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a) b) c) d) e) external potential one-way-wall Figure 1.5: (a) An atom is placed in an external confining potential along with a one-way-wall which is initially placed such that the atom does not have sufficient energy to reach it. (b) The one-way-wall is slowly swept towards the trap center, so that the atom first encounters it at its turning point. (c) The one-way-wall continues to sweep in, eventually returning the cold atom to the center of the external confining potential (d). (e) The one-way-wall moves away from the region containing the atoms. the increase in potential energy of the atom [21]. This is completely analogous to the fact that the work done by an ideal elevator is equal to the change in the potential energy of its occupants. After sweeping through the center of the external confining potential the atom remains trapped at its center, but is now cold [Fig. 1.5(d)]. The one-way-wall continues its sweep out of the region of the atom [Fig. 1.5(e)]. Because this scheme is fundamentally a single atom process, it works equally well on an ensemble of non-interacting atoms. To work on an ensemble the one-way-wall must be initially positioned such that the most energetic atom in the group does not have sufficient energy to reach it (Fig. 1.6). The rate at which the one-way-wall is swept must be slow enough to allow all atoms in the ensemble to reach it with negligible kinetic energy. Because this technique operates at the single particle level it does not rely on a specific form of inter- 14
a) b) c) external potential one-way-wall Figure 1.6: (a) A non-interacting atomic ensemble is placed in an external confining potential along with a one-way-wall which is initially placed such that none of the atoms have sufficient energy to reach it. (b) The one-waywall is slowly swept towards the trap center, capturing atoms as it encounters them at their turning points. (c) The one-way-wall continues its sweep, eventually capturing all the atoms and returning them to the center of the external confining potential with reduced kinetic energy. particle interactions to work, as does evaporative cooling [23]. This feature further generalizes and extends its potential applicability. This section served as an introduction to the concept of single-photon cooling. In summary, this technique begins by trapping an atomic ensemble in a conservative potential. Then, a one-way-wall for atoms is positioned in the wings of the trap. Cooling is initiated by slowly sweeping the one-waywall towards the center of the conservative potential. The sweep must be slow compared to the oscillation frequency of the trapped atoms, so that they first encounter it near a turning point. After transmitting through the one-waywall near a turning point atoms become trapped with little kinetic energy. The atoms become trapped because they are placed into a different internal state 15
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: demonstrates the cooling power of a
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
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σ σ σ Figure 2.10: Geomet
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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
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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
Page 201 and 202:
[15] C. C. Bradley, C. A. Sackett,
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[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
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adicals,” Phys. Rev. Lett. 94, 02
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