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

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epresents the energetically open channel, also called the entrance channel. The second potential, VC, is known as the closed channel. This potential (VC) can support a bound molecular state near the threshold of the entrance channel. Energy 0 V C (R) V bg (R) closed channel E C E entrance channel atomic separation R Figure 2.11: Two channel model for a Feshbach resonance. Consider two atoms scattering with energy E and the existence of a closed channel VC that can support a bound state with energy EC. If resonant coupling to the closed channel exists, for example through hyperfine interactions, the phenomenon of a Feshbach resonance occurs. For cold atoms, where E → 0, resonant coupling can be realized by tuning EC towards zero by means of an external magnetic field, if the magnetic moments of the entrance and closed channels differ. When the energy of the bound state EC approaches the energy of the scattering state of the entrance channel, small interactions, for example hyperfine interactions, lead to a strong mixing between the two channels and a Feshbach resonance occurs, see figure 2.12. For cold atoms, where E → 0, resonant coupling can be realized by tuning EC towards zero by means of an external magnetic field, if the magnetic moments of the entrance and closed channels differ. In case of a magnetically tuned Feshbach resonance the s-wave scattering length can be described by a simple model [31], as(B) = abg 1− ∆ , (2.18) B −B0 where abg is the background scattering length, B0 describes the resonance position and the parameter ∆ describes the width of the resonance. 15
(a) (b) scattering length a 0 Energy E 0 bound state B 0 continuum magnetic eld B magnetic eld B Figure 2.12: Scattering length and molecular state energy near a magnetic Feshbach resonance. (a) The scattering length varies with the magnetic field strength, if the magnetic moments of the entrance and closed channels differ. (b) The hyperfine coupling between the entrance and closed channel leads to an avoided crossing between the free atomic state and the bound molecular state. Because Feshbach resonances allow tuning of the s-wave scattering length, they are a very useful tool during evaporative cooling of cold atomic clouds, see chapter 2.10. Evaporative cooling using two different spin states in 6 Li is typically done using states |1〉 and |2〉, see figure 2.10. For these states a Feshbach resonance with a width of ∆ ≈ −300 G is located at 834 G [30]. The broad width of this resonance makes it particularly useful [32]. The scattering length of these states as a function of the magnetic field B can be found in [32–34]. 2.6 Interaction of Atoms with Light One of the most powerful methods to trap, cool, and manipulate the internal quantum states of atoms is through interaction with light. One can roughly distinguish between two regimes that will be treated separately in this discussion: the interaction with near-resonant light, which leads to a strong scattering force, and the far-detuned regime, which leads to an AC Stark shift or an optical dipole force. Both regimes are 16
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: interaction. The shift in the 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 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
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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
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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
Page 203 and 204:
[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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