Experiments with Supersonic Beams as a Source of Cold Atoms

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The method chosen for measuring the field is the Faraday effect. Some materi- als (called Faraday rotators) rotate the plane of polarization of light when a magnetic field in the direction of propagation of the light is present. The angle of rotation of linearly polarized light passing through a Faraday rotator in the presence of a magnetic field in the propagation direction is ψ = z2 z1 vB(z)dz, (4.31) where v is the Verdet constant of the material, B is the field in the direction of propagation, and x1 and x2 are the coordinates of material boundaries. For a constant field this simplifies to ψ = vBd, (4.32) where d is the length of the Faraday rotator. Importantly, since this is an optical process, the effect takes place on time scale much shorter than the coil switching time, and has even been resolved in the femtosecond domain [85]. The Faraday rotator used to measure the field in the coilgun coils is a terbium gallium garnet (TGG) crystal, which has a Verdet constant at room temperature of −134 rad/T/m for 633 nm wavelength light, where the sign indicates the direction of rotation. For a negative Verdet constant, the rotation will be in the direction opposite the direction of current in a coil around the crystal creating a magnetic field. This is independent of the direction of propagation of the light. A schematic drawing of the Faraday rotation measurement setup is shown in figure 4.25. Polarized light from a Helium-Neon laser passes through a polarizing beamsplitter cube, which sets the polarization angle of the light. This angle can be further adjusted using a λ/2 plate, which is the next element in the setup. The light is then focused by an 83 mm focal length lens down to a waist of 40 μm inthe center of the coil. The TGG crystal is inserted into the bore of the coil, and care is 97
HeNe M2 M1 BB /2 L BB PC coil PC PD Figure 4.25: A schematic drawing of the Faraday rotation setup. M1 and M2 are beam steering mirrors which are used to align the light to the remainder of the apparatus. The beam passes though a polarizing beamsplitter cube (PC) and a λ/2 plate before being focused by an 83 mm focal length lens (L) to a 40 μm waist in the center of the coil. The TGG crystal is inserted into the coil, and the light is rotated in proportion to the magnetic field. The light passes though another polarizing cube before being detected on a photodiode (PD). The stray beams coming out of the polarizing cubes are blocked with beam blocks (BB). Figure Courtesy Christian Parthey. taken to ensure that the crystal is centered axially in the coil (the crystal used has a 3 mm diameter, and thus fills the coil radially). The light then passes though another polarizing cube before being detected on a photodiode. Because the magnetic field changes the angle of rotation, but the photodiode measures the power of the light hitting its surface, it is necessary to convert between the two. This gives the relation I I0 =Cos 2 z2 z1 vB(z)dz , (4.33) where I is the detected intensity on the photo diode, and I0 is the maximum intensity corresponding to no light being split off by the second polarizing cube. As the field in the coil varies along the axis of the coil, the measured change in intensity corresponds to the integral of the field along the length of the crystal. The measured field values on the axis of the coil are used to calibrate the current used in the finite element calculation of the spatial field profile. When actually measuring the field in the coil, crystals of several lengths are 98
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Copyright by Adam Alexander Libson
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General Methods of Controlling Atom
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Acknowledgments First and foremost,
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to problems, and I frequently went
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General Methods of Controlling Atom
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Table of Contents Acknowledgments v
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Chapter 5. Towards Trapping and Coo
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List of Figures 2.1 Comparison of e
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5.12 Faraday Rotation Signal During
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producing a cold sample. Alternativ
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place inside a dilution refrigerato
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atoms or molecules are slowed using
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2.1 Thermodynamics of Ideal Gases F
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Since there will be no heat exchang
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Using equation 2.17 to modify equat
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Normalized Effusive Beam Flux Norma
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general method for producing cold a
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The gas throughput of the nozzle ca
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Chapter 3 Slowing Supersonic Beams
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3.1 Using Helium for Atom Optics Ex
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Figure 3.1: Calculated elastic scat
