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

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assume that l1 >> l2 and that the action of the one-way-wall heats the ensemble only a negligible amount then the phase-space compression C achieved is given simply by C ≡ ρafter ρbefore ≈ l1 l2 (1.2) While instructive, this simple example is clearly unphysical. The action of the barrier violates time reversal symmetry! Additionally, we have gotten something, namely atomic cooling, for nothing – in clear violation of the second law of thermodynamics. The resolution of these troubling facts comes from recognition that any physical realization of an atomic one-way-wall must affect the atoms beyond simply transmitting or reflecting them. For the action of the one-way-wall as presented thus far to obey time reversal symmetry the atoms on the left of the wall must be different in some way from the atoms on the right of the wall. Additionally, the decrease in entropy produced through the action of the one-way-wall must be compensated for by an increase in entropy elsewhere if this scheme is to obey the second law of thermodynamics. Indeed, in the physical realization of this cooling process presented in this dissertation the one-way-wall labels the atoms on either side of the barrier by placing them into distinct hyperfine states through an irreversible spontaneous scattering process of a single photon as atoms transit the barrier. This scattering process is of course the origin of the name “single-photon cooling.” Much more will be said of this in Ch. 4 where a complete description of the cooling process applied to 87 Rb is described. Now consider a second example, a slight variation of the first, which 12
demonstrates the cooling power of a one-way-wall process in a geometry more similar (but not identical) to that used in the actual experiment. In this example, depicted in Fig. 1.5, an atom is placed into an external, conservative potential. This potential in indicated by the “V”-shape in each sub-figure (a-e). As shown in Fig. 1.5(a) the one-way-wall is initially positioned such that the atom does not have sufficient energy to reach it. To initiate cooling, the one-way-wall is slowly swept towards the center of the confining external potential. If this is done slowly enough, the atom will first encounter the one-way-wall near its turning point, where it has exchanged most of its kinetic energy for potential energy. The sweep must be done slowly because as the one- way-wall is swept its intersection point with the confining potential decreases in energy at a rate ˙ E. If the oscillation time of the trapped atom in the confining potential is given by Tatom then the average residual kinetic energy Kres retained by the atom after transiting the one-way-wall due to the motion of the one-way-wall is Kres = 1 2 ˙ ETatom (1.3) Experimental factors force one to compromise between a small Kres and a reasonable sweep duration. After transiting the one-way-wall the atom is captured with little residual kinetic energy Fig. 1.5(c). According to our working definition of temperature given in Eq. 1.5 this atom has been cooled. As the one-way-wall then continues to sweep towards the center of the external confining potential one may expect that the atom will heat back up. This is not so. The work done on the atom by the one-way-wall as it moves is equal to 13
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: Figure 1.4: Depiction of a simple,
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 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
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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
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
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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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