: The right hand side of equation 7.1
Page 163 and 164: = E0 1 −n2 √2 exp σ0 ± iE0
Page 165 and 166: esidual potentials besides gravitat
Page 167 and 168: Figure 8.1: MOT loading. Typical lo
Page 169 and 170: A linear ramp typically changes the
Page 171 and 172: A typical MOT is density-limited at
Page 173 and 174: ubidium [113-115] and cesium[116].
Page 175: that most of the noise is due to th
Page 179 and 180: Figure 8.11: Different shapes of MO
Page 181 and 182: ZnSe lens f=5 in knife edge ZnSe wi
Page 183 and 184: shown in figure 8.13. By matching t
Page 185 and 186: Figure 8.15: Atom number and temper
Page 187 and 188: 275 Hz. Using these values the beam
Page 189 and 190: system. Maybe the easiest way to ac
Page 191 and 192: Appendix A Magic Wavelength of Hydr
Page 193 and 194: transitions for the excited state p
Page 195 and 196: Bibliography [1] J.J. Thomson. Cath
Page 197 and 198: [22] C.J. Foot. Atomic Physics. Oxf
Page 199 and 200: [46] E.D. Black. An introduction to
Page 201 and 202: [67] J.L. Hanssen. Controlling Atom
Page 203 and 204: [88] D.S. Naik, C.G. Peterson, A.G.
Page 205 and 206: [110] J.W. Goodman. Introduction to
Page 207: [132] C. Degenhardt, H. Stoehr, U.
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