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

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used for loading, is above 2 mK. The trap depth of the optical dipole trap, however, is only about 700 µK. A simple model estimates the equilibrium atom number trapped in an optical dipole trap [28] N = N0 F U0 U0 = nMOTVtrap F , (8.1) kBT kBT whereN0 is the number of atoms within the volumeVtrap of the dipole trap at the density nMOT = N0/Vtrap. F[q] is given by with F[q] = q3/2 2 g1(x) = (−ln(1−x))3/2 (1−x) 1/2 x 2 1 0 16 π dxx 2 g1(x)exp[q(1−x)], (8.2) 1 Figure 8.2 shows F as a function of U0/kBT. F 15 10 5 0 duu 2 exp[(ln(1−x))(1−u 2 )]−1. (8.3) 0 0 1 2 3 4 5 U 0kBT Figure 8.2: Dipole trap loading efficiency as a function of U0/kBT. The number of atoms loaded into the into the CO2 dipole trap is greatly enhanced as the temperature of atoms in the MOT is reduced. It is therefore necessary to compress the MOT in order to reduce the temperature and increase the number of atoms in the optical dipole trap, even though compressing the MOT leads to atom loss. Typically the compression sequence is run after the MOT is loaded at a detuning of 38 MHz. The Zeeman slower beams and field are turned off and the atomic beam shutter is closed. 151
A linear ramp typically changes the MOT beam detuning from 38 MHz to the final detuning in 3 to 10 ms using the frequency-offset lock. Figure 8.3 shows the temperature of the atoms in the MOT as a function of the detuning and clearly indicates that changing the detuning is able to reduce the temperature drastically. The temperatures are measured using time-of-flight techniques. At larger detunings the uncertainty in the measurement is large, as only very short expansion times can be realized. The higher the temperature, the faster the atomic cloud expands, reducing the atomic density. Determining the size of the atomic cloud is more difficult at lower atomic densities. In addition, the maximum size of the atomic cloud that can be measured is determined by the size of the chip in the CCD camera. Figure 8.3: MOT temperature as a function of the MOT beam detuning. The black squares (red circles) represent Tx (Ty). Along with changing the beam detuning, it is necessary to reduce the beam power in the MOT beams at the same time. Too large an intensity in the beams will heat the atoms, rather than achieving the desired cooling effect. Figure 8.4 shows the temperature at a fixed final detuning (6 MHz) as a function of final beam power. At −30 dB only about 40 µW (31 µW) of MOT (repump) power are in each of the MOT beams. 152
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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
Page 117 and 118: not trapped by the MOT impinge on t
Page 119 and 120: Should contamination of the vacuum
Page 121 and 122: Figure 7.12: The assembled Zeeman s
Page 123 and 124: 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: Figure 8.1: MOT loading. Typical lo
Page 171 and 172: A typical MOT is density-limited at
Page 173 and 174: ubidium [113-115] and cesium[116].
Page 175 and 176: that most of the noise is due to th
Page 177 and 178: (a) (c) y . x z X=0.0mm Z=2.5mm 1)
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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