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

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2.5 Magnetic Interactions with Atoms This section describes the effect of an external magnetic field on the atomic energy structure (anomalous and normal Zeeman effect) and on the scattering properties of atoms (magnetic Feshbach resonance). The Zeeman effect is utilized both in the Zeeman slower (see chapters 2.7 and 7.2.1) in a magneto-optical trap. In addition, magnetic trapping of atoms would not be possible without the Zeeman effect. Magnetic Feshbach resonances lead to a strong dependence between the scattering length of the atoms and an externally applied homogeneous magnetic field. This effect can be exploited, for example, to decrease evaporation times, see chapter 2.10. 2.5.1 Anomalous and Normal Zeeman Effect The anomalous Zeeman effect describes the energy shift of atomic states in the presence of a weak external magnetic field. Weak in this context means that the interaction energy between the total angular momentum of the atom and the external magnetic field is small compared to the interaction energy between the electron spin and the nuclear spin of the atom. This means that the total angular momentum F will precess along the magnetic field axis, see figure 2.7. In stronger magnetic fields, angular momenta start to decouple. This is described by the normal Zeeman effect and the Paschen-Back effect. Figure 2.7: In the anomalous Zeeman regime the total angular momentum F = I + J precesses around the magnetic field axis. Figure courtesy of Gabriel Price. B 11 F J I
The total magnetic moment of an atom is given by the sum of its electronic and nuclear moments, µ = µB(gJ J +gI I), (2.13) where µB is the Bohr magneton, J and I are the electronic angular momentum and nuclear spin, and gJ and gI are the electronic and nuclear magnetic g-factors. The Hamiltonian describing the interaction between the atomic magnetic moment µ and the external magnetic field B is given by [22, 23, 25] H = −µ· B. (2.14) This Hamiltonian can be diagonalized in the hyperfine basis |F,mF〉. Each of the hyperfine levels F consists of 2F +1 magnetic sublevels (mF), corresponding to the different projections of the total atomic angular momentum along the quantization axis given by the direction of the magnetic field. The associated energy shift of the state |F,mF〉 is given by where F(F +1)−I(I +1)+J(J +1) gF = gJ +gI 2F(F +1) ∆E = µBgFmF|B|, (2.15) F(F +1)+I(I +1)−J(J +1) . (2.16) 2F(F +1) Table 2.3 summarizes the values of gI and gJ for the transitions important to this dissertation for both rubidium and lithium. Rubidium gI -0.0009951414(10) gJ(5 2 S1/2) 2.00233113(20) gJ(5 2 P1/2) 2/3 gJ(5 2 P3/2) 1.3362(13) Table 2.3: g-factors for rubidium and lithium Lithium gI -0.0004476540 gJ(22S1/2) 2.00233113(20) gJ(22P1/2) 0.6668 gJ(22P3/2) 1.335 Figure 2.8 shows the anomalous Zeeman splitting of the ground state of 87 Rb. The magnetic field strengths used during the course of the rubidium single-photon cooling experiment remain in the anomalous Zeeman regime. This figure shows that it is possible 12
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: The Wigner-Eckhart theorem can be u
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 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
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provides the beam for the upper MOT
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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
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[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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