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

More documents

Recommendations

Info

momentum at the time of release. The final atomic distribution is therefore a convolution of the initial atomic distribution with the initial momentum distribution. This can be made more concrete by considering atoms originating from r0 and arriving at r after a time-of-flight t. If we assume that the velocity distribution for these particles is ζ(v) then we expect to find the number of atoms in a volume element d 3 r located at position r at time t to be [80] dn = G(r,t;r0)d 3 r = ζ(v = [r − r0/t])d 3 v, (2.108) where G(r,t;r0) is the boundary Green’s function describing the evolution of the spatial distribution of the atoms. If the atoms have a 3-D Maxwell- Boltzmann velocity distribution initially, then the Green’s function is given by [80] G(r,t;r0) = m 2πkBTt 2 3/2 e −m|r−r0| 2 /2kBTt2 . (2.109) If we assume that the atomic sample has a Gaussian spatial distribution initially, given by n0(r) = 1 (2πσ 2 n) 3/2e−r2 /2σ 2 n, (2.110) then we can solve for the spatial distribution after an expansion time t by evaluating The result is n(r,t) = n(r,t) = G(r,t;r0)n0(r0)0d 3 r0. (2.111) 1 (2πσ 2 c) 3/2e−r2 /2σ 2 c, (2.112) 82
where σ 2 c = σ 2 2 kBTt n + m . (2.113) By taking multiple images of the atomic cloud as it expands and fitting the measured widths to this expression, the temperature can be extracted. Examples of this technique applied to our atomic samples of 87 Rb are given in Ch. 4. 2.8.2 Fluorescence Imaging In addition to using absorption imaging, we also use the technique of fluorescence imaging to determine the total number of atoms present in our sample. The idea is quite straightforward: atoms are placed into optical molasses which slows their motion via photon scattering as discussed in Sec. 2.5.2.2. The scattered photons are partially collected on a CCD and used to estimate the number of atoms taking part in the scattering process. The atom number can be estimated with help from Eq. 2.76 to be [43] Natom = 8π [1 + 4(∆/Γ)2 + (6I0/Isat)] Γ(6I0/Isat)texpηcountdΩ Ncounts, (2.114) where I0 is the intensity in each of the six molasses beams, texp is the CCD exposure time, ηcounts is the CCD efficiency in (counts/photon) and dΩ is the solid angle of photon collection. In the experiment this technique is used when the atom number is too low to yield an absorption signal or when we are interested solely in atom 83
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 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: where n is the number density of at
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?