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

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Chapter 6 Fock States and Laser Culling In typical cold atom experiments, the number of atoms of the ensemble is unknown, and is usually determined after the experimental sequence via absorption or fluorescence imaging. Furthermore, repeating the experiment will lead to a different atom number, and the distribution will in general follow Poissonian statistics. Control- ling the particle number precisely is a first step towards studying quantum entanglement and quantum collision on the few particle level, without resorting to ensemble averaged measurements, were even small variations from the average can have a large influence on the experimental result. 6.1 Atomic Fock States In general a Fock state is a quantum state with a well-defined number of particles, e.g. photons or phonons, in a single mode. They are also frequently referred to as number states. Fock states are most commonly encountered when solving the quantum harmonic oscillator. In this case the energy levels are equally spaced, and the energy eigenstates are also the eigenstates of the number of phonons with energy equal to the energy splitting. An N-photon Fock state in a cavity is defined as having N photons in a partic- ular cavity mode. Photon Fock states have been realized experimentally using several different approaches, for example photon down-conversion [81], using a high-Q cavity [82], using a single atom trapped in a cavity [83], and by controlling emission from a single molecule [84]. Properties of photon Fock states have been studied in a number of experiments [85, 86], and the application of these photon Fock states to quantum computing and quantum cryptography has been considered [87, 88]. 85
By comparison an atomic Fock state can be defined as having N atoms in a well- defined state of a trap. Photon Fock states can be achieved by creating and destroying photons directly. Atoms, in contrast, cannot be created or destroyed, and other methods are required to create an N-atom Fock state. In principle the atoms could be in any state of the trap, but the ground state appears to be the easiest to realize experimentally. Multiple experiments have realized the production of N atoms in a trap without controlling the state [89–93]. For most quantum measurements the quantum state is very important, and the creation of a true atomic Fock state is therefore desirable. The original proposal to generate atomic Fock States was to implement a ’quantum tweezer’ to deterministically remove N atoms from a reservoir of condensate atoms through Landau-Zener tunneling [94]. In a second scheme, atoms are deterministically transferred from a Bose-Einstein condensate, confined in a weak trapping potential, to a selected state of a strongly confining potential [95]. A simpler scheme, called laser culling, has been utilized to observe sub-Poissonian number statistics in a trapped sample of bosonic 87 Rb [96] and to create two-atom fermionic Fock states with a fidelity (probability of finding two atoms in the ground state of the trap) of 96% [97]. The following section will describe the method of laser culling in more detail. 6.2 Laser Culling After evaporative cooling, the atom number of a degenerate gas in a trap is unknown. If the trap depth is reduced, eventually the trap will be completely filled and any further trap reduction will force atoms to leave the trap. The atom number in this trap can be controlled, if the relation between the supported number of atoms and the trapping potential is known. Of course this implies that the potential can be controlled precisely enough, and that the trap reduction does not cause excitation within the degenerate gas. For a quasi one-dimensional Bose-Einstein condensate in the Thomas-Fermi limit, the atom number is related to the trap depth by N ∝ U 5/2 0 , and thus a precise control of 86
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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
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 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
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Page 101: ferred via the single-photon coolin
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
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
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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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