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

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ack into the AOM in a standard double pass configuration. The 1 st order spot from the double passed beam passes through the PBSC once again, but because it has passed through a λ/4 waveplate twice its polarization has rotated 90 ◦ and so is transmitted by the cube. The pump beam then passes though the Rb vapor cell, overlapping the probe beam. Because the probe beam has double passed a 44 MHz AOM (each time the 1 st order beam was used) its frequency has been shifted up by 88 MHz. This results in the pump and probe beam interacting with atoms which have velocity such that they are Doppler shifted by 44 MHz and not with the stationary atoms as discussed in Sec. 2.7.2. The result is that the signal produced by the fast photodiode reflects the Doppler-broadened transition with peaks at each of the real transitions (F = 2 → F ′ = 1, 2, 3) as well as the cross-over resonances (F = 2 → 1/2, 1/3, 2/3) shifted by 44 MHz from their zero velocity value. This signal is mixed in a lock-in amplifier (SRS SR510) with the f.m. modulation frequency, resulting in a Doppler-free dispersion signal (see Sec. 2.7.2). Any of the dispersive curves, shown in Fig. 3.9, could be used as an error signal to lock the master laser frequency, but we used the F = 2 → 2/3 cross-over transition because it is the most prominent. This signal serves as an error signal and is sent to a home-built PID [89] lockbox, which outputs a control signal which we amplify with a Trek 601B-2 high voltage amplifier. The amplified signal drives the piezo stack, controlling the lasing frequency and closing the loop. While this setup allows us to lock the MOT master laser, the laser out- 102
Voltage a b c d e f Frequency Figure 3.9: The MOT saturated absorption spectroscopy dispersive signal. The real and cross-over transitions corresponding to each dispersive lineshape are as follows: a)F = 2 → F ′ = 1 b)F = 2 → F ′ = 1/2 c)F = 2 → F ′ = 2 d)F = 2 → F ′ = 1/3 e)F = 2 → F ′ = 2/3 f)F = 2 → F ′ = 3. put is not at the F = 2 → F ′ = 3 transition frequency, which is needed for the operation of the MOT. The AOM which initially picked off the small portion of the beam sent to the saturation absorption spectroscopy setup shifted the beam up by 103 MHz. Because the probe beam was shifted up by 88 MHz the spectrum obtained corresponded to atoms shifted by 44 MHz so the MOT master laser output is therefore shifted 147 MHz to the red of the F = 2 → 2/3 cross-over resonance transition frequency. The F = 2 → 2/3 cross-over resonance transition frequency is 133 MHz to the red of the F = 2 → F ′ = 3 transition so the MOT master output is 280 MHz to the red of this transition. 103
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Copyright by Gabriel Noam Price 200
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Single-Photon Atomic Cooling by Gab
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Acknowledgments First, I would like
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Rubidium group when I first joined.
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Single-Photon Atomic Cooling Public
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2.5.2.4 Magneto-Optical Trap . . .
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List of Tables 2.1 87 Rb Physical P
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3.1 Vacuum Chamber . . . . . . . .
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Chapter 1 Introduction This chapter
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the momentum kicks due to absorptio
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samples by allowing for very long i
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Figure 1.2: The energy level struct
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quency regime [19]. This then led t
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Figure 1.4: Depiction of a simple,
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demonstrates the cooling power of a
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a) b) c) external potential one-way
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worked on by Brillouin [27-29], ide
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the atomic ensemble. Not surprising
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are untrappable. The SI unit for en
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the atomic transition and is called
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2.1 Rubidium Rubidium (Rb) is an al
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constant which is given by α = e2
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only one value of J is possible fro
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the latter of which only applies to
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Figure 2.1: 87 Rb D2 Transition Hyp
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Pluging Eq. 2.18 into this Hamilton
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Following the same logic leads to a
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gF = −1/2 using the approximate e
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mize their energy in high magnetic
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If we now consider the field from t
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where P is in torr. The lifetime of
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component of the dipole oscillation
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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
Page 91 and 92: 2.7.2 Saturation Absorption Spectro
Page 93 and 94: ground state depletion due to the p
Page 95 and 96: oadened background can be removed f
Page 97 and 98: where n is the number density of at
Page 99 and 100: where σ 2 c = σ 2 2 kBTt n + m .
Page 101 and 102: Chapter 3 Experimental Apparatus Th
Page 103 and 104: Figure 3.1: The vacuum chamber duri
Page 105 and 106: Nor-Cal Products Inc. (AMV-1502-CF)
Page 107 and 108: and monitor the necessary vacuum le
Page 109 and 110: 3.1.3 Lower Chamber The lower chamb
Page 111 and 112: a) top ridge 1 cm b) metal jacket h
Page 113 and 114: to the appropriate frequency throug
Page 115 and 116: plexiglass cover piezo U stack grat
Page 117: λ Figure 3
Page 121 and 122: eams. For example the MOT and optic
Page 123 and 124: λ Figure 3.12: The slave lasers
Page 125 and 126: λ λ λ
Page 127 and 128: λ λ λ λ
Page 129 and 130: needed when forming a MOT or optica
Page 131 and 132: master laser is dithered at 20 kHz.
Page 133 and 134: λ λ
Page 135 and 136: Output Power > 10 W Wavelength 532
Page 137 and 138: labeled 1, 2 and 3 in the Fig. 3.21
Page 139 and 140: λ λ λ λ
Page 141 and 142: process. The two coils are arranged
Page 143 and 144: 19) connected in parallel. This arr
Page 145 and 146: 3.4.2 Horizontal Imaging The horizo
Page 147 and 148: Chapter 4 Single-Photon Atomic Cool
Page 149 and 150: 1 s, after which time ∼ 10 8 87 R
Page 151 and 152: (a) x z magnetically trapped atoms
Page 153 and 154: h x z magnetically trapped atoms y
Page 155 and 156: z y x magnetically trapped atoms cr
Page 157 and 158: Figure 4.5: The effective potential
Page 159 and 160: depopulation present and it indicat
Page 161 and 162: numbers sufficiently large to quant
Page 163 and 164: μ μ μ
Page 165 and 166: the potential landscape due to the
Page 167 and 168: 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
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[15] C. C. Bradley, C. A. Sackett,
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[31] E.T. Jaynes, “Information th
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[49] J. Ye, S. Swartz, P. Jungner,
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[66] J.P. Gordon and A. Ashkin, “
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[85] C.-S. Chuu, Direct Study of Qu
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adicals,” Phys. Rev. Lett. 94, 02
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