Experiments with Supersonic Beams as a Source of Cold Atoms

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Figure 3.12: Finite element calculation of rotor vibrational modes. This was performed using the built in finite element package in Solid Edge. The vibrational mode shown has a resonance frequency of 47Hz. The calculation does not take into account the fact that the rotor and spindle are made from different materials, as only one material can be simulated. As such the entire structure is simulated as stainless steel, since most of the weight is in the stainless steel spindle. Additionally, the shaft of the spindle, which is found to be region that flexes most, is stainless steel. Reducing the weight of the rotor (it is titanium in the experiment) would likely result in a slightly higher resonant frequency in the real system. in black. The dashed lines indicate resonances by at least one of these methods. Ad- ditionally, these resonances can be heard as increased noise from the chamber, and the chamber vibrations are easily felt by placing a hand on the chamber. The solid lines in figure 3.11 are Lorentzian fits of the limiting resonance, which is predicted be lie around 48 − 50 Hz. From these fits, the peak vibrational amplitude can be estimated to be 1000 − 2000 μm which is too large to be comfortably passed through, and thus limits the rotor velocity to 42 Hz. A finite element calculation of the vibrational modes of the rotor and spindle was performed to investigate the source of this unexpected resonance using the built in finite element package of CAD program Solid Edge. This analysis shows the nature of the resonance which limits the rotor velocity, and the results of this calculation are shown in figure 3.12. The finite element calculation predicts two pendulum modes, one at 34 Hz and one at 47 Hz, in addition to a twisting mode at 35 Hz. Several 41
approximations are made in this calculation. The first approximation is that the coupling between the spindle and feedthrough is truly rigid. The second approximation comes from the fact that this finite element package cannot simulate two materials simultaneously. The entire rotor structure is simulated as stainless steel, since the stainless steel spindle comprises most of the mass, and because the point which the calculations indicate is flexing the most is the stainless steel shaft of the spindle. In the experimental setup, the rotor is made from titanium and weighs about 700 g less than the stainless steel rotor of the finite element calculation. This decrease in mass should result in increased resonant frequencies in the actual rotor. A final uncertainty lies in the fact that this calculation does not include the shaft of the feedthrough, as the rigidity of the bearings is unknown. However, given that the finite element calculation predicts resonant frequencies in the same region where they are observed leads to a belief that the pendulum modes of the spindle shaft are the cause of the resonance which limits the rotor velocity. 3.3.2.3 Improved Spindle Design Led by the finite element calculation described in section 3.3.2.2, the spindle was redesigned with the goal of increasing the resonant frequencies of the vibrational modes. To do this, the spindle material is changed to titanium instead of stainless steel, and redesigned to have minimal mass, which reduced the weight of the spindle from 4.07 kg to .88 kg. The reduction in spindle mass means that the rotor does not spin around the axis with the greatest moment of inertia, but this is viewed as an acceptable trade off. Additionally, the method of clamping the spindle to the shaft of the feedthrough is completely redesigned. Rather than having a thin shaft extend from the top of the spindle, which is connected to the shaft of the feedthrough by a clamp, the spindle is designed to be a clamp itself. This design is similar to the 42
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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,
Page 7 and 8: to problems, and I frequently went
Page 9 and 10: General Methods of Controlling Atom
Page 11 and 12: Table of Contents Acknowledgments v
Page 13 and 14: Chapter 5. Towards Trapping and Coo
Page 15 and 16: List of Figures 2.1 Comparison of e
Page 17 and 18: 5.12 Faraday Rotation Signal During
Page 19 and 20: producing a cold sample. Alternativ
Page 21 and 22: place inside a dilution refrigerato
Page 23 and 24: atoms or molecules are slowed using
Page 25 and 26: 2.1 Thermodynamics of Ideal Gases F
Page 27 and 28: Since there will be no heat exchang
Page 29 and 30: Using equation 2.17 to modify equat
Page 31 and 32: Normalized Effusive Beam Flux Norma
Page 33 and 34: general method for producing cold a
Page 35 and 36: The gas throughput of the nozzle ca
Page 37 and 38: 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: Figure 3.11: This plot shows the am
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 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
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(a) (b) (c) (e) Figure 4.21: A pict
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258V 1MΩ TTL 2.2mF 50Ω TTL 5V 5V
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closed. With the new thyristor gate
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HeNe M2 M1 BB /2 L BB PC coil PC PD
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Table 4.1: Peak magnetic fields mea
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Figure 4.28: A cut-away CAD image o
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ameters. The coilgun chamber consis
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Table 4.2: Final velocities (vf), s
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MCP Signal [arb. units] 2.0 1.5 (1)
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viability for molecules essential.
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8 Ω LN2 Liquid Nitrogen Dewar Nozz
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Figure 4.33: Molecular oxygen slowi
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Chapter 5 Towards Trapping and Cool
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Energy meV 0.05 0.00 0.05 0.0 0.2 0
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10 mm 2.0 T 1.8 1.6 1.4 1.2 1.0 0.8
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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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