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ent results in a magnetic field gradient of B ′ = 48 G/cm. Mode mismatch between the optically pumped atomic sample and the magnetic trap results in heating. The final temperature of the magnetically trapped sample was typically in range of 50-100µK. Under these conditions, the 1/e 2 radius of the magnetically trapped atomic cloud was ∼ 500µm. These atoms serve as the initial condition for further cooling via the single-photon cooling process during which time they are transfered into an optical trap. Then next step in the single-photon cooling process involves position- ing a conservative optical dipole trapped in the wings of the magnetically trap sample. As stated in the introduction to this chapter, the details of the optical dipole trap evolved as the experiment progressed. To keep this overview simple, I will introduce an optical trap representative of the actual potentials used which encompasses their key features. The details of each iteration of the optical trap used during the experiments are discussed in the next several sections. For now, consider a blue detuned optical sheet placed below the magnetically trapped atomic sample. Because the sheet is tuned below the atomic resonance frequency, it produces a repulsive barrier. This barrier is capable of levitating the atoms with sufficiently high optical intensity. Figure 4.1(a) il- lustrates the geometry under consideration. Figure 4.1(b) shows the potential landscape for atoms in the |F = 2,mF = 2〉 state due to the magnetic field gradient, gravity, and the optical sheet. For comparision, Fig. 4.1(c) shows the potential landscape for atoms in the |F = 1,mF = 0〉 state due to gravity and the optical sheet. Notice that atoms in this state are decoupled, to first 134
(a) x z magnetically trapped atoms y g repulsive optical sheet (b) U(z) (c) U(z) i f vertical position (z) vertical position (z) Figure 4.1: Overview of the single-photon cooling process. (a) Cross-sectional view of magnetically trapped atoms above a repulsive optical sheet. (b) Effective potential along the vertical (ˆz) axis for atoms in the |F = 2,mF = 2〉 state due to the combined potentials of a quadrupole magnetic field, gravity, and a repulsive optical sheet. (c) Potential for atoms in the magnetically decoupled |F = 1,mF = 0〉 state. order, from the magnetic field and the tilt in the potential is due entirely to gravity. The idea behind single-photon atomic cooling is to transfer the magnetically trapped atoms, which are in the |F = 2,mF = 2〉 state, into the magnetically decoupled |F = 1,mF = 0〉 state preferentially when they are near their classical turning point and close to the optical sheet. There are two key ideas here that I want to make clear. First, by transferring the atoms from the magnetically coupled to the magnetically decoupled state near their 135
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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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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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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)
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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
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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
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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 and 136: Output Power > 10 W Wavelength 532
Page 137 and 138: labeled 1, 2 and 3 in the Fig. 3.21
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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
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Page 149: 1 s, after which time ∼ 10 8 87 R
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 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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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
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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
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Page 197 and 198: the short lived 2p state. Atoms whi
Page 199 and 200: 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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