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

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Central potential approximation 2 P (L=1) 2 S (L=0) Fine Structure 2 P3/2 (J=3/2) 2 P1/2 (J=1/2) 2 S1/2 (J=1/2) Hyperne Structure F=3 F=2 F=1 F=0 F=2 F=1 F=2 F=1 495.8 MHz 814.5 MHz 6.835 GHz Figure 2.4: Central potential approximation, fine, and hyperfine structure of 87 Rb. Energy splittings are not to scale. Central potential approximation 2 P (L=1) 2 S (L=0) Fine Structure 2 P3/2 (J=3/2) 2 P1/2 (J=1/2) 2 S1/2 (J=1/2) Hyperne Structure F=1/2 F=3/2 F=5/2 F=3/2 F=1/2 F=3/2 F=1/2 4.4 MHz 26.1 MHz 228.2 MHz Figure 2.5: Central potential approximation, fine, and hyperfine structure of 6 Li. Energy splittings are not to scale. 9
The Wigner-Eckhart theorem can be used to determine the relative strength of each of the allowed transition by reducing the transition matrix element [26], 〈F,mF|µq|F ′ ,mF ′〉 = 〈F||µ||F′ 〉(−1) F′ √ ′ −1+mF F 2F +1 1 F , (2.10) mF ′ q −mF ′ where |F,mF〉 (|F ′ ,mF ′〉) are the ground (excited) state hyperfine quantum numbers, µq is the component of the spherical electric dipole operator for polarization q and the quantity in parentheses is known as the Wigner 3-j symbol. Applying the Wigner- Eckhart theorem again, the transition matrix element reduces even further to 〈F||µ||F ′ 〉 = 〈J||µ||J ′ 〉(−1) F′ +J+1+I (2F ′ +1)(2J +1) with the use of the Wigner 6-j symbol. J J ′ 1 F ′ F I , (2.11) The matrix element 〈J||µ||J ′ 〉 can be determined experimentally by measuring the transition frequency and the lifetime of a given transition, where 1 τ = ω3 3πǫ0c 3 Values of 〈J||µ||J ′ 〉 for 87 Rb and 6 Li can be found in [17, 20]. 5 2 P 3/2 5 2 S 1/2 2J +1 2J ′ +1 |〈J||µ||J′ 〉| 2 . (2.12) m -1 0 1 F F’=1 m F m F .02 .42 .05 .42 .10 -2 -1 0 1 2 Figure 2.6: Branching ratios for the 87 Rb transitions for the implementation of singlephoton cooling. Figure 2.6 shows the relevant branching ratios for the transition for the implementation of single-photon cooling in rubidium. 10 F=2 F=1
Page 1 and 2: Copyright by Kirsten Viering 2012
Page 3 and 4: Experiments to Control Atom Number
Page 5 and 6: Acknowledgments First of all, I wou
Page 7 and 8: Experiments to Control Atom Number
Page 9 and 10: Table of Contents Acknowledgments v
Page 11 and 12: Chapter 7. Lithium Apparatus 92 7.1
Page 13 and 14: List of Tables 2.1 Physical propert
Page 15 and 16: 4.1 Vacuum chamber . . . . . . . .
Page 17 and 18: 7.39 Future vertical axis optics .
Page 19 and 20: The development of techniques to la
Page 21 and 22: Ptorr 10 5 10 6 10 7 10 8 10 9 260
Page 23 and 24: Property Symbol Value Reference Ato
Page 25: 2.3.2 Hyperfine Structure So far th
Page 29 and 30: The total magnetic moment of an ato
Page 31 and 32: interaction. The shift in the energ
Page 33 and 34: (a) (b) scattering length a 0 Energ
Page 35 and 36: a laser field with frequency ω. Th
Page 37 and 38: Here ω0 is the resonance frequency
Page 39 and 40: Optical molasses do not provide a s
Page 41 and 42: J=1 J=0 -1 Δ σ + σ - σ - 0 +1 -
Page 43 and 44: phase-space density is defined as
Page 45 and 46: which maintains a constant η = U/k
Page 47 and 48: 2.12.1 Saturated Absorption Spectro
Page 49 and 50: Figure 2.22: Saturation absorption
Page 51 and 52: Signal 0 Signal (a) (b) Signal Freq
Page 53 and 54: (a) (b) (c) (d) Figure 2.24: Absorp
Page 55 and 56: y more complex energy level structu
Page 57 and 58: ight side of the box. An irreversib
Page 59 and 60: time (a) (b) (c) Figure 3.3: Single
Page 61 and 62: them to move from B to A, but close
Page 63 and 64: Figure 4.1: Vacuum chamber. Photogr
Page 65 and 66: ( ( Figure 4.3: Helicoflex seal. (a
Page 67 and 68: 88 mm 4.2.3 Auxiliary Coils 62 mm Q
Page 69 and 70: 5 2 P 3/2 5 2 S 1/2 384. 230 484 46
Page 71 and 72: distribution of the MOT master lase
Page 73 and 74: shifts. First a frequency shift of
Page 75 and 76: transition. However, the laser freq
Page 77 and 78:
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
Page 137 and 138:
The error signal shows three lines,
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into the CO2 laser. The optical lay
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Thorlabs PDA10A Coupler ZDC-10-1 to
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Imaging ber Imaging ber from Imagin
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Table 7.4 summarizes the beam power
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CO2 laser 40 MHz AOM f=2 in f=2 in
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132 Figure 7.38: Optical layout aro
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Feshbach coil objective lenses atom
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MOT beams are no longer traveling a
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The second card (NI6733) offers eig
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Averaging over the magnetic subleve
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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
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= E0 1 −n2 √2 exp σ0 ± iE0
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esidual potentials besides gravitat
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Figure 8.1: MOT loading. Typical lo
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A linear ramp typically changes the
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A typical MOT is density-limited at
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ubidium [113-115] and cesium[116].
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that most of the noise is due to th
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(a) (c) y . x z X=0.0mm Z=2.5mm 1)
Page 179 and 180:
Figure 8.11: Different shapes of MO
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ZnSe lens f=5 in knife edge ZnSe wi
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shown in figure 8.13. By matching t
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Figure 8.15: Atom number and temper
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275 Hz. Using these values the beam
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system. Maybe the easiest way to ac
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Appendix A Magic Wavelength of Hydr
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transitions for the excited state p
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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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