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

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the ˆy direction serve as “end caps” sealing the optical trap along the ˆx direction. Each beam had approximately 0.7 W of optical power and together with gravity form a trap ∼ 10µK deep. g x z y Atoms can be trapped here Figure 3.20: The optical trough used to catch atoms during the single-photon cooling process. The trough comprises four blue-detuned Gaussian sheets. Two sheets travel along ˆx and form a “V”-shape. Two vertical sheets travel along ˆy and serve as end caps sealing the trough along ˆx. With gravity along ˆz this forms a potential capable of trapping atoms. All four of the sheets used to form the optical trough are derived from the output of the Verdi V10. The optics used to distribute and shape the beam are shown in Fig. 3.21. The Verdi V10 output beam passes through a series of λ/2 waveplates and polarizing beam splitters allowing us to split the beam along three paths with the needed intensity ratios. The three paths are 120
labeled 1, 2 and 3 in the Fig. 3.21. Beam paths 1 and 2 are used to form the “V”-shaped portion of the optical trough. Each of these beams passes through a telescope formed with a 60 mm and 200 mm lens. The beams are spatially filtered at the focus of the 60 mm lenses. The nominal spacing of the telescope was 260 mm but the 200 mm lenses were placed on translation stages, giving control of the beam curvature after the telescope. We used this degree of freedom to adjust the location of the focus of each beam in the optical trough. After passing though the telescope, each beam passes through a cylindrical lens. These two cylindrical lenses were oriented at a right angle to each other so that when the two beams were combined with a polarizing beam splitter they would form the correct “V” shape. After being combined, the two beams were focused into the chamber with a 63.5 mm lens along the ˆx direction. The astigmatism introduced into each beam by the cylindrical lens caused the beams to have 1/e 2 waists of 10µm × 100µm at the location of the optical trough. The optical end caps were derived from beam path 3. To produce two end caps we pass this beam through an AOM driven at two frequencies which were nominally 84 MHz and 123 MHz. After passing though the AOM unneeded orders were blocked. The unblocked orders passed through a cylindrical lens and were focused into the lower chamber by a 50 mm lens. The end caps travel along the ˆy direction and intersect the two beams which form the “V”-shape. The spacing of the end caps was typically 110µm, but by changing the frequencies driving the AOM this could be adjusted. The measured and 121
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Copyright by Gabriel Noam Price 200
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Single-Photon Atomic Cooling by Gab
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Acknowledgments First, I would like
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Rubidium group when I first joined.
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Single-Photon Atomic Cooling Public
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2.5.2.4 Magneto-Optical Trap . . .
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List of Tables 2.1 87 Rb Physical P
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3.1 Vacuum Chamber . . . . . . . .
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Chapter 1 Introduction This chapter
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the momentum kicks due to absorptio
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samples by allowing for very long i
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Figure 1.2: The energy level struct
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quency regime [19]. This then led t
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Figure 1.4: Depiction of a simple,
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demonstrates the cooling power of a
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a) b) c) external potential one-way
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worked on by Brillouin [27-29], ide
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the atomic ensemble. Not surprising
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are untrappable. The SI unit for en
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the atomic transition and is called
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2.1 Rubidium Rubidium (Rb) is an al
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constant which is given by α = e2
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only one value of J is possible fro
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the latter of which only applies to
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Figure 2.1: 87 Rb D2 Transition Hyp
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Pluging Eq. 2.18 into this Hamilton
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Following the same logic leads to a
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gF = −1/2 using the approximate e
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mize their energy in high magnetic
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If we now consider the field from t
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where P is in torr. The lifetime of
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component of the dipole oscillation
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maxima. Our experiment makes extens
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atoms its wavefunction Ψ(t) is typ
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In this equation we let H = H0 + Hc
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The significance of Isat is that at
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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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Page 89 and 90: D2 transition in 87 Rb has a natura
Page 91 and 92: 2.7.2 Saturation Absorption Spectro
Page 93 and 94: ground state depletion due to the p
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Page 97 and 98: where n is the number density of at
Page 99 and 100: where σ 2 c = σ 2 2 kBTt n + m .
Page 101 and 102: Chapter 3 Experimental Apparatus Th
Page 103 and 104: Figure 3.1: The vacuum chamber duri
Page 105 and 106: Nor-Cal Products Inc. (AMV-1502-CF)
Page 107 and 108: and monitor the necessary vacuum le
Page 109 and 110: 3.1.3 Lower Chamber The lower chamb
Page 111 and 112: a) top ridge 1 cm b) metal jacket h
Page 113 and 114: to the appropriate frequency throug
Page 115 and 116: plexiglass cover piezo U stack grat
Page 117 and 118: λ Figure 3
Page 119 and 120: Voltage a b c d e f Frequency Figur
Page 121 and 122: eams. For example the MOT and optic
Page 123 and 124: λ Figure 3.12: The slave lasers
Page 125 and 126: λ λ λ
Page 127 and 128: λ λ λ λ
Page 129 and 130: needed when forming a MOT or optica
Page 131 and 132: master laser is dithered at 20 kHz.
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Page 135: Output Power > 10 W Wavelength 532
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Page 141 and 142: process. The two coils are arranged
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Page 145 and 146: 3.4.2 Horizontal Imaging The horizo
Page 147 and 148: Chapter 4 Single-Photon Atomic Cool
Page 149 and 150: 1 s, after which time ∼ 10 8 87 R
Page 151 and 152: (a) x z magnetically trapped atoms
Page 153 and 154: h x z magnetically trapped atoms y
Page 155 and 156: z y x magnetically trapped atoms cr
Page 157 and 158: Figure 4.5: The effective potential
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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
Page 171 and 172: netic trap and transfer into the op
Page 173 and 174: 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
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Figure 4.25: Number (■) and tempe
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traps. If we model the ensembles in
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Figure 4.26: Radius of the atomic c
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atoms were removed from the magneti
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trappable |F = 1,mF = −1〉 state
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the short lived 2p state. Atoms whi
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Bibliography [1] R. Frisch, “Expe
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[15] C. C. Bradley, C. A. Sackett,
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[31] E.T. Jaynes, “Information th
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[49] J. Ye, S. Swartz, P. Jungner,
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[66] J.P. Gordon and A. Ashkin, “
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[85] C.-S. Chuu, Direct Study of Qu
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adicals,” Phys. Rev. Lett. 94, 02
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