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waists of 200 × 10µm. The measured and calculated trap depth is ∼ 10µK. Figure 4.17 shows the calculated potential of this optical dipole trap in the ˆy-ˆz plane centered between the end caps along ˆx. This potential was calculated using Eq. 2.53, the trap geometry, and assuming each sheet had μ μ μ μ μ Figure 4.17: “Optical Trough” potential in the ˆy-ˆz plane centered between the end caps. 1 W of optical power. The presentation in this figure requires explanation. In this figure gravity (−ˆz) points from the lower corner of the plot towards the vertex of the potential. The trough levitates atoms against gravity and confines them along the ˆy dimension with the aid of gravity. Figure 4.18 show the same potential from a side perspective allowing one to see the potential depth more easily. Figure 4.19(a) shows the calculated potential along a line parallel to ˆz intersecting the trough at its geometric center. Figure 4.19(b) shows the calculated potential along the trough vertex. The curvature of the base of this potential is due to the finite Rayleigh length of the beams forming 160
μ μ μ Figure 4.18: Side view of the optical trough potential displaying the trap depth. the ‘V’. One further change made during this iteration was that we placed the optical trough below the magnetically trapped atoms in contrast to the last section in which the optical box was placed above the magnetic trap. Placing the trough below the magnetically trapped atoms is a more favorable geometry because atoms do not have to climb an optical potential hill to enter the optical trap. This is clearly advantageous for this cooling process because atoms climbing a potential hill subsequently fall down it, increasing their kinetic energy in the process. This places a lower limit on the final temperature of the sample. As described in the previous two sections, the depopulation beam drives atoms from the |F = 2,mF = 2〉 state into the 5 2 S1/2(F = 1) manifold. It does this by exciting them into the |F ′ = 1,m ′ F 161 = 1〉 state from where they
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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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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
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
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
Page 171 and 172: netic trap and transfer into the op
Page 173 and 174: temperature TB of atoms loaded into
Page 175: used to construct it into the remai
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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