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that they can be prepared ex-situ a
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successful. Any water that remains
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Skimmer 300 l/s Turbo Pump Even-Lav
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Figure 3.5: A CAD image of the dete
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from tubular aluminum welded togeth
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Figure 3.7: A CAD image of the roto
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Figure 3.10: A CAD image of large c
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Figure 3.11: This plot shows the am
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approximations are made in this cal
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3.3.3 Detection An SRS [61] residua
Page 63 and 64: TTL pulse to the data acquisition c
Page 65 and 66: A comparison of the time-of-flight
Page 67 and 68: eceding crystal. Each curve is the
Page 69 and 70: calculated slow beam velocity is qu
Page 71 and 72: the RGA does have an effect on the
Page 73 and 74: Chapter 4 The Atomic and Molecular
Page 75 and 76: field. In the L − S coupling regi
Page 77 and 78: 3 P2 E Figure 4.2: This graph gives
Page 79 and 80: For intermediate fields, the full p
Page 81 and 82: Figure 4.4: This figure illustrates
Page 83 and 84: The same effect is also responsible
Page 85 and 86: (a) (b) (c) Time Figure 4.5: A pict
Page 87 and 88: which the particles enter). The oth
Page 89 and 90: the coil can instead be switched be
Page 91 and 92: the magnitude of the field some dis
Page 93 and 94: nozzle front surface aluminum catho
Page 95 and 96: Figure 4.9: A CAD overview of the s
Page 97 and 98: 258V 1MΩ 5V 1mF DC/DC Converter TT
Page 99 and 100: Figure 4.12: An oscilloscope trace
Page 101 and 102: (a) (b) Figure 4.14: A CAD image of
Page 103 and 104: -HV PS 4 M MCP Anode 10 M 1 M Trans
Page 105 and 106: Signal [V] 2.5 2.0 1.5 1.0 0.5 refe
Page 107 and 108: Figure 4.20: An exploded view of th
Page 109 and 110: (a) (b) (c) (e) Figure 4.21: A pict
Page 111 and 112: 258V 1MΩ TTL 2.2mF 50Ω TTL 5V 5V
Page 113: closed. With the new thyristor gate
Page 117 and 118: Table 4.1: Peak magnetic fields mea
Page 119 and 120: Figure 4.28: A cut-away CAD image o
Page 121 and 122: ameters. The coilgun chamber consis
Page 123 and 124: Table 4.2: Final velocities (vf), s
Page 125 and 126: MCP Signal [arb. units] 2.0 1.5 (1)
Page 127 and 128: viability for molecules essential.
Page 129 and 130: 8 Ω LN2 Liquid Nitrogen Dewar Nozz
Page 131 and 132: Figure 4.33: Molecular oxygen slowi
Page 133 and 134: Chapter 5 Towards Trapping and Cool
Page 135 and 136: Energy meV 0.05 0.00 0.05 0.0 0.2 0
Page 137 and 138: 10 mm 2.0 T 1.8 1.6 1.4 1.2 1.0 0.8
Page 139 and 140: 250V 1MΩ 3x 2.2mF TTL 5V feedback
Page 141 and 142: Magnetic Field (T) 1.9 1.7 1.5 1.3
Page 143 and 144: 5.2.2.1 Principle of Operation of t
Page 145 and 146: Figure 5.8: Photograph of the trapp
Page 147 and 148: 4.1.3. In an anti-Helmholtz trap, t
Page 149 and 150: Figure 5.11: Photograph of the hydr
Page 151 and 152: Photodiode Signal (V) Time (s) Figu
Page 153 and 154: Figure 5.13: Time of flight plot of
Page 155 and 156: 500 l/s Turbo Pump Supersonic Nozzl
Page 157 and 158: Ionizer 500 l/s Turbo Pump Ion Opti
Page 159 and 160: guided the design of the apparatus.
Page 161 and 162: Z − Velocity (m/s) 100 60 30 0
Page 163 and 164: Atom Number 60 50 40 30 20 10 0.6 0
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scattered photon to extract informa
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where k1 · pi = − k2 · pi, wh
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the electron g-factor which causes
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Figure 5.24: A schematic of the tel
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prevent the determination of the is
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(a) (b) time Figure 5.25: A 1D illu
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experiment, where a being is capabl
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potential position 2 x 243 nm Lα |
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Appendix 164
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y x V i Figure A.1: The geometry us
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Bibliography [1] H.J.MetcalfandP.va
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[17] Brian C. Sawyer, Benjamin L. L
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[34] R. Campargue. Progress in over
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[51] O. Carnal, M. Sigel, T. Sleato
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[70] Edvardas Narevicius, Adam Libs
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[87] Willis E. Lamb and Robert C. R
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[96] G.Gabrielse,N.S.Bowden,P.Oxley
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[110] N. Kolachevsky, J. Alnis, S.
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[125] Andreas Osterwalder, Samuel A
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[142] C. Cohen-Tannoudji, B. Diu, a
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[161] Paulo F. Bedaque, Aurel Bulga
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Experiments with Supersonic Beams as a Source of Cold Atoms

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