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

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In general the polarizability, and thus the energy shift, is different for all atomic energy levels. It is thus possible for the ground and excited state to have opposite signs, and in general the energy shift of the two levels will not be identical. The AC-Stark effect poses a number of challenges for spectroscopic measurements. Since the AC-Stark shift depends on the intensity of light, the transition frequency will vary inside the trap, leading to a broadening of the observed transition linewidth. In addition, the absolute value of the frequency will depend on the trapping laser intensity, and will be broadened by any intensity fluctuations in the trapping potential. If the polarizability has different signs for the two states involved in the transition, it is possible to drive an atom to an anti-trapped state, leading to trap loss. The special wavelength at which the ground and excited state polarizabilities are identical is called the ”magic” wavelength. At the magic wavelength the transition frequency is independent of the laser intensity, and broadening mechanisms are suppressed. It is possible to extend this concept and impose additional requirements, such as coin- cidence between the magnetic dipole or electric quadrupole interactions [129, 130]. For the purpose of this dissertation the analysis is restricted to the electric dipole moment. Magic wavelengths have been calculated and measured for a number of elements, mostly alkaline and alkaline earth elements [83, 131–135]. A.2 Calculations for Hydrogen Hydrogen is the simplest atom in the periodic table of elements. Due to its simplicity it allows precise comparison between theory and experiment, and the spectroscopy of hydrogen has led to precise measurements of fundamental constants such as the Rydberg constant [136]. The spectroscopy of hydrogen and its isotopes is therefore of tremendous value to fundamental physics research. Using equation A.1 the scalar polarizability of the 1s and 2s states of atomic hydrogen are calculated. The polarizability α is approximated using the leading terms in the sum. Figure A.1 shows the polarizability as a function of the wavelength when the first 12 transitions are included for the ground state polarizability, and the first 10 175
transitions for the excited state polarizability (data taken from [137]). At wavelengths where the 2s polarizability matches the 1s polarizability, a magic wavelength exists. In the range from 400 nm to 1 µm and above three distinct magic wavelengths exist. The broadest of these is located around 512.4 nm. polarizabilitya.u. 1000 500 0 500 4.10 7 1000 5.10 7 6.10 7 7.10 7 wavelengthm 8.10 7 9.10 7 1.10 6 Figure A.1: Scalar polarizability of the 1s (red) and 2s (blue) states of atomic hydrogen, calculated using equation A.1. The method outlined above is limited in precision by the number of states that are included in the sum. Fortunately, there are other approaches to calculating the scalar polarizability of hydrogenic atoms [138, 139]. A closed analytical expression for the scalar polarizability (in atomic units) is given by [138] α1s(ω) = − 1 2 512ν − ω2 m=1 9 1m (ν2 1m −1) 2 (ν1m +1) 8 (ν1m −2) 2 ν1m −1 ·2F1 4,2−ν1m,3−ν1m; ν1m +1 α2s(ω) = − 1 − ω2 ·2F1 2 m=1 2 18 ν 9 2m (ν 2 2m +2) 7 (ν2m −4) 3 4,2−ν2m,3−ν2m; 176 2 ν2m −2 , ν2m +2 (A.3) (A.4)
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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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BGauss 250 200 150 100 50 30 20 10
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are required to create the high mag
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The coils are then checked for shor
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+ B A Figure 7.23: Feshbach coil H-
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ensure that no particulates build u
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118 Figure 7.26: Optical layout of
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The error signal shows three lines,
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into the CO2 laser. The optical lay
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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 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: Appendix A Magic Wavelength of Hydr
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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