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

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The fidelity of the laser culling process is analyzed by a 1-dimensional harmonic trap of size z, truncated at the energy Et [102]. A schematic of the truncated potential is shown in figure 6.1. ( ) Figure 6.1: Trapping potentials used to calculate the fidelity of laser culling in 6 Li. (a) Truncated harmonic trap. The truncation energy is Et and the trap size is z. (b) Truncated harmonic trap with a magnetic field gradient. The trap size z is defined as the length of the parabolic part of the potential profile. The lines represent the ground and first excited state energy levels. The unit of length is given by x0 = /mω, the unit of energy is ω. Figure courtesy of Shoupu Wan. Controlling the strength of the trapping potential is not the only option one has to control the number of trapped atoms. In addition, a magnetic field gradient can be applied, see figure 6.1 (b). This has two effects: all atoms that are no longer held within the trapping potential will be moved away from the system quickly. In addition, the magnetic field gradient allows for additional control of the overall trapping potential. In the presence of a magnetic field gradient true bound states no longer exist. Instead a series of quasi-bound states exists (figure 6.1 shows the ground and first excited state). In this situation the atoms can tunnel out of the trap. However, the atoms in the first excited state will tunnel out much faster than atoms bound more deeply. Once the excited state atoms have left the trap, the magnetic field gradient can be removed and the trap depth deepened to protect the remaining ground state atoms (the Fock state). The difference in the lifetimes of the ground and first excited quasi-bound states determines the fidelity of creating a pair of atoms in the ground state of the trap. The 89 ( )
difference in the lifetimes is determined by the energy splitting between the energy levels. A tight confining potential is therefore desirable. Figure 6.2 shows the fidelity of the laser culling process as a function of trap size and applied magnetic gradient force. Figure 6.2: Fidelity of laser culling. Shown is the ground state fidelity loss in base-10 logarithm. Red (blue) represents high (low) fidelity. The white areas are out-of-range clippings and should be more intense than the color surrounding them. The unit of length is given by x0 = /mω, the unit of force is ω/x0. Figure courtesy of Shoupu Wan. For an experimentally feasible set of parameters with trapping frequency ω = 2π × 1 kHz, magnetic field gradient dB/dz = 0.66 G/cm, a truncated trap size z = 8.8 µm and a tunneling time of 218 ms the fidelity of creating the two-atom Fock state is predicted to be larger than 0.99998 [102]. One additional step is required to create a one-atom Fock state: adiabatic splitting of the optical dipole trap into two separate wells. This step can be achieved with ultrahigh fidelity [106] and it is thus possible to initialize a qubit pair or an entangled (EPR) pair of atoms. At very low magnetic fields, one of the two atoms will be a high- field seeker, the other will be a low-field seeker. By applying a weak magnetic field gradient during the separation process, the high-field seeker and the low-field seeker can 90
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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
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J=1 J=0 -1 Δ σ + σ - σ - 0 +1 -
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phase-space density is defined as
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which maintains a constant η = U/k
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2.12.1 Saturated Absorption Spectro
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Figure 2.22: Saturation absorption
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Signal 0 Signal (a) (b) Signal Freq
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(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 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: of atoms in the two hyperfine groun
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
Page 143 and 144: Imaging ber Imaging ber from Imagin
Page 145 and 146: Table 7.4 summarizes the beam power
Page 147 and 148: CO2 laser 40 MHz AOM f=2 in f=2 in
Page 149 and 150: 132 Figure 7.38: Optical layout aro
Page 151 and 152: Feshbach coil objective lenses atom
Page 153 and 154: MOT beams are no longer traveling a
Page 155 and 156: 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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