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

More documents

Recommendations

Info

and Claude Cohen-Tannoudji discovered that cooling beyond the Doppler limit was due to an interaction between the optical field and the atom’s magnetic sublevels [12]. The effect responsible for the additional cooling can be understood by considering an atom with a ground state total electronic angular momentum J = 1/2 and an excited state total electronic angular momentum J ′ = 3/2 moving through a standing wave formed by two counter-propagating beams with orthogonal linear polarization. As indicated in Fig. 2.9(a) the relative strength of the transitions de- pend on the value of mJ in the lower (J = 1/2) and upper (J ′ = 3/2) state. For example, for σ + polarized light, which by definition drives transitions with ∆mJ = +1, the coupling of the|J = 1/2,mJ = 1/2〉 → |J = 3/2,mJ = 3/2〉 transition is three times stronger than the coupling of the |J = 1/2,mJ = −1/2〉 → |J = 3/2,mJ = 1/2〉 transition. On the contrary, for σ − polarized light, which drives transitions with ∆mJ = −1, the coupling of the |J = 1/2,mJ = −1/2〉 → |J = 3/2,mJ = −3/2〉 transition is three times stronger than the coupling of the |J = 1/2,mJ = 1/2〉 → |J = 3/2,mJ = −1/2〉 transition. The relative strength of all allowed electric dipole transition are given as integer values in this figure and can be calculated using the formalism outlined in Sec. 2.6. 60
λ λ Figure 2.9: The Sisyphus cooling effect. (a) The relative coupling strength of all allowed electric dipole transitions are shown as integer values. (b) The standing wave formed by two counter-propagating beams with orthogonal linear polarizations results in a polarization gradient. (c) The ground state energy levels are shifted periodically by the polarization gradient. The result of the superposition of the counter-propagating beams with orthogonal linear polarization is a standing wave with a spatially varying polarization. This is indicated in Fig. 2.9(b) where a beam traveling to the 61
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 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: where I/Isat ≪ 1 has been assumed
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 and 118: λ Figure 3
Page 119 and 120: Voltage a b c d e f Frequency Figur
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
Page 169 and 170:
Figure 4.13: Incremental atom captu
Page 171 and 172:
netic trap and transfer into the op
Page 173 and 174:
temperature TB of atoms loaded into
Page 175 and 176:
used to construct it into the remai
Page 177 and 178:
μ μ μ Figure 4.18: Side view of
Page 179 and 180:
Figure 4.20: Geometry of the optica
Page 181 and 182:
could potentially have undergone th
Page 183 and 184:
detunings. The result of scattering
Page 185 and 186:
are switched off causing non-optica
Page 187 and 188:
Figure 4.25: Number (■) and tempe
Page 189 and 190:
traps. If we model the ensembles in
Page 191 and 192:
Figure 4.26: Radius of the atomic c
Page 193 and 194:
atoms were removed from the magneti
Page 195 and 196:
trappable |F = 1,mF = −1〉 state
Page 197 and 198:
the short lived 2p state. Atoms whi
Page 199 and 200:
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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?