Experiments with Supersonic Beams as a Source of Cold Atoms

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atom or molecule in a low-field-seeking state moves from a region of low field to a region of high field, its potential energy increases. Since force F = −∇U where U is the potential energy, a spatially varying magnetic field produces a force, and a low-field-seeking atom or molecule is repelled from regions of high field. Conservation of energy dictates that a particle loses kinetic energy equal to its gain in potential energy. Thus, as a low-field-seeking atom enters a region of high field it will lose a kinetic energy equivalent to the Zeeman shift of the internal states. For a particle moving in an electromagnetic coil, the loss of kinetic energy T in the Zeeman regime (assuming L − S coupling) is ΔT = −μBgJmJΔB, (4.29) and similarly in the Paschen-Back regime the change in kinetic energy is ΔT = −μB (2mS + mL)ΔB. (4.30) While a low-field-seeking particle loses kinetic energy moving from a region of low field to a region of high field, the reverse is also true. Hence, a low field seeking particle moving in an electromagnetic coil loses energy as it enters the coil, and if the field is unchanged it regains the kinetic energy as it exits the coil. However, if the coil is switched off quickly while the particle is in a region of high field, the particle loses kinetic energy. This process can be repeated through multiple coils, each removing kinetic energy from the beam, until the desired velocity is attained. The slowing sequence for a single coil is illustrated in figure 4.5. While equations 4.29 and 4.30 are exact for an ideal coil that switches instan- taneously, a real coil is more complicated. In a real coil, the magnetic field turns off over some period of time, during which the particle will continue to move in the coil. For this reason, it is important to optimize the coil and switching electronics 67
(a) (b) (c) Time Figure 4.5: A pictorial illustration of the principal of operation of the coilgun. In (a) a low field seeking atom approaches an energized coil with the coil’s field illustrated in red. The atom enters the magnetic field region and is slowed down as illustrated in (b). The field is then turned off, allowing the atom to exit the coil without regaining the lost energy, as shown in (c). 68
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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
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 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: The same effect is also responsible
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 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
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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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