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

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fE. Furthermore, assume that the conservative confining potential and the position of the one-way-wall is well known at all times during the cooling process. As shown in Fig. 1.7(b), as the one-way-wall is slowly swept towards a) 0.4 0.3 fE 0.2 0.1 Energy Distribution 2 4 6 8 E/k B T b) photodetector spon.scattered photon x one-way-wall c) I pd trap center Reconstruction x ensemble edge Figure 1.7: (a) The initial energy distribution of a non-interacting atomic ensemble. (b) This ensemble is placed into a conservative trapping potential. As the one-way-wall sweeps through the ensemble it encounters the most energetic atoms first, which spontaneously scatter photons as they transit the barrier. A photodetector monitors the scattered light. (c) A plot of the photodetector signal Ipd as a function of the position of the one-way-wall x reconstructs the original energy distribution of the ensemble. the center of the confining potential, it first encounters the most energetic atom at a position where the atom has converted (nearly) all of its energy into potential energy. When the atom transits the one-way-wall it undergoes an irreversible process which involves the scattering of a spontaneous photon. Detection of this photon reveals the atom’s initial energy through knowledge of the location of the one-way-wall x at the time of scatter and the shape of the confining potential. By detecting and recording each spontaneously scattered photon as a function of the one-way-wall’s position with respect to the confining potential, the initial energy distribution can be reconstructed, as shown in Fig. 1.7(c). Of course, this sweep also has the effect of cooling 18
the atomic ensemble. Not surprisingly and as shown in [34], the information entropy content carried away by the scattered photons is equal to the reduction in the entropy of the cooled atomic ensemble. What is really striking is how extremely efficient the single-photon cooling process is in using information entropy to cool. In the ideal case described above it is perfectly efficient; the reduction in entropy of the atomic ensemble equals the information entropy carried away by the spontaneously scattered photons. When compared to other established atomic laser cooling techniques, where the increase in photon entropy is typically several orders of magnitude higher than the decrease in the entropy of the atomic ensemble cooled [35], we see just how truly remarkable this process is. Additionally, single-photon cooling is a passive technique in the sense that one need not monitor the scattered photons at all for the process to work. In contrast, stochastic cooling methods, which like single-photon techniques scatter photons which carry information related the ensemble’s properties, must actively feedback on the data gathered from scattered photons to operate [36, 37]. 1.6 A Note on Units A brief discussion of the terminology and units used throughout is warranted. Of particular note is the loose manner in which the term “temperature” is used in the laser cooling community and indeed in this text. The concept of temperature is defined in thermodynamics as a property of a closed system in thermal equilibrium with its surroundings [38, 39]. In typical atomic 19
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: worked on by Brillouin [27-29], ide
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 and 82: σ σ σ Figure 2.10: Geomet
Page 83 and 84: 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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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
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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
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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