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

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force confines the atoms. The principle of the MOT is illustrated in Fig. 2.11 for the simple case of an atom with a ground state with J = 0 and an excited state with J = 1 in a 1-D geometry. Due to the symmetry of the coils the magnetic field Δ σ Figure 2.11: A 1-D magneto-optical trap for the simple case of a J = 0 → J = 1 transition. A linear magnetic gradient shifts the energy of the J = 1 Zeeman sublevels linearly with position along ˆz. A pair of counter-propagating beams with opposite circular polarization tuned below the atomic resonance frequency impinge on the atom. An atom located at z = z ′ has its Zeeman sublevels shifted such that the mJ = −1 sublevel is closer to atomic resonance than the mJ = 1 sublevel. This causes the atom to scatter photons out of the σ − beam at a greater rate than out of the oppositely traveling beam. The net force pushes the atom back towards the center of the trap. vanishes at the center of the pair. Near the field zero the field increases linearly. The magnetic field perturbs the energy of the Zeeman sublevels causing them 66 σ Δ − Δ +
to vary linearly with position along ˆz. The counter-propagating beams are tuned below the atomic resonance by an amount ∆ and have opposite circular polarizations as shown in the figure. To see how this leads to a trap based on imbalanced scattering rates consider an atom displaced from the center of the trap to a position z = z ′ . At this location the magnetic field causes the Zeeman sublevel mJ = −1 to be brought closer into resonance with the atomic transition while bringing the mJ = 1 sublevel further from resonance. The detuning of each of these states from resonance is indicated by ∆− and ∆+ respectively, with ∆+ > ∆−. Transition selection rules then indicate that the atom will scatter at a greater rate from the σ − beam, pushing it back towards the center. If the atom is displaced in the opposite direction then the Zeeman shift in the sublevels will cause it to scatter preferentially out of the σ + beam, again pushing back towards the center. Of course with the 3-D geometry shown in Fig. 2.10 any displacement from the trap center will lead to a restoring force. Additionally, the red detuning of the beams causes the atoms to cool according to the discussion of optical molasses, therefore MOTs both confine and cool atomic ensembles. We can describe the simple 1-D situation more quantitatively by in- cluding the Zeeman shift into Eq. 2.78, which was used to describe optical molasses FMOT = F σ+ scatt[ω − kv − (ω0 + βz)] + F σ− scatt[ω + kv − (ω0 + βz)], (2.84) where β is the magnetic field gradient. This can be approximated near the 67
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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
Page 31 and 32: a) b) c) external potential one-way
Page 33 and 34: worked on by Brillouin [27-29], ide
Page 35 and 36: the atomic ensemble. Not surprising
Page 37 and 38: are untrappable. The SI unit for en
Page 39 and 40: the atomic transition and is called
Page 41 and 42: 2.1 Rubidium Rubidium (Rb) is an al
Page 43 and 44: constant which is given by α = e2
Page 45 and 46: only one value of J is possible fro
Page 47 and 48: the latter of which only applies to
Page 49 and 50: Figure 2.1: 87 Rb D2 Transition Hyp
Page 51 and 52: Pluging Eq. 2.18 into this Hamilton
Page 53 and 54: Following the same logic leads to a
Page 55 and 56: gF = −1/2 using the approximate e
Page 57 and 58: mize their energy in high magnetic
Page 59 and 60: If we now consider the field from t
Page 61 and 62: where P is in torr. The lifetime of
Page 63 and 64: component of the dipole oscillation
Page 65 and 66: maxima. Our experiment makes extens
Page 67 and 68: atoms its wavefunction Ψ(t) is typ
Page 69 and 70: In this equation we let H = H0 + Hc
Page 71 and 72: The significance of Isat is that at
Page 73 and 74: Δ ω =ω−Δ ω =ω−Δ Δ
Page 75 and 76: where I/Isat ≪ 1 has been assumed
Page 77 and 78: λ λ Figure 2.9: The Sisyphus cool
Page 79 and 80: process repeats. If however, it dec
Page 81: σ σ σ Figure 2.10: Geomet
Page 85 and 86: 0, ±1 and ∆mF = 0, ±1, allow ex
Page 87 and 88: this figure only the relevant hyper
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
Page 95 and 96: oadened background can be removed f
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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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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λ λ λ λ
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process. The two coils are arranged
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19) connected in parallel. This arr
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3.4.2 Horizontal Imaging The horizo
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Chapter 4 Single-Photon Atomic Cool
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1 s, after which time ∼ 10 8 87 R
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(a) x z magnetically trapped atoms
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h x z magnetically trapped atoms y
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z y x magnetically trapped atoms cr
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Figure 4.5: The effective potential
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depopulation present and it indicat
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numbers sufficiently large to quant
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μ μ μ
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the potential landscape due to the
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Figure 4.12: The number of atoms lo
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Figure 4.13: Incremental atom captu
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netic trap and transfer into the op
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temperature TB of atoms loaded into
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used to construct it into the remai
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μ μ μ Figure 4.18: Side view of
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Figure 4.20: Geometry of the optica
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could potentially have undergone th
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detunings. The result of scattering
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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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