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

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(a) (b) (c) n(E) n(E) n(E) E avg E avg E avg Figure 2.19: Evaporative Cooling Process. (a) The thermal distribution of the trapped cloud of atoms extends far above the well depth U of the optical trap. (b) The hottest atoms leave the atoms, effectively reducing the average energy of the trapped atoms. (c) Collisions between the atoms lead to a rethermalizing of the cloud at a lower temperature. The process then repeats itself. The processes of leaving the trap and rethermalization happen continously and is not a discrete process. Once the thermal tail does not extend above the trap depth anymore, additional techniques (i.e. lowering of the trap depth) are required to continue the evaporative cooling process. U The speed of evaporative cooling is highly dependent on the timescale of rethermalization and thus on the scattering cross section of the atoms. Using the broad Feshbach resonance in 6 Li the scattering cross section can be significantly increased, thus reducing evaporation times dramatically. The efficiency of the evaporative cooling process will depend on the shape of the trap depth lowering curve. For an energy-independent scattering cross section the ideal shape is given by [40] U(t) U0 = E 1+ t −2(η−3)/η , (2.36) τ 27 E E
which maintains a constant η = U/kBT during the evaporation process. Near the Feshbach resonance, in the unitary regime, the scattering cross section becomes energy- dependent. The ideal shape of the trap depth lowering curve is then described by [41] U(t) U0 2.11 Degenerate Fermi Gas = 1− t 2(η−3)/(η−6) . (2.37) τ In the quantum regime the properties of bosons and fermions are very different. While the wave-function of bosons, like 87 Rb, is symmetric under the exchange of two particles, the wavefunction of fermions, like 6 Li, is anti-symmetric under the exchange. In addition, fermions obey the Pauli-exclusion principle and two indistinguishable fermions cannot occupy the same energy level. These differences lead to bosons following Bose- Einstein statistics and fermions obeying Fermi-Dirac statistics. In the thermal regime the difference between bosons and fermions can be neglected, both following Maxwell- Boltzmann statistics. However, as the temperature of the gas falls below a transition temperature and degeneracy is approached, exciting new physics can be discovered. This section focuses on properties of degenerate non-interacting fermions. For non-interaction fermions the Fermi-Dirac distribution is given by f(ǫν) = exp 1 ǫν−µ kBT , (2.38) +1 where µ is the chemical potential [42]. At zero temperature the energy distribution is f(ǫ) = 1 below the Fermi energy EF = µ(T = 0,N) and f(ǫ) = 0 above. For higher temperatures the distribution is smeared out around EF. In a harmonic trap the density of states is given by [43] g(ǫ) = ǫ 2 2 3 ωxωyωz = ǫ2 2 3 ¯ω 3, (2.39) where ωi are the trapping frequencies and ¯ω 3 ≡ ωxωyωz. The total number of particles is therefore determined by N = dǫf(ǫ)g(ǫ). (2.40) 28
Page 1 and 2: Copyright by Kirsten Viering 2012
Page 3 and 4: Experiments to Control Atom Number
Page 5 and 6: 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: phase-space density is defined as
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 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
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Figure 5.10: Radius of the magnetic
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on the collision rate of atoms insi
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ferred via the single-photon coolin
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By comparison an atomic Fock state
Page 105 and 106:
of atoms in the two hyperfine groun
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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
Page 155 and 156:
The second card (NI6733) offers eig
Page 157 and 158:
Averaging over the magnetic subleve
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2 2 P 3/2 D 2=670.977nm 2 2 S 1/2 m
Page 161 and 162:
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
Page 201 and 202:
[67] J.L. Hanssen. Controlling Atom
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[88] D.S. Naik, C.G. Peterson, A.G.
Page 205 and 206:
[110] J.W. Goodman. Introduction to
Page 207:
[132] C. Degenhardt, H. Stoehr, U.
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