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

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used during the course of the experiments described in this dissertation: Near-resonant light slows atoms in a Zeeman slower and traps atoms in a magneto-optical trap; far-off resonant light on the other hand creates optical dipole traps. In the lithium experiment an optical dipole trap is used for optical evaporation in order to cool the atoms to degeneracy. In the rubidium experiment an optical dipole trap stores the atoms after they have undergone single-photon cooling. 2.6.1 Near-Resonant Light - Scattering Force The dominant effect of near-resonant light is the creation of a strong scattering force. If an atom absorbs a photon, the photon momentum is transferred to the atom. If the absorption of the photon is followed by a spontaneous emission process, on average the emission will not cause a change in the momentum of the atom. The net force an atom experiences from absorption is thus given by [35] Fscatt = kΓρee, (2.19) where k is photon momentum, Γ is the rate of the process and ρee is part of the density matrix and describes the probability to find an atom in the excited state. Choosing ρee over ρgg includes the effects of saturation and detuning. The expression for ρee can be derived from the optical Bloch equations and is given by [35] ρee = 1 2 I/Isat 1+(I/Isat)+4(∆/Γ) 2, (2.20) where ∆ = ωlaser −ωresonant. This implies that the scattering rate and scattering force are given by Rscatt = Γ 2 Fscatt = k Γ 2 I/Isat 1+(I/Isat)+4(∆/Γ) 2 I/Isat 1+(I/Isat)+4(∆/Γ) 2. 2.6.2 Far-Detuned Light - AC Stark Shift and Optical Dipole Force (2.21) (2.22) Far-off resonant light creates an AC Stark shift, while scattering forces are neg- ligible in this regime. Consider an atom placed into an electric field E generated by 17
a laser field with frequency ω. This electric field induces an atomic dipole moment p, where [36] p = α(ω) E. (2.23) α(ω) is the complex polarizability, which depends on the laser frequency ω. The induced dipole gives rise to an energy shift given by ∆EAC = − 1 2 〈p· E〉 = − 1 Re(α)I, (2.24) 2ǫ0c where the angular brackets indicate the time average. The intensity I is given by I = 2ǫ0c| E| 2 . In a quantum-mechanical description the scalar polarizability α is given by α = 1 2 k |〈k|µ|j〉| 2 1 ωkj +ω + 1 ωkj −ω . (2.25) The energy shift of an energy level j in the presence of a laser beam with intensity I is thus described by ∆EAC = − 1 4ǫ0c k |〈k|µ|j〉| 2 1 ωkg +ω + 1 ωkg −ω I, (2.26) where the sum is over all possible energy levels k. This formula is evaluated further in appendix A. In a semi-classical approximation the AC-Stark shift of the ground state, typically called the dipole potential, can be expressed by 1 ωD2 +ω + Udip(r) = − Γ2 D2 8Isat 1 ωD2 −ω I(r), (2.27) where ΓD2 is the D2-line transition linewidth and Isat is the saturation intensity. In cases where the rotating wave approximation can be invoked, this equation simplifies to Udip(r) = 3πc2 2ω 3 Γ I(r), (2.28) ∆ where the expression of the saturation intensity is inserted [36], and ∆ describes the detuning from resonance, ∆ ≡ ωlaser − ωD2. The dipole potential then scales as I ∆ . Depending on the sign of ∆, a repulsive (for blue-detuned light) or an attractive (for 18
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: (a) (b) scattering length a 0 Energ
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 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
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Atoms are then optically pumped to
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ferred into the |F = 1,mF = 0〉 or
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5.2 Branching Ratios and Population
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effect of the reflected beam at zer
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y the repulsive trough beams, gaini
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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
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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
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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
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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