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

More documents

Recommendations

Info

atomic number Z 11 number of nucleons Z+N 23 relative natural abundance η( 23 Na) 100% nuclear spin I 3/2 D2-line frequency ω 2π· 508.8487162(13)THz D2-line lifetime τ 16.249(19)ns D1-line frequency ω 2π· 508.3324657(13)THz D1-line lifetime τ 16.299(21)ns Landé-g-factor gJ 3 2 S1/2 2.0022969(7) Landé-g-factor gJ 3 2 P1/2 0.66581(12) Landé-g-factor gJ 3 2 P3/2 1.332(2) Table B.1: Physical properties of Sodium atoms [20] For high magnetic fields, the levels split according to the Paschen-Back-effect 3(mJmI) ∆E = Ah f smJmI + Bh f s 2 + 3 2mJmI − I(I + 1)J(J + 1) + µB(gJmJ + gImI)Bz, (B.5) 2J(2J − 1)I(2I − 1) where Ah f s and Bh f s are hyperfine structure constants. For intermediate magnetic fields the splitting is in general difficult to calculate, but if either J = 1/2 or I = 1/2 an analytic description is given by the Breit-Rabi-formula. For the ground state manifold in Sodium the Breit-Rabi-formula is ∆E = − Ah f s(I + 1/2) 2(2I + 1) + gIµBmB ± Ah f s(I + 1/2) 1 + 2 4mx 1/2 + x2 , (B.6) 2I + 1 with m = mI ± mJ (sign to be taken as in eq. B.6) and x = (gJ − gI)µBB . (B.7) Ah f s(I + 1/2) Fig. B.4 shows the magnetic field dependance of the ground state manifold. 57
Figure B.4: Sodium 3 2 S1/2 ground state hyperfine structure in an external magnetic field. In the anomalous Zeeman-regime the levels are grouped according to the value of F, in the Paschen-Back-regime according to the value of mJ [20]. 58
Page 1 and 2:
Copyright by Kirsten Viering 2006
Page 3 and 4:
Spatially resolved single atom dete
Page 5 and 6:
Acknowledgments First of all I woul
Page 7 and 8:
Spatially resolved single atom dete
Page 9 and 10:
Chapter 5 Stimulated Raman transiti
Page 11 and 12:
List of Figures 2.1 Schematic of th
Page 13 and 14:
6.1 Schematic of the possible Raman
Page 15 and 16:
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 and 68: Figure B.1: Grotrian diagram for So
Page 69: Figure B.3: Schematic of the cyclin
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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?