Single-Photon Atomic Cooling - Raizen Lab - The University of ...

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List of Figures 1.1 A Two-Level Atom . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 A Three-Level Atom . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 One-Way-Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Simple One-Way-Wall Cooling Scheme . . . . . . . . . . . . . 11 1.5 One-Way-Wall Cooling Scheme in an External Potential . . . 14 1.6 Cooling an Atomic Ensemble . . . . . . . . . . . . . . . . . . . 15 1.7 Reconstruction of an Initial Energy Distribution . . . . . . . . 18 1.8 Trap Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 87 Rb D2 Transition Hyperfine Structure . . . . . . . . . . . . . 33 2.2 Vector Model of the Hyperfine Interation . . . . . . . . . . . . 35 2.3 Zeeman Spitting of the F = 1 Hyperfine Manifold . . . . . . . 39 2.4 Magnetic Field from a Circular Loop . . . . . . . . . . . . . . 42 2.5 Magnitude of the Magnetic Field Produced by the Anti-Helmholtz Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.6 Ensemble of Two-Level Atoms Interacting with a Monochromatic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.7 Geometry of Optical Molasses . . . . . . . . . . . . . . . . . . 56 2.8 Optical Molasses in 1-D . . . . . . . . . . . . . . . . . . . . . 57 2.9 Sisyphus Cooling Effect . . . . . . . . . . . . . . . . . . . . . . 61 2.10 Magneto-Optical Trap Geometry . . . . . . . . . . . . . . . . 65 2.11 1-D MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.12 Decay Mode Branching Ratios from the |F ′ = 1,mF = 1〉 State 71 2.13 The Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . 74 2.14 Typical Saturation Absorption Spectroscopy Layout . . . . . . 75 2.15 Saturation Absorption Spectroscopy: Two-Level Atom . . . . 76 2.16 Cross-over Resonance . . . . . . . . . . . . . . . . . . . . . . . 77 2.17 Laser Frequency Locking Layout . . . . . . . . . . . . . . . . . 78 xiv
3.1 Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.2 Upper Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . 88 3.3 Middle Vacuum Chamber . . . . . . . . . . . . . . . . . . . . 92 3.4 Lower Glass Cell . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.5 Helicoflex Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.6 Near-Resonance Laser Frequencies . . . . . . . . . . . . . . . . 97 3.7 MOT Master Laser . . . . . . . . . . . . . . . . . . . . . . . . 99 3.8 MOT Master Saturation Absorption Spectroscopy Layout . . . 101 3.9 MOT master saturation absorption signal . . . . . . . . . . . . 103 3.10 MOT Master Beam Distribution . . . . . . . . . . . . . . . . . 104 3.11 Slave Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.12 Injection of Slave Lasers . . . . . . . . . . . . . . . . . . . . . 107 3.13 Upper MOT Horizontal Slave Laser Beam Distribution . . . . 109 3.14 Upper MOT Diagonal Slave Laser Beam Distribution . . . . . 111 3.15 Lower MOT Slave Laser Beam Distribution . . . . . . . . . . 112 3.16 Repump Master Saturation Absorption Spectroscopy Layout . 114 3.17 Repump Master Saturation Absorption Signal . . . . . . . . . 115 3.18 Repump Master Beam Distribution . . . . . . . . . . . . . . . 116 3.19 Depopulation Beam . . . . . . . . . . . . . . . . . . . . . . . . 117 3.20 The Optical Trough . . . . . . . . . . . . . . . . . . . . . . . . 120 3.21 Verdi Beam Distribution . . . . . . . . . . . . . . . . . . . . . 123 3.22 Picture of Magnetic Trap . . . . . . . . . . . . . . . . . . . . . 124 3.23 Picture of Single Quadrupole Coil . . . . . . . . . . . . . . . . 125 3.24 Schematic of Magnetic Trap . . . . . . . . . . . . . . . . . . . 126 3.25 Vertical Probe Beam Path . . . . . . . . . . . . . . . . . . . . 128 3.26 Horizontal Probe Beam Path . . . . . . . . . . . . . . . . . . . 129 4.1 Overview of the Single-Photon Cooling Process . . . . . . . . 135 4.2 Depopulation Sheet . . . . . . . . . . . . . . . . . . . . . . . . 137 4.3 Crossed Beam Dipole Trap Geometry . . . . . . . . . . . . . . 139 4.4 Effective Combined Potential in Cross Beam Configuration for the |F = 2,mF = 2〉 state . . . . . . . . . . . . . . . . . . . . 140 4.5 Comparison of Effective Potentials . . . . . . . . . . . . . . . 141 xv
Page 1 and 2: Copyright by Gabriel Noam Price 200
Page 3 and 4: Single-Photon Atomic Cooling by Gab
Page 5 and 6: Acknowledgments First, I would like
Page 7 and 8: Rubidium group when I first joined.
Page 9 and 10: Single-Photon Atomic Cooling Public
Page 11 and 12: 2.5.2.4 Magneto-Optical Trap . . .
