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

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Chapter 2 Operational Concepts This chapter discusses many of the concepts necessary for a complete understanding of the experimental procedure and results presented in this dissertation. It begins with a general discussion of the element used during this experimental work, rubidium. A description of the source and size of energy level splittings resulting in the fine and hyperfine structure is given. The interaction of atoms with external magnetic fields is discussed, as well as how this interaction, known as the Zeeman effect, can be used to trap rubidium. A discussion of the interaction of atoms with external optical fields is given, both in the near and far off resonance limits. How these interactions lead to forces which can be used to cool and control external atomic degrees of freedom is explained. The frequency of applied optical fields must be precisely controlled and the method used to accomplish this, a feedback loop based on saturation absorption spectroscopy of a room temperature vapor cell, is discussed. Finally the two methods used in this dissertation to image atomic samples, optical absorption and atomic fluorescence are discussed. 24
2.1 Rubidium Rubidium (Rb) is an alkali metal. Its common use in atomic exper- iments is due in part to its relatively simple energy level structure and its possession of an accessible effective cycling transition. The simplicity of the energy level structure is due to the fact that of Rb’s 37 electrons only one is in the outermost shell. 85 Rb is the most abundant and only stable isotope of rubidium, however the experimental work performed in this dissertation was done entirely on 87 Rb. The reason for this is that 87 Rb has a simpler hyperfine structure, the topic of the next section. 87 Rb has a relative natural abundance of 27.83(2)% and decays to β − + 87 Sr with a total disintegration energy of 0.283 MeV [40]. While unstable, the nuclear lifetime is 4.88×10 10 yr [40] making this form of rubidium effectively stable over the duration of our experiment. The mass of 87 Rb was accurately determined from a Penning trap measurement to be m = 1.443 160 648(72) × 10 −25 kg [41]. The vapor pressure of solid Rb is an important experimental quantity because it dictates the load- ing rate into the first stage of our experimental procedure. This value can be taken from a vapor-pressure model for solid Rb given by [42], which is log10Pv = 2.881 + 4.857 − 4215 , (2.1) T where Pv is the vapor pressure in torr and T is in K. This model is specified to have an accuracy better than ±5% from 298-550K. The ambient temperature surrounding our experimental chamber is approximately 295K resulting in a vapor pressure of 2.9 × 10 −7 torr. More will be said about how this relates 25
Page 1 and 2: Copyright by Gabriel Noam Price 200
Page 3 and 4: Single-Photon Atomic Cooling by Gab
Page 5 and 6: Acknowledgments First, I would like
Page 7 and 8: 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: the atomic transition and is called
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 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
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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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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
Page 179 and 180:
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
Page 185 and 186:
are switched off causing non-optica
Page 187 and 188:
Figure 4.25: Number (■) and tempe
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traps. If we model the ensembles in
Page 191 and 192:
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
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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