Experiments with Supersonic Beams as a Source of Cold Atoms

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The apertures set the transverse temperature, and hotter atoms are removed from the beam by the apertures, leaving only the colder atoms in the beam. For this reason, it is appropriate to concentrate on the parallel component of the velocity, giving the Gaussian velocity profile m p(v) = e 2πkBT − m(v −w) 2 2kB T = σ 1 √ e 2π −(v −w) 2 2σ 2 , (2.25) where σ is the standard deviation in the velocity parallel to the beam axis. This velocity distribution is compared to the Maxwellian velocity distribution for a few relevant gas species and reservoir temperatures in figure 2.1. As can be seen in the figure, the width of the velocity profile is significantly narrower for the case of a supersonic beam. Expressed in terms of temperature, beams of a few tens to a few hundred milliKelvin are common. This is significantly colder than the reservoir temperatures, and the supersonic expansion has effectively cooled the beam. The cooling achieved by supersonic expansion is extremely general and can be used to cool any desired species. In the above discussion on isotropic expansion, it is assumed that the gases were truly ideal gases. Supersonic beams are generally created with a noble carrier gas that generally behaves as an ideal gas at higher pressures and lower temperatures than many other gas species. Other species of interest are mixed in the reservoir before the expansion, or added just outside the nozzle during the expansion. If the species of interest is a gas at the reservoir temperature, it is typically seeded into the carrier gas in the reservoir. A species that is not a gas at the reservoir temperature is typically entrained into the beam at the exit of the nozzle. Laser ablation can be used to produce an atomic sample of a solid at the exit of a nozzle, or alternatively, an oven can produce an atomic beam that is then entrained in the supersonic beam. In either case, the added species is cooled by thermalizing with the dominant carrier gas and is carried along with the supersonic beam, providing a 15
general method for producing cold atoms. Different carrier gases have their own advantages and disadvantages that must be weighed when selecting a species to use in an experiment. The mass term in equation 2.23 means that a heavier carrier gas will produce a slower beam. This can be a large advantage, since supersonic beam velocities can range from several hundred to over a thousand meters per second. There are, however, some disadvantages to using heavier atoms as the carrier gas. Due to the dynamics of the collisions in the beam, light atoms being carried by a heavier carrier gas will tend to be pushed to the edges of the beam, and so the centerline flux of the species of interest will be reduced. The other possible disadvantage of a heavier carrier gas is the possibility of a hotter beam due to clustering. The binding energy of a cluster is released as heating in the beam itself. The cluster fraction can be estimated using the Hagena parameter [29, 30], and clustering becomes increasingly likely for the heavier noble gases. 2.3 The Even-Lavie Nozzle for Generating Pulsed Beams The experiments described by this dissertation all use a pulsed valve for generating supersonic beams [31–33]. The valves used are made by Uzi Even and Nachum Lavie at Tel Aviv University. There are several advantages to using a pulsed valve. The methods used to control the beams are pulsed and having a pulsed beam matches well with the control mechanisms. Additionally, the vacuum pumping requirements are significantly reduced by using a pulsed beam. Instead of using large diffusion pumps to maintain vacuum in the valve chamber, the experiments are able to use turbomolecular pumps that cannot contaminate the chamber with pump oils the way a diffusion pump can. The Even-Lavie uses a nozzle with a 200 μm diameter and a trumpet shaped expansion region. This shape helps to remove hot spots in the beam and reduces 16
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: Normalized Effusive Beam Flux Norma
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
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(a) (b) (c) Time Figure 4.5: A pict
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which the particles enter). The oth
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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
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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
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-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
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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
Page 171 and 172:
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
Page 187 and 188:
[17] Brian C. Sawyer, Benjamin L. L
Page 189 and 190:
[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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