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

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where is used. ˆǫ ′ inc ·ˆǫ ∗ 1 = 1 √ (ˆx 2 ′ ∓iˆy ′ )· ˆx ′ = 1 √ 2 ˆǫ ′ inc ·ˆǫ ∗ 2 = 1 √ (ˆx 2 ′ ∓iˆy ′ )· ˆy ′ = ∓ i √ 2 The scattered field is then found by subtracting the incident field: Escat = Eobj −Einc = E0 −nξ1σ0 √2 exp 2(1+δ 2 (1+iδ) ˆǫ1 ∓ ) iE0 √2 ˆǫ2 − = E0 −nξ1σ0 √2 exp 2(1+δ 2 (1+iδ) −1 ˆǫ1 ) 1 E0√ (ˆǫ 2 ′ 1 ∓iˆǫ ′ 2) (7.21) (7.22) (7.23) To derive the intensity profile in the imaging plane, the effect of the imaging optics on the fields has to be taken into account. In the thin lens approximation [110] the scattered and incident fields are thus given by Escat(x ′ ,y ′ ) = E0 −nξ1σ0 √2 exp 2(1+δ 2 ik (1+iδ) −1 exp ) ik Einc = E0 exp = E0 exp 2f (x′2 +y ′2 ) ik 2f (x′2 +y ′2 ) ˆǫ ′ inc = E0 exp 1 ˆǫ1 (7.24) 2f (x′2 +y ′2 ) ik 2f (x′2 +y ′2 1√2 ) (ˆǫ ′ 1 ∓iˆǫ ′ 2) √2 (ˆx ′ ±iˆy ′ ). (7.25) The total electric field in the image plane is determined by the sum of the scattered and the incident field: Etot = Escat +Einc = E0 −nξ1σ0 √2 exp 2(1+δ 2 ik (1+iδ) −1 exp ) ik E0 exp 2f (x′2 +y ′2 1√2 ) (ˆǫ ′ 1 ∓iˆǫ ′ 2) = E0 1 −n2 √2 exp σ0 2(1+δ 2 ik (1+iδ) −1 exp ) 1√2 E0 exp (ˆx ′ ±iˆy ′ ) ik 2f (x′2 +y ′2 ) 145 2f (x′2 +y ′2 ) 2f (x′2 +y ′2 ) ˆǫ1 + ˆx ′ +
= E0 1 −n2 √2 exp σ0 ± iE0 √2 exp 2(1+δ 2 ) ik 2f (x′2 +y ′2 ) (1+iδ) ˆy ′ ik exp 2f (x′2 +y ′2 ) ˆx ′ Defining I = k|Etot| 2 and I0 = k|Einc| 2 leads to |E0| I0 = k 2 2 |E0| + = k|E0| 2 2 2 |E0| I = k 2 2 exp 1 −n 2σ0 1+δ 2 + |E0| 2 2 and thus I I0 = 1 2 exp 1 −n 2σ0 1+δ 2 + 1 2 1 = 2 exp ∗ −nσ 1+δ 2 (7.26) (7.27) (7.28) + 1 . (7.29) 2 The effective scattering cross section σ ∗ is only half of σ0. In addition, only half the light interacts with the atoms. The temperature of the MOT and the compressed MOT is measured using the setup shown in 7.38, where this calculation applies. For imaging atoms trapped in the CO2 laser a few changes to the optical setup shown in figure 7.38 are necessary. First, the f = 50 mm lens is removed, changing the magnification to be roughly 1:4. Because of the lower atom number and the increased magnification the signal-to-noise ratio is reduced as compared to imaging of the MOT. Instead of using a polarizing beam splitter cube to combine the MOT and the imaging beam, a mirror mounted on a motorized flipper is added to the setup. It is then possible to use linearly polarized light for imaging the atoms. The intensity in the image plane is then given by [109] I I0 1 −n 2 = exp σ0 1+δ 2 . (7.30) The disadvantage of this setup is that atoms cannot be imaged in the MOT, because the time the flipper requires exceeds the storage time of the atoms. Lithium atoms expand faster than other alkali atoms. This means that especially at MOT temperatures the atoms can move a significant distance even during the imaging exposure time. The imaging pulse duration is therefore restricted to between 10 µs and 20 µs to minimize this effect. 146
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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
Page 111 and 112: angle valve rotary feedthrough ion
Page 113 and 114: an ion gauge controller (Granville
Page 115 and 116: 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
Page 125 and 126: BGauss 250 200 150 100 50 30 20 10
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: The right hand side of equation 7.1
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 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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