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

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We can therefore Taylor expand the full solution and take only the leading, linear term. The result of this expansion and simplification is where the field gradient B ′ is Bz = 2B ′ z (2.38a) Bρ = B ′ ρ (2.38b) B ′ = 3 2 µI (d/2)R2 [(d/2) 2 + R2 ] 5/2. (2.39) For magnetic trapping the magnitude of the field is the important quantity. It is given by B = B ′ ρ 2 + 4z 2 . (2.40) Note that this potential is linear in all radial directions, however the gradient varies along each direction because of the factor of 4 in Eq. 2.40. Also this potential is not harmonic nor central, and so angular momentum is not conserved in this trap. The main source of trap loss is collisions between trapped atoms and the residual thermal background gas present in our vacuum chamber. Unfor- tunately, the cross section for destructive collisions is large because even large impact parameter collisions can impart enough energy to eject atoms from our trap. At pressures P, which are low enough to be of practical interest, the trapping time can be approximated by [38] t ∼ (10 −8 /P) s (2.41) 44
where P is in torr. The lifetime of atoms in our magnetic trap is ∼ 30 s, suggesting that the background pressure is ∼ 3 × 10 −10 torr. 2.5 Interaction of Light with Atoms Interactions of light with atoms fall into two very broad regimes. In the first, the so called far-detuned regime, the frequency of light is far from any atomic resonance. The primary effect of the light is to mix states of opposite parity, inducing a dipole moment in the atom [58]. The induced dipole moment can then interact with an optical intensity gradient present in the dipole inducing beam. As will be discussed, this situation can lead to an almost completely conservative optical trap for neutral atoms. In the second, near-resonant regime, light interacts with atoms primarily through forces due to photon scattering. As will be explored in some detail, this regime can be used to cool and trap atomic ensembles. 2.5.1 The Optical Dipole Force The use of the optical dipole force for confining atoms was first consid- ered by Askar’yan in 1962 [59]. Eight years later Ashkin trapped micron-sized particles with a laser using a combination of radiation pressure and the optical dipole force [60]. He later suggested a 3-D trap for neutral atoms based on his previous work [61]. In 1978 Bjorkholm experimentally demonstrated the dipole force by focusing a beam of neutral atoms [62]. These ideas and work culminated in 1986 with the first optical dipole trap for neutral atoms 45
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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.
Page 9 and 10: Single-Photon Atomic Cooling Public
Page 11 and 12: 2.5.2.4 Magneto-Optical Trap . . .
Page 13 and 14: List of Tables 2.1 87 Rb Physical P
Page 15 and 16: 3.1 Vacuum Chamber . . . . . . . .
Page 17 and 18: Chapter 1 Introduction This chapter
Page 19 and 20: the momentum kicks due to absorptio
Page 21 and 22: samples by allowing for very long i
Page 23 and 24: Figure 1.2: The energy level struct
Page 25 and 26: quency regime [19]. This then led t
Page 27 and 28: Figure 1.4: Depiction of a simple,
Page 29 and 30: 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: If we now consider the field from t
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 and 82: σ σ σ Figure 2.10: Geomet
Page 83 and 84: to vary linearly with position alon
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
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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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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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