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used to cool 87 Rb experimentally, emphasizing those features common to all iterations of the experiment. This section represents an updated version of our original paper proposing a single-photon cooling scheme appropriate for 87 Rb [94]. In all iterations of the experimental process a sample of magnetically trapped 87 Rb was transfered into a conservative optical dipole trap via the single-photon cooling process. The shape and construction of the optical dipole trap varied with each iteration. For the sake of simplicity, I will use a generic optical potential in this overview of the single-photon cooling process and describe the details of each iteration in later sections. To obtain the magnetically trapped sample of 87 Rb, several steps are taken. Atoms are initially loaded into the upper MOT from room temperature 87 Rb vapor. A discussion of the design of the upper chamber and source of Rb can be found in Sec. 3.1.1. As the upper MOT is loaded, the push beam transfers 87 Rb atoms into the lower chamber where they are recaptured in the lower MOT. When optimized, we are able to collect atoms in the lower MOT at a rate of roughly 10 8 atoms/sec. This rate drops off after a few seconds due to saturation effects. When loading the lower MOT we run approximately 1.6 A of current through the lower magnetic quadrupole coils thereby producing a magnetic field gradient of B ′ = 8 G/cm (see Sec. 2.4 and Sec. 3.3 for more details). The lower MOT beams are typically detuned −15 MHz from the |F = 2〉 → |F ′ = 3〉 cycling transition, have a waist of ∼ 1 cm and an optical power of 7 mW each. We typically operated the lower MOT loading stage for approximately 132
1 s, after which time ∼ 10 8 87 Rb atoms were present. To efficiently transfer these atoms into the magnetic trap they underwent two more prepara- tory steps in the lower chamber. The first of these is optical molasses (see Sec. 2.5.2.2). This step reduces the temperature of the atoms from 100-150µK to approximately 10µK. During the optical molasses stage the MOT beams are reduced in intensity by approximately 1/2, the frequency detuning is increased to −50 MHz from the |F = 2〉 → |F ′ = 3〉 transition frequency, and the magnetic field is shut off. The duration of this stage was normally 5 ms, although, as will be seen in Sec. 4.4, we adjusted the duration to control the temperature of the magnetically trapped atoms. Optical molasses leaves the internal state of the atoms distributed among the various Zeeman magnetic sublevels. To maximize loading into the magnetic trap we optically pump atoms into the |F = 2,mF = 2〉 state. This is accomplished by producing a weak, uniform magnetic field with the quadrupole auxiliary coils to define a quantization axis. Then a σ + polarized beam tuned to resonance with the |F = 2〉 → |F ′ = 2〉 transition frequency is sent along this axis, driving atoms into the |F = 2,mF = 2〉 dark state. This process is very fast, taking place in approximately 100µs, and results in an increased transfer efficiency at the price of slightly heating (∼ 5µK) the atomic sample. After being magneto-optically trapped, cooled, and placed into the |F = 2,mF = 2〉 state, the atoms are ready to be magnetically confined. This is accomplished by turning off all optical fields and ramping the current in the magnetic quadrupole coils to 10 A in a few milliseconds. This cur- 133
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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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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
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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.
Page 133 and 134: λ λ
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
Page 143 and 144: 19) connected in parallel. This arr
Page 145 and 146: 3.4.2 Horizontal Imaging The horizo
Page 147: Chapter 4 Single-Photon Atomic Cool
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 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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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 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
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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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