Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

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Figure B.2: Schematic of the ground state and the first excited state energy level. The hyperfine splitting is indicated for the 3 2 S1/2 ground state and the 3 2 P3/2 state. The magnetic splitting is according to the anomalous Zeeman effect. The wavelengths for the resonant transitions are presented, as are the Landé-g-factors. Energy is not to scale. B.2 Sodium in an external magnetic field The degeneracy of the (2F+1) magnetic levels breaks down in an external magnetic field. If we take the magnetic field to be along the atomic quantization axis (z-axis), the Hamiltonian HB = µB gSSz + gLLz + gIIz Bz (B.1) describes the interaction of the atom with the magnetic field. gS, gL and gI are the Landé-g-factors for the electron spin, electron orbital and nuclear spin respectively [20]. If hyperfine splittings are important, F is a good quantum number, and the 55
Figure B.3: Schematic of the cycling transition F = 2 → F ′ = 3 with the red detuned beam (orange) and the repump beam (blue). Energy is not to scale. interaction Hamiltonian becomes HB = µBgFFzBz. (B.2) In a weak external magnetic field the magnetic levels split according to the anomalous Zeeman effect. The perturbation of the interaction Hamiltonian to the zero field eigenstates is, to lowest order, given by where gF ≈ gJ ∆E = µBgFmFBz, (B.3) F(F + 1) − I(I + 1) + J(J + 1) . (B.4) 2F(F + 1) 56
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Copyright by Kirsten Viering 2006
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Spatially resolved single atom dete
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Acknowledgments First of all I woul
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Spatially resolved single atom dete
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Chapter 5 Stimulated Raman transiti
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List of Figures 2.1 Schematic of th
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6.1 Schematic of the possible Raman
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are therefore useful tools. A tweez
Page 17 and 18: eigenfunctions |n〉 with the corre
Page 19 and 20: and c ′ g(t) = cg(t) (2.12) c ′
Page 21 and 22: 2.3 Interaction of a multi-level sy
Page 23 and 24: Figure 2.2: Plot of the AC-Stark sh
Page 25 and 26: |µ kj| ∆Ej = k 2E2 1 1 − ω
Page 27 and 28: on the transition frequency but als
Page 29 and 30: Figure 3.2: Plot of the AC-Stark sh
Page 31 and 32: Chapter 4 Experiments on the magic
Page 33 and 34: I Figure 4.1: Scattering Rate depen
Page 35 and 36: Figure 4.3: Sketch of the Zeeman-Sh
Page 37 and 38: Chapter 5 Stimulated Raman transiti
Page 39 and 40: The scheme for a Resonant Raman tra
Page 41 and 42: variation of the resonance transiti
Page 43 and 44: Figure 5.3: Possible configurations
Page 45 and 46: to adiabatically reduce the three-l
Page 47 and 48: as the final state probability. 5.4
Page 49 and 50: Rabi frequency β given by β f i
Page 51 and 52: larizations stay constant, while th
Page 53 and 54: Chapter 6 Raman transitions of Sodi
Page 55 and 56: e in the ˆz-direction, B = Bˆz. T
Page 57 and 58: With the calculation of the detunin
Page 59 and 60: Figure 6.3: Dependance of the final
Page 61 and 62: In the absence of a magnetic field,
Page 63 and 64: used to determine the necessary mag
Page 65 and 66: The product of the two rotation mat
Page 67: Figure B.1: Grotrian diagram for So
Page 71 and 72: Figure B.4: Sodium 3 2 S1/2 ground
Page 73 and 74: F’=2 F’=1 F’=0 mF = −1 mF =
Page 75 and 76: Appendix C Einstein-coefficients fo
Page 77 and 78: Bibliography [1] J. V. Prodan, W. D
Page 79 and 80: [24] K. D. Stokes, C. Schnurr, J. R
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