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pled cooled with optical molasses to be much colder than the lower bound set by theory [11] (See Sec. 1.6 for a discussion of the use of “temperature” in this context). This conflict was a result of the assumption made in theoretical de- scriptions of the process which modeled the atom as a purely two-level system, devoid of magnetic substructure. An improved theory, including magnetic substructure, was developed by C. Cohen-Tannoudji and J. Dalibard in 1989 [12] and it resolved the discrepancy between theory and experiment and placed a new and much colder lower bound temperature, the recoil temperature Tr, on optical molasses. These achievements resulted in tremendous interest in laser based atomic cooling methods and resulted in a Nobel prize awarded to Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips in 1997. 1.2 Laser Cooling as an Enabling Tool Laser cooling of atomic vapors has served as a technique which has enabled the study of more idealized physical systems, expanding and refining scientific knowledge in a vast amount of areas. Laser cooling made possible the creation and study of Bose-Einstein condensates (BEC) of dilute atomic vapors [13–15]. It plays a central role in the latest generation of atomic fountain clocks [16] and has made possible the creation of optical frequency standards [17]. The study of cold atomic collisions, nonlinear optical effect and basic quantum mechanical phenomena have greatly benefited from the ability to cool atoms. Precision spectroscopic investigations of the energy structure of atoms have benefited tremendously from the ability to trap and cool atomic 4
samples by allowing for very long interaction times and a suppression of the Doppler effect (including time dilation). Cooled atoms with sufficiently long deBroglie wavelengths are of use in atom interferometers which can function as accelerometers, rotation sensors, gravimeters, and gradiometers. While this list is in no way exhaustive, it is merely to justify the incredibly important contribution laser cooling has provided to the scientific community. 1.3 Limitations of Laser Cooling While the contributions of atomic laser cooling are substantial, no technique is without limitation. The major limitation of established atomic laser cooling techniques is that they rely on the transfer of momentum from photon to atom to work. This seemingly trivial statement places quite stringent re- quirements on atomic species amenable to these techniques. As a first step in seeing why, consider the number of scattering events necessary to stop a room temperature 87 Rb atom with photons resonant with its D2 transition. We can approximate this number as m¯v/k ≈ 45, 000 where m and ¯v are the mass and velocity of a 87 Rb atom at 300K and where k = 2π/780 nm. From this consideration it is clear that a very large number of photon scattering events are necessary to stop a room temperature atom. In order to scatter such a large number of photons in an experimentally realizable way the atom must possess an effective two-level structure, depicted in Fig.1.1, that is accessible with a sufficiently intense available laser source. The reason an effective two-level atom is required for laser cooling is 5
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: the momentum kicks due to absorptio
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 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
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where I/Isat ≪ 1 has been assumed
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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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