Experiments to Control Atom Number and Phase-Space Density in ...

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they have time to rethermalize to thermodynamic equilibrium. Thus T (z) O representation of the velocity distribution along the vertical dimension. is a direct Figure 5.7: Atom number (black squares) and vertical temperature (blue circles) of atoms trapped in the optical trough as a function hp (height above the demon beam above the trough). The largest number of atoms can be transferred into the optical trap at a demon beam position of hp = 100 µm, while the point corresponding to the highest phase- space density is located at hp = 41 µm. To understand the temperature and transfer efficiency curves, consider the atoms being transferred into the |F = 1,mF = 1〉 state. After the atoms encounter the demon beam they regain kinetic energy by falling into the bottom of the trough. For a demon beam height hp > 100 µm, this energy gain is sufficient to overcome the optical potential created by the optical trough, resulting in loss from the gravito-optical trap. One might therefore think that in order to minimize this energy gain, the height of the demon beam hp should be as close to the trough vertex as possible. However, as the demon beam gets closer to the trough vertex, the potentials of the demon beam and the optical trough beams start to overlap. This means that fewer atoms are reaching the demon beam, leading to a reduced transfer efficiency. By reducing the height hp below zero, the atoms need to climb up the potential created 75
y the repulsive trough beams, gaining potential energy, before being transferred into the optical trough. The temperature T (z) o of the beams will then again increase. 5.5 Transfer Efficiency and Phase-Space Compression The fundamental limit of the temperature of single-photon cooling is given by the photon recoil temperature. For 87 Rb the recoil temperature is about 0.36 µK. Clearly the lowest temperatures measured along the vertical direction T (z) O are far above that limit. Away from the optimum value for hp, part of the energy can be attributed to energy regained after the transfer into the optical trough. But even at the optimum location, the temperature T (z) O is above the recoil limit. The ramp time employed during the single-photon cooling sequence lies within the adiabatic regime, and the expectation is to capture atoms near their classical turning points. In fact, the energy increase due to transferring atoms away from their classical turning points is estimated to be only about 0.5µK. The explanation for the excess energy lies with the geometry of the optical trough. In this implementation, single-photon cooling is essentially a one-dimensional cooling technique, removing energy only along the vertical (z) direction. However, the optical trough geometry mixes the temperatures along the y and z dimensions quickly, due to the trough beams alignment at 45 ◦ in the y-z-plane. This leads to an increased value in the measurement of T (z) O . The optical trough also has an effect on the expected temperature along the x and y dimensions. The trap depth of the optical trough is small compared to the trap depth of the magnetic trap. Hence the optical trough will necessarily truncate the transverse (x and y dimensions) temperature distribution of the atomic ensemble. The amount of truncation can be controlled by adjusting the trap depth of the optical trough (varying the beam power in the optical trough beams), as shown in figure 5.8. As the trap depth increases, atoms with higher energy along the transverse directions can be trapped, leading to an increase in the overall number of atoms trapped in the optical trough. 76
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Copyright by Kirsten Viering 2012
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Experiments to Control Atom Number
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Acknowledgments First of all, I wou
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Experiments to Control Atom Number
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Table of Contents Acknowledgments v
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Chapter 7. Lithium Apparatus 92 7.1
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List of Tables 2.1 Physical propert
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4.1 Vacuum chamber . . . . . . . .
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7.39 Future vertical axis optics .
