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

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possible if the internal energy of the gas, or the temperature of the atoms, could be reduced at the same time. This extension of the concept of the one-way wall is single- photon cooling. Single-photon cooling was proposed and realized in a proof-of-principle experiment at the same time the one-way wall scheme was demonstrated experimentally [60, 61]. Assume an ensemble of trapped atoms confined in a gradient potential as shown in figure 3.3. Consider first the situation shown in (a). A stationary one-way wall is placed in the center of the potential. As atoms move through the trap volume they pass the one way wall from right to left but cannot move back through the barrier and are thus accumulated on the left hand side. More efficient cooling schemes are shown in (b) and (c). In figure 3.3 (b) a moving one-way wall passes through the trap. Atoms are captured near their classical turning points and kinetic energy is removed. If the sweep of the one-way wall through the trap is adiabatic, the atoms will not regain potential energy, and the final result is an ensemble of cooled atoms at the bottom of the trap. In figure 3.3 (c) the one-way wall is placed just outside the region initially occupied by atoms. As the gradient potential collapses adiabatically, atoms cross the one-way barrier near their classical turning points. The cooled atoms are accumulated on the left side of the one-way wall. The change in entropy, again assuming an ideal gas, is given by ∆S = Si −Sf = NkB ln Vi U 3/2 i Vf U 3/2 f , (3.4) where the subscripts f and i refer to the final and initial states respectively. V is the volume occupied by the trapped atoms, U is the internal energy. The maximum amount of entropy is thus removed by minimizing both the final volume Vf and the final internal energy Uf. In this sense the methods proposed in figure 3.3(b) and (c) are more efficient than the method proposed in 3.3 (a). By translating the one-way wall or collapsing the potential slow enough, atoms are caught near their classical turning points. Increasing the translation or collapsing time sufficiently should decrease the value of Uf to arbitrarily small numbers, if one can 41
time (a) (b) (c) Figure 3.3: Single-photon cooling in a gradient potential. (a) A one-way wall is placed in the center of a the confining potential. As atoms explore the trap volume, they unidirectionally pass through the one-way wall. (b) The one-way wall moves adiabatically through the gradient potential. Atoms pass through the one-way wall near their classical turning points, losing kinetic energy. At the end of the sweep cold atoms are accumulated at the bottom of the gradient potential. (c) The one-way wall is stationary near the outer limits of the initial trap. The gradient potential adiabatically collapses and atoms pass through the one-way wall near their classical turning points. Cold atoms are accumulated on the left hand side of the one-way wall. Figure courtesy of Travis Bannerman. 42
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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
Page 7 and 8: Experiments to Control Atom Number
Page 9 and 10: Table of Contents Acknowledgments v
Page 11 and 12: Chapter 7. Lithium Apparatus 92 7.1
Page 13 and 14: List of Tables 2.1 Physical propert
Page 15 and 16: 4.1 Vacuum chamber . . . . . . . .
Page 17 and 18: 7.39 Future vertical axis optics .
Page 19 and 20: The development of techniques to la
Page 21 and 22: Ptorr 10 5 10 6 10 7 10 8 10 9 260
Page 23 and 24: Property Symbol Value Reference Ato
Page 25 and 26: 2.3.2 Hyperfine Structure So far th
Page 27 and 28: The Wigner-Eckhart theorem can be u
Page 29 and 30: The total magnetic moment of an ato
Page 31 and 32: interaction. The shift in the energ
Page 33 and 34: (a) (b) scattering length a 0 Energ
Page 35 and 36: a laser field with frequency ω. Th
Page 37 and 38: Here ω0 is the resonance frequency
Page 39 and 40: 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: ight side of the box. An irreversib
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 and 92: effect of the reflected beam at zer
Page 93 and 94: y the repulsive trough beams, gaini
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
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Chapter 7 Lithium Apparatus Creatin
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angle valve rotary feedthrough ion
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an ion gauge controller (Granville
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viewports (MDC, 450002) are attache
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not trapped by the MOT impinge on t
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Should contamination of the vacuum
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Figure 7.12: The assembled Zeeman s
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7.2.2 MOT Coils A second set of coi
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BGauss 250 200 150 100 50 30 20 10
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are required to create the high mag
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The coils are then checked for shor
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+ B A Figure 7.23: Feshbach coil H-
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ensure that no particulates build u
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118 Figure 7.26: Optical layout of
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The error signal shows three lines,
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into the CO2 laser. The optical lay
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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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