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

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Using this relation and introducing the on-resonance damping rate Γ ≡ Γω0 = (ω0/ω) 2 ΓL allows the polarizability to be written as [68] Γ/ω 2 0 α = 6πǫ0c 3 ω2 0 − ω2 − i(ω3 /ω3 . (2.51) 0)Γ Interestingly, the semi-classical approach which treats the atom as a two-level quantum system interacting with a classical field yields the same result in the low-saturation limit with one notable exception. The damping rate must be found from the dipole matrix element between the ground and excited state. Γ = ω3 0 |〈e|µ|g〉|2 3πǫ0c3 (2.52) But for the D lines in alkali atoms, including 87 Rb, which are strongly allowed dipole transitions the classical estimation agrees with the true decay rate to within a few percent [68]. Using the classical estimation for α in the equation for the dipole potential (Eq. 2.46) yields a very useful result, valid in the limit of large detuning and negligible saturation Udip(r) = 3πc2 2ω 3 0 Γ I(r). (2.53) ∆ Here ∆ ≡ ω − ω0 is the optical detuning from resonance. Udip is inversely proportional to the optical detuning which can take on both positive and neg- ative values. When ω > ω0, so-called blue-detuning, the potential is positive, and atoms experience a repulsive force pushing them away from local intensity maxima. When ω < ω0, so-called red-detuning, atoms are pulled into local 48
maxima. Our experiment makes extensive use of blue-detuned optical sheets which act as repulsive walls. We combine several of these sheets to form optical boxes for trapping atoms. Specific detail on this technique can be found in Ch. 4. Although not derived here, a very similar consideration leads to an expression for the optical scattering rate valid in the same limits as Eq. 2.53 [68]. Γsc(r) = 3πc2 2ω 2 0 2 Γ I(r) (2.54) ∆ Notice that the scattering rate varies as ∼ 1/∆ 2 , so that for a sufficiently large detuning the optical dipole force completely dominates forces due to optical scattering. 2.5.2 Scattering Forces When an optical field is near an atomic resonance it is scattering forces that dominate the atom-light interaction. The non-conservative nature of the spontaneous scattering process means that radiative forces can be used to cool atomic ensembles. Here I will discuss the scattering rate and resulting force in the semi-classical approximation, treating the atom as a two-level quantum system and the optical field as classical. I will then shows how this is used to cool and confine atoms in our experiment. 49
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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 . . .
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 and 60: If we now consider the field from t
Page 61 and 62: where P is in torr. The lifetime of
Page 63: component of the dipole oscillation
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
Page 111 and 112: a) top ridge 1 cm b) metal jacket h
Page 113 and 114: 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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