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

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ed-detuned light) potential is created. In the experiments described in the following chapters, an attractive dipole potential for lithium atoms is formed by focusing a CO2 laser beam (λ = 10.6 µm), and repulsive potentials for rubidium atoms are created by multiple laser beams at a wavelength of λ = 532 nm. 2.7 Zeeman Slower A magneto-optical trap, see chapter 2.9, is able of capturing atoms at a speed of a few tens of m/s. However, to get a large enough number of lithium atoms into the gas phase to create an effusive atomic beam, it is necessary to heat the lithium reservoir to a temperature of about 350 ◦ C. At this temperature atoms within the effusive beam move at a mean velocity of 1100 m/s (the most probable velocity is about 860 m/s) and are thus too fast to be captured directly in the MOT. The standard way of slowing atoms to lower speeds is to use a Zeeman slower [5–7, 22, 35]. Due to the higher vapor pressure of rubidium, a Zeeman slower is not needed in the rubidium setup. Instead a double MOT setup is used, see chapter 4. A Zeeman slower has two main components: a magnetic field which strength varies along the propagation axis of the atomic beam, and a counter-propagating laser beam. This basic setup is schematically shown in figure 2.13. The Zeeman slower decel- erates atoms in the effusive atomic beam by transferring momentum from the scattered photons from the resonant laser beam to the atoms. With each scattering event an atom in the atomic beam loses on average a momentum of p = h/λ. In order to transfer momentum efficiently from the photons to the atoms, the frequency of the laser beam has to be close to the resonant frequency. As the speed of the atoms decreases, the transition frequency changes as a consequence of the Doppler-effect. A spatially varying external magnetic field (usually created by electromagnetic coils) induces a Zeeman-shift of the energy levels of the atoms. By matching the Doppler- and Zeeman-shifts it is possible to maintain a resonant scattering condition and thus a large scattering rate. The ideal magnetic field is thus given by ω0 + µBB(z) 19 = ωlaser +kv. (2.29)
Here ω0 is the resonance frequency at zero magnetic field, ωlaser the laser frequency, and v the speed of the atoms. A schematic of a Zeeman slower and the ideal magnetic field profile are shown in figure 2.13. oven atomic beam Zeeman slower coils B z Zeeman slower beam Figure 2.13: Zeeman slower setup in decreasing field configuration. An effusive atomic beam is created by heating the oven housing a reservoir. The beam then travels along the Zeeman slower axis. The atoms scatter photons from a counter-propagating laser beam and are decelarated by the exerted scattering force. A magnetic field created by electromagnetic coils causes a Zeeman shift, keeping the laser frequency on resonance with the atomic transition as the Doppler shift of the atom changes due to deceleration. The ideal profile of the magnetic field is shown below the magnetic field region. 2.8 Optical Molasses Optical Molasses is a laser cooling technique solely relying on the transfer of momentum from photons to atoms. The standard configuration of an optical molasses setup consists of three pairs of counter-propagating laser beams [22, 35], see figure 2.14. All beams have the same frequency, tuned slightly below resonance, and each pair has balanced intensities. The effect of this configuration is understood the easiest in one dimension. A stationary atom experiences no net force and on average the interaction vanishes. However, if an atom is moving, the symmetry of the situation is broken. Consider an atom moving to the right with velocity v as shown in figure 2.14. Due to the Doppler-shift, the atom will then scatter more photons from the beam coming 20
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: a laser field with frequency ω. Th
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
Page 85 and 86: 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
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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
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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