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cooling process compresses one dimension of the magnetic trap completely both in position and momentum space (neglecting a photon recoil). This can be expressed in Eq. 4.5 by setting the product over the vertical dimension (ˆz) to 1. With this assumption we can write an upper bound on the expected transfer efficiency of the single-photon cooling process as ηspc = σ (i) (i) O T O ∝ (σB TB) −2 , (4.6) i={x,y} σ (i) B T (i) B where TB = T (i) B reflects a thermalized magnetic trap, and σB ≡ σ (x) B = 2σ(y) B reflects the anisotropic geometry of our magnetic quadrupole trap. We see then, for a fixed optical trap geometry and depth that ηspc is determined by the initial conditions in the magnetic trap. This expression can be simplified even further by noting that for a thermalized ensemble the size of the cloud in the magnetic trap is function of its temperature σB = σB(TB). Figure 4.26 shows a plot of the size of the magnetic cloud as a function of magnetic trap temperature. We find that a linear fit of the measured radii in this regime yields σB = (25.8 + 5.5TB µK −1 )µm. Figure 4.27 shows the experimentally measured transfer efficiencies along with the predicted upper bound, given in Eq. 4.6, for several magnetic trap temperatures. Data in this figure show fair agreement with Eq. 4.6 below 40µK, but there is a trend of increasing efficiency, with respect to the upper bound, with increasing temperature. We believe that this can be understood by noting that our derivation of ηspc is for a non-interacting ensemble. In this case, the initial trajectories of atoms in the magnetic trap fully determine the 174
Figure 4.26: Radius of the atomic cloud in the magnetic trap as a function of temperature. We find that a linear fit of the measured radii in this regime yields σB = (25.8 + 5.5TB µK −1 )µm. dynamics of the cooling process. Only a small fraction of those atoms, repre- sented by Eq. 4.6, will become trapped in the optical trough. In reality, atoms in the magnetic trap weakly interact through collisions. The average single particle collision rate in the magnetic trap is given by Γ = N −1 n(r) 2 σs〈vr〉 dr, (4.7) where N is the total number of trapped atoms, n(r) is the atom number density, σs is the s-wave scattering cross section, and 〈vr〉 = 16kBT/πm is the mean relative speed in a three-dimensional Boltzmann distribution. The inset in Fig. 4.27 shows the calculated average single particle collision rate in the 175
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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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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
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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
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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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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
Page 187 and 188: Figure 4.25: Number (■) and tempe
Page 189: traps. If we model the ensembles in
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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