Page 13: List of Tables 2.1 87 Rb Physical P
Page 17 and 18: Chapter 1 Introduction This chapter
Page 19 and 20: the momentum kicks due to absorptio
Page 21 and 22: samples by allowing for very long i
Page 23 and 24: Figure 1.2: The energy level struct
Page 25 and 26: quency regime [19]. This then led t
Page 27 and 28: Figure 1.4: Depiction of a simple,
Page 29 and 30: demonstrates the cooling power of a
Page 31 and 32: a) b) c) external potential one-way
Page 33 and 34: worked on by Brillouin [27-29], ide
Page 35 and 36: the atomic ensemble. Not surprising
Page 37 and 38: are untrappable. The SI unit for en
Page 39 and 40: the atomic transition and is called
Page 41 and 42: 2.1 Rubidium Rubidium (Rb) is an al
Page 43 and 44: constant which is given by α = e2
Page 45 and 46: only one value of J is possible fro
Page 47 and 48: the latter of which only applies to
Page 49 and 50: Figure 2.1: 87 Rb D2 Transition Hyp
Page 51 and 52: Pluging Eq. 2.18 into this Hamilton
Page 53 and 54: Following the same logic leads to a
Page 55 and 56: gF = −1/2 using the approximate e
Page 57 and 58: mize their energy in high magnetic
Page 59 and 60: If we now consider the field from t
Page 61 and 62: where P is in torr. The lifetime of
Page 63 and 64: component of the dipole oscillation
Page 65 and 66:
maxima. Our experiment makes extens
Page 67 and 68:
atoms its wavefunction Ψ(t) is typ
Page 69 and 70:
In this equation we let H = H0 + Hc
Page 71 and 72:
The significance of Isat is that at
Page 73 and 74:
Δ ω =ω−Δ ω =ω−Δ Δ
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where I/Isat ≪ 1 has been assumed
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λ λ Figure 2.9: The Sisyphus cool
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process repeats. If however, it dec
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σ σ σ Figure 2.10: Geomet
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to vary linearly with position alon
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0, ±1 and ∆mF = 0, ±1, allow ex
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this figure only the relevant hyper
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D2 transition in 87 Rb has a natura
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2.7.2 Saturation Absorption Spectro
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ground state depletion due to the p
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oadened background can be removed f
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where n is the number density of at
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where σ 2 c = σ 2 2 kBTt n + m .
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Chapter 3 Experimental Apparatus Th
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Figure 3.1: The vacuum chamber duri
Page 105 and 106:
Nor-Cal Products Inc. (AMV-1502-CF)
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and monitor the necessary vacuum le
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3.1.3 Lower Chamber The lower chamb
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a) top ridge 1 cm b) metal jacket h
Page 113 and 114:
to the appropriate frequency throug
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plexiglass cover piezo U stack grat
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λ Figure 3
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Voltage a b c d e f Frequency Figur
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eams. For example the MOT and optic
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λ Figure 3.12: The slave lasers
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λ λ λ
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λ λ λ λ
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needed when forming a MOT or optica
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master laser is dithered at 20 kHz.
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λ λ
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Output Power > 10 W Wavelength 532
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labeled 1, 2 and 3 in the Fig. 3.21
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λ λ λ λ
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process. The two coils are arranged
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19) connected in parallel. This arr
Page 145 and 146:
3.4.2 Horizontal Imaging The horizo
Page 147 and 148:
Chapter 4 Single-Photon Atomic Cool
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1 s, after which time ∼ 10 8 87 R
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(a) x z magnetically trapped atoms
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h x z magnetically trapped atoms y
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z y x magnetically trapped atoms cr
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Figure 4.5: The effective potential
Page 159 and 160:
depopulation present and it indicat
Page 161 and 162:
numbers sufficiently large to quant
Page 163 and 164:
μ μ μ
Page 165 and 166:
the potential landscape due to the
Page 167 and 168:
Figure 4.12: The number of atoms lo
Page 169 and 170:
Figure 4.13: Incremental atom captu
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netic trap and transfer into the op
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temperature TB of atoms loaded into
Page 175 and 176:
used to construct it into the remai
Page 177 and 178:
μ μ μ Figure 4.18: Side view of
Page 179 and 180:
Figure 4.20: Geometry of the optica
Page 181 and 182:
could potentially have undergone th
Page 183 and 184:
detunings. The result of scattering
Page 185 and 186:
are switched off causing non-optica
Page 187 and 188:
Figure 4.25: Number (■) and tempe
Page 189 and 190:
traps. If we model the ensembles in
Page 191 and 192:
Figure 4.26: Radius of the atomic c
Page 193 and 194:
atoms were removed from the magneti
Page 195 and 196:
trappable |F = 1,mF = −1〉 state
Page 197 and 198:
the short lived 2p state. Atoms whi
Page 199 and 200:
Bibliography [1] R. Frisch, “Expe
Page 201 and 202:
[15] C. C. Bradley, C. A. Sackett,
Page 203 and 204:
[31] E.T. Jaynes, “Information th
Page 205 and 206:
[49] J. Ye, S. Swartz, P. Jungner,
Page 207 and 208:
[66] J.P. Gordon and A. Ashkin, “
Page 209 and 210:
[85] C.-S. Chuu, Direct Study of Qu
Page 211 and 212:
adicals,” Phys. Rev. Lett. 94, 02
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