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The development of techniques to la
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Ptorr 10 5 10 6 10 7 10 8 10 9 260
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Property Symbol Value Reference Ato
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2.3.2 Hyperfine Structure So far th
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The Wigner-Eckhart theorem can be u
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The total magnetic moment of an ato
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interaction. The shift in the energ
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(a) (b) scattering length a 0 Energ
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a laser field with frequency ω. Th
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Here ω0 is the resonance frequency
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Optical molasses do not provide a s
Page 41 and 42: J=1 J=0 -1 Δ σ + σ - σ - 0 +1 -
Page 43 and 44: phase-space density is defined as
Page 45 and 46: which maintains a constant η = U/k
Page 47 and 48: 2.12.1 Saturated Absorption Spectro
Page 49 and 50: Figure 2.22: Saturation absorption
Page 51 and 52: Signal 0 Signal (a) (b) Signal Freq
Page 53 and 54: (a) (b) (c) (d) Figure 2.24: Absorp
Page 55 and 56: y more complex energy level structu
Page 57 and 58: ight side of the box. An irreversib
Page 59 and 60: time (a) (b) (c) Figure 3.3: Single
Page 61 and 62: them to move from B to A, but close
Page 63 and 64: Figure 4.1: Vacuum chamber. Photogr
Page 65 and 66: ( ( Figure 4.3: Helicoflex seal. (a
Page 67 and 68: 88 mm 4.2.3 Auxiliary Coils 62 mm Q
Page 69 and 70: 5 2 P 3/2 5 2 S 1/2 384. 230 484 46
Page 71 and 72: distribution of the MOT master lase
Page 73 and 74: shifts. First a frequency shift of
Page 75 and 76: transition. However, the laser freq
Page 77 and 78: 4.3.1.4 Upper MOT Horizontal Slave
Page 79 and 80: provides the beam for the upper MOT
Page 81 and 82: demon beam λ λ horizontal MOT bea
Page 83 and 84: scholar, Florian Schreck. It is wri
Page 85 and 86: Atoms are then optically pumped to
Page 87 and 88: ferred into the |F = 1,mF = 0〉 or
Page 89 and 90: 5.2 Branching Ratios and Population
Page 91: effect of the reflected beam at zer
Page 95 and 96: Figure 5.9: Atom number as a functi
Page 97 and 98: Figure 5.10: Radius of the magnetic
Page 99 and 100: on the collision rate of atoms insi
Page 101 and 102: ferred via the single-photon coolin
Page 103 and 104: By comparison an atomic Fock state
Page 105 and 106: of atoms in the two hyperfine groun
Page 107 and 108: difference in the lifetimes is dete
Page 109 and 110: Chapter 7 Lithium Apparatus Creatin
Page 111 and 112: angle valve rotary feedthrough ion
Page 113 and 114: an ion gauge controller (Granville
Page 115 and 116: viewports (MDC, 450002) are attache
Page 117 and 118: not trapped by the MOT impinge on t
Page 119 and 120: Should contamination of the vacuum
Page 121 and 122: Figure 7.12: The assembled Zeeman s
Page 123 and 124: 7.2.2 MOT Coils A second set of coi
Page 125 and 126: BGauss 250 200 150 100 50 30 20 10
Page 127 and 128: are required to create the high mag
Page 129 and 130: The coils are then checked for shor
Page 131 and 132: + B A Figure 7.23: Feshbach coil H-
Page 133 and 134: ensure that no particulates build u
Page 135 and 136: 118 Figure 7.26: Optical layout of
Page 137 and 138: The error signal shows three lines,
Page 139 and 140: into the CO2 laser. The optical lay
Page 141 and 142: Thorlabs PDA10A Coupler ZDC-10-1 to
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Imaging ber Imaging ber from Imagin
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Table 7.4 summarizes the beam power
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CO2 laser 40 MHz AOM f=2 in f=2 in
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132 Figure 7.38: Optical layout aro
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Feshbach coil objective lenses atom
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MOT beams are no longer traveling a
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The second card (NI6733) offers eig
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Averaging over the magnetic subleve
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2 2 P 3/2 D 2=670.977nm 2 2 S 1/2 m
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The right hand side of equation 7.1
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= E0 1 −n2 √2 exp σ0 ± iE0
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esidual potentials besides gravitat
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Figure 8.1: MOT loading. Typical lo
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A linear ramp typically changes the
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A typical MOT is density-limited at
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ubidium [113-115] and cesium[116].
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that most of the noise is due to th
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(a) (c) y . x z X=0.0mm Z=2.5mm 1)
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Figure 8.11: Different shapes of MO
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ZnSe lens f=5 in knife edge ZnSe wi
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shown in figure 8.13. By matching t
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Figure 8.15: Atom number and temper
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275 Hz. Using these values the beam
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system. Maybe the easiest way to ac
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Appendix A Magic Wavelength of Hydr
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transitions for the excited state p
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Bibliography [1] J.J. Thomson. Cath
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[22] C.J. Foot. Atomic Physics. Oxf
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[46] E.D. Black. An introduction to
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[67] J.L. Hanssen. Controlling Atom
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[88] D.S. Naik, C.G. Peterson, A.G.
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[110] J.W. Goodman. Introduction to
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[132] C. Degenhardt, H. Stoehr, U.
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