Experiments with Supersonic Beams as a Source of Cold Atoms

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Magnetic field (T) 1.8 1.75 1.7 1.65 1.6 1.55 1.5 1.45 1.4 1.35 −4 −3 −2 −1 0 1 2 3 4 x 10 −3 1.3 Radial position (m) (a) Magnetic field (T) 0.7 0.65 0.6 0.55 0.5 0.45 −4 −3 −2 −1 0 1 2 3 4 x 10 −3 0.4 Radial position (m) Figure 4.7: This figure illustrates the manner in which the magnitude of the magnetic field varies with radial position in a 1.05 cm diameter coil. The field at the center of the coil (z = 0) is plotted in (a). The magnitude of the field is at a radial minimum on the axis of the coil at this axial position, which provides a focusing force to lowfield-seeking particles. The field, as a function of radial position well outside of the coil is plotted in (b). Here, the radial dependence of the field magnitude is at a maximum on the axis of the coil, providing a de-focusing effect for low-field-seekers. The interplay between the focusing effects inside the coil and the de-focusing outside the coil is complex, and depends on the velocity of the particles passing though the coil, as well as the switch-off timing. large effect on the number of slowed atoms or molecules. Maxwell’s equations dictate that there can be no free space maximum in magnetic field. Though the magnitude of the magnetic field on the axis of a coil (z-axis) is at a maximum at center of the coil, this cannot be a true local maximum. Instead, this point at the center of a coil is a saddle point, and is at a minimum of the field radially. The magnitude of the field of a coil as a function of radial position at z = 0 is plotted in figure 4.7(a). The fact that the field is at a minimum on axis here means that low-field-seeking atoms feel a force pushing them towards the axis of the coil, producing a focusing effect on the beam of particles. This allows the coilgun to act as a waveguide, and can provide a degree of transverse stability to the slowed bunch of atoms in the coilgun. (b) Though the magnitude of the field is radially minimal on axis at the center of the coil, this is not true at all locations. Examining the radial dependence of 73
the magnitude of the field some distance along the axis from the center, the field is eventually a maximum along the axis, instead of a minimum. This aspect of the field is illustrated in figure 4.7(b). This means that while low-field-seekers are focused at the center of the coil, outside the coil the magnetic field de-focuses low-field-seekers. The transverse stability of the particles in the slowed bunch depends on the interplay between these two effects. For typical coils, the focusing effect in the center of the coil is much stronger than the de-focusing effect outside the coil. However, from the discussion in section 4.3.1, there is a benefit to turning the coils off before particles reach the center of the coil. The degree to which the atoms are focused instead of de-focused depends on their location in the coil when the field is switched off. While the longitudinal stability of the slowed packet is greatest when the coils are switched when particles are far from the center of the coil, this provides the least transverse stability, and may even lead to a de-focusing effect on particles being slowed. However, at the cost of additional laboratory space, it may be beneficial not to switch off some coils, enabling the particles to feel the full focusing effects of these coils and providing a counter to the de-focssing effects of switching far from the coil. This concept of transverse stability also shows up in the pulsed electric field decelerator [79, 80], and is further discussed for the coilgun in [25, 81]. The concept of using strong magnetic fields to focus atoms without slowing them is discussed in [82]. 4.4 Proof-of-Principle Experiment: Slowing Metastable Neon The goal of the initial experiment was to show that the concept presented above works, and that measurable slowing of a beam can be achieved over a short distance. To accomplish this, an apparatus consisting of 20 coils was produced, and this apparatus was inserted into the same vacuum chamber that houses the rotor, 74
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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
Page 39 and 40: 3.1 Using Helium for Atom Optics Ex
Page 41 and 42: Figure 3.1: Calculated elastic scat
Page 43 and 44: that they can be prepared ex-situ a
Page 45 and 46: successful. Any water that remains
Page 47 and 48: Skimmer 300 l/s Turbo Pump Even-Lav
Page 49 and 50: Figure 3.5: A CAD image of the dete
Page 51 and 52: from tubular aluminum welded togeth
Page 53 and 54: Figure 3.7: A CAD image of the roto
Page 55 and 56: Figure 3.10: A CAD image of large c
Page 57 and 58: Figure 3.11: This plot shows the am
Page 59 and 60: approximations are made in this cal
Page 61 and 62: 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: the coil can instead be switched be
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 and 114: closed. With the new thyristor gate
Page 115 and 116: HeNe M2 M1 BB /2 L BB PC coil PC PD
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
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Magnetic Field (T) 1.9 1.7 1.5 1.3
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5.2.2.1 Principle of Operation of t
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Figure 5.8: Photograph of the trapp
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4.1.3. In an anti-Helmholtz trap, t
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Figure 5.11: Photograph of the hydr
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Photodiode Signal (V) Time (s) Figu
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Figure 5.13: Time of flight plot of
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500 l/s Turbo Pump Supersonic Nozzl
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Ionizer 500 l/s Turbo Pump Ion Opti
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guided the design of the apparatus.
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Z − Velocity (m/s) 100 60 30 0
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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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