Experiments with Supersonic Beams as a Source of Cold Atoms

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sulting in the brightest supersonic beams and providing further motivation to find methods of controlling ground state helium beams. In large part because of the advantages described above, there is a long history of using helium beams and helium scattering as an experimental probe. Stern and Estermann used helium diffraction from lithium fluoride crystals to demonstrate the wave nature of atoms and to experimentally confirm equation 3.1 [46]. Detailed examination of the diffraction of helium from surfaces has provided many insights into the details of surface structure and the atom-surface potential [47]. More recent work has used transmission diffraction gratings to study helium clustering in supersonic beams [35]. While ground state noble gases are more difficult to control than atoms which are laser coolable, several techniques have been developed which can be applied to the control of ground state helium. A standard optical toolbox includes mirrors, beamsplitters, and lenses. To effectively use ground state helium for atom optics, analogs of these tools are required. One such approach to creating these tools has been to use species independent methods such as transmission diffraction gratings [48–50] and transmission Fresnel lenses [51, 52]. Another approach is to make use of the high elastic scattering probability of helium from crystal surfaces. Flat surfaces create mirrors and the equivalent of a lens can be formed by bending the crystal, creating a curved mirror [12]. Finally, the periodic structure of a crystal surface can be used as a diffraction grating [53], creating a beamsplitter for the atoms. In this manner, the entire optical toolbox can be created using crystal surfaces. 3.2 Reflecting Atoms from Surfaces: Atomic Mirrors Having a large fraction of the helium beam be elastically scattered from the crystal surface is important when manipulating a supersonic beam using reflection 23
Figure 3.1: Calculated elastic scattering probability for helium incident on Si(111) for different beam velocities as a function of crystal temperature. These are calculated using the Debye-Waller factor described in equations 3.3 and 3.4. While the elastic fraction is well approximated by the Debye-Waller factor, atoms may still be diffracted and these numbers do not represent the fraction of specularly reflected atoms. Figure Courtesy Max Riedel. from crystals. Assuming the atom surface potential has zero well depth (which means that there is no Beeby correction), the elastic scattering fraction from single crystalline surfaces is governed by the Debye-Waller factor [54], I I0 = e −2W where I is the elastically reflected intensity, I0 is the incident intensity, and (3.3) W = 12mE⊥Ts MkBθ2 . (3.4) s Here m is the mass of the incident atom, E⊥ is the incident energy, Ts is the temperature of the crystal, M is the mass of the atom in the crystal, and θs is the Debye temperature of the crystal. 24
Page 1 and 2: Copyright by Adam Alexander Libson
Page 3 and 4: General Methods of Controlling Atom
Page 5 and 6: 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: 3.1 Using Helium for Atom Optics Ex
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 and 90: the coil can instead be switched be
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the magnitude of the field some dis
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nozzle front surface aluminum catho
Page 95 and 96:
Figure 4.9: A CAD overview of the s
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258V 1MΩ 5V 1mF DC/DC Converter TT
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Figure 4.12: An oscilloscope trace
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(a) (b) Figure 4.14: A CAD image of
Page 103 and 104:
-HV PS 4 M MCP Anode 10 M 1 M Trans
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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
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
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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.
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
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
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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
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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
Page 165 and 166:
scattered photon to extract informa
Page 167 and 168:
where k1 · pi = − k2 · pi, wh
Page 169 and 170:
the electron g-factor which causes
Page 171 and 172:
Figure 5.24: A schematic of the tel
Page 173 and 174:
prevent the determination of the is
Page 175 and 176:
(a) (b) time Figure 5.25: A 1D illu
Page 177 and 178:
experiment, where a being is capabl
Page 179 and 180:
potential position 2 x 243 nm Lα |
Page 181 and 182:
Appendix 164
Page 183 and 184:
y x V i Figure A.1: The geometry us
Page 185 and 186:
Bibliography [1] H.J.MetcalfandP.va
Page 187 and 188:
[17] Brian C. Sawyer, Benjamin L. L
Page 189 and 190:
[34] R. Campargue. Progress in over
Page 191 and 192:
[51] O. Carnal, M. Sigel, T. Sleato
Page 193 and 194:
[70] Edvardas Narevicius, Adam Libs
Page 195 and 196:
[87] Willis E. Lamb and Robert C. R
Page 197 and 198:
[96] G.Gabrielse,N.S.Bowden,P.Oxley
Page 199 and 200:
[110] N. Kolachevsky, J. Alnis, S.
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[125] Andreas Osterwalder, Samuel A
Page 203 and 204:
[142] C. Cohen-Tannoudji, B. Diu, a
Page 205 and 206:
[161] Paulo F. Bedaque, Aurel Bulga
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Experiments with Supersonic Beams as a Source of Cold Atoms

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