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

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to minimize residual kinetic energy. Notice that in contrast to the potential produced by the optical box (Fig. 4.11), atoms do not have to climb a potential hill to reach the depopulation beam, resulting in a final population with less residual kinetic energy. In this iteration of the experiment, the cooling process was initiated by adiabatically lowering the magnetic trapping potential. This is done by linearly ramping down the current in the quadrupole coils in a time tramp, which is on the order of 1 s. As the magnetic field gradient is reduced, the atomic cloud expands and the turning point of each atom (in the vertical direction) approaches the depopulation beam which is held a fixed distance below the magnetic trap. To ensure that each atoms encounters the depopulation beam near its classical turning point, the adiabaticity condition 〈τB〉/tramp ≪ 1 must be satisfied, where 〈τB〉 is the average oscillation period in the magnetic trap. We found this scheme to be advantageous over simply moving the centers of the traps together, as in the previous two sections, because it reduced optical trap loss due to atomic collisions with magnetically trapped atoms. As discussed above, when the atoms encounter the depopulation beam they are driven from the initial |F = 2,mF = 2〉 state into the 5 2 S1/2(F = 1) manifold. Once decoupled from the magnetic trap they fall into the optical trough where they are captured. Once the cooling process is complete, atoms transfered into the optical trough via single-photon atomic cooling are imaged using the vertical probe beam (see Sec. 3.4.1). To remove any residual atoms, all magnetic fields 168
are switched off causing non-optically trapped atoms to free fall under the influence of gravity, as in the last section. Then a beam resonant with the 5 2 S1/2(F = 2) → 5 2 P3/2(F = 3) transition is used to blow away atoms not in the 5 2 S1/2(F = 1) manifold. The remaining atoms have undergone the single- photon cooling process. Then, the optical dipole beams are turned off and a probe beam propagating along the ˆz-axis illuminates the atoms for 200µs. This beam is subsequently imaged onto a CCD camera and compared to a reference image taken with no atoms present. The result is integrated to yield the total number of atoms present in the sample (see Sec. 2.8.1). Temper- ature measurements obtained through the time-of-flight method are possible by varying the delay between the release of the cloud and illumination by the probe beam. Figure 4.24 shows an absorption image of approximately 1.5×10 5 atoms trapped in the optical trough. In this image false color is used to repre- sent atomic density, magenta being the most dense. The rapid density fall-off along the ˆx direction is due to the end caps. The density gradient along the ˆy direction is due to the geometry of the trough. To properly judge the performance of the single-photon cooling process, several effects introduced by the geometry of the optical trough should be considered. For example, the height of the pump beam above the trough vertex hp must be strategically set to optimize cooling. Figure 4.25 shows the effect of hp on both the number of atoms transfered into the optical trough via single- photon cooling NO and the vertical temperature of the optically trapped atoms T (z) O . The temperature data was taken before atoms in the trough had time to 169
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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
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atoms its wavefunction Ψ(t) is typ
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In this equation we let H = H0 + Hc
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The significance of Isat is that at
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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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Page 135 and 136: Output Power > 10 W Wavelength 532
Page 137 and 138: labeled 1, 2 and 3 in the Fig. 3.21
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Page 141 and 142: process. The two coils are arranged
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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: detunings. The result of scattering
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
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