Experiments with Supersonic Beams as a Source of Cold Atoms

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to reduce the switching time as much as possible. The time varying potential adds significant complication, and numerical simulation is used to determine the energy lost by a hypothetical particle. Since the amount of kinetic energy lost by a particle depends on its position in the coil when the coil is switched off, the timing of the coil switching is criti- cally important. Varying the switching time of a coil changes the velocity and thus the arrival time of the particles at the next coil. The switching times of the coils are calculated numerically by simulating the trajectory of a single particle traveling through the experiment. This particle is henceforth referred to as the synchronous atom or molecule, and can generally be thought of as being in the phase space center of the slowed bunch of atoms. The average initial velocity of the pulsed beam can be found before the start of the experiment by observing the beam with no magnetic fields present and simply calculating the velocity from the time of flight to the de- tector. The synchronous particle is then assigned this velocity as its initial velocity. The short opening time of the Even-Lavie supersonic nozzle means that the atoms leave the nozzle at a precise time, and so the time-of-flight measurement of the initial velocity of the beam is very precise. From this, the arrival time of the beam at the entrance of the coilgun can be computed easily and precisely, and the entire coil timing sequence can be referenced to the valve pulse. 4.3.1 Phase Stability For an instantaneously switched coil, maximal slowing is achieved by switching the coil when the synchronous particle is at the peak field location. However, this is not the ideal position to switch a real coil for several reasons. The first reason is that a real coil will require some time to turn off, and thus the switching position that imparts maximal slowing is moved towards the front of the coil (the direction from 69
which the particles enter). The other reason to switch the coil when the synchronous particle is in front of the coil is to maximize the volume in phase space of the slowed bunch of particles. The volume of phase space which the coilgun is able to slow is an important consideration, since the number of slowed particles is a key factor in many future uses the coilgun. It is desirable to maximize the phase space acceptance of the coilgun, where the ideal acceptance maximizes its overlap with the phase space occupied by the incoming supersonic beam. While it may not be possible to match the phase space acceptance of the coilgun to the beam, any increase in the accepted phase space volume is beneficial. For the purposes of the following discussion, it is assumed that the coils are switched instantaneously. While this is not a valid assumption in general, the qualitative behavior of the slowed bunch in this scenario is easier to ascertain, and the same behavior is exhibited, though with greater complexity, in the case of real coils with finite switching times. As stated above, maximal slowing is achieved, by timing the coils to turn off when the synchronous particle is at the peak magnetic field. This timing scenario is illustrated in figure 4.6(a). In this scenario, the particles which are behind and ahead of the center of the slowed bunch are not slowed as much as the synchronous particle, since they do not experience as great a field when the coil is switched. Because particles which are ahead of the center of bunch are not slowed as much, they get out of phase with the coil pulse sequence and are eventually lost from the slowed bunch. Particles that are behind the center of the bunch are not slowed as much, so they catch up with the center of the bunch, but any particle that gets ahead of the synchronous atom is eventually lost, leading to a vanishingly small region of phase space which stays in phase with the full coil sequence. Instead of switching when the synchronous atom is at the peak of the field, 70
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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
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 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: (a) (b) (c) Time Figure 4.5: A pict
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 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
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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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