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

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Contents Acknowledgments v Abstract vii List of Figures xi Chapter 1 Introduction 1 Chapter 2 Interaction of atoms with non-resonant light 3 2.1 Time-dependant Schrödinger equation . . . . . . . . . . . . . . . . . . . . 3 2.2 Interaction of a two-level atom with non-resonant light . . . . . . . . . . 4 2.3 Interaction of a multi-level system with non-resonant light . . . . . . . . 8 2.4 Dipole matrix elements, Einstein-coefficients and the AC-Stark shift . . . 9 Chapter 3 Magic Wavelength 13 3.1 Calculation of the magic wavelength in Sodium . . . . . . . . . . . . . . 14 3.2 Magic wavelength in Rubidium . . . . . . . . . . . . . . . . . . . . . . . . 16 Chapter 4 Experiments on the magic wavelength 18 4.1 Scattering Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2.1 Oven and Zeeman-slower . . . . . . . . . . . . . . . . . . . . . . . 19 4.2.2 Magneto-Optical Trap . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 viii
Chapter 5 Stimulated Raman transitions 24 5.1 General description of spatially resolved stimulated Raman transitions . 24 5.2 Limitations for spatially resolved Raman transitions . . . . . . . . . . . . 26 5.2.1 Spectral resolution limit . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2.2 Velocity-limited resolution . . . . . . . . . . . . . . . . . . . . . . 28 5.2.3 Acceleration-limited resolution and the Heisenberg uncertainty principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Raman transitions in a three level atom . . . . . . . . . . . . . . . . . . . 29 5.3.1 Three-level amplitude equations . . . . . . . . . . . . . . . . . . . 30 5.3.2 Adiabatic Reduction to a two-level system . . . . . . . . . . . . . 31 5.4 Raman transition in a multi-level atom . . . . . . . . . . . . . . . . . . . . 34 5.4.1 Multiple initial and final states . . . . . . . . . . . . . . . . . . . . 35 5.4.2 Multiple intermediate states . . . . . . . . . . . . . . . . . . . . . . 35 5.5 Raman transitions in a magnetic field . . . . . . . . . . . . . . . . . . . . 36 Chapter 6 Raman transitions of Sodium atoms 40 6.1 Magnetic detuning from Raman Resonance . . . . . . . . . . . . . . . . . 40 6.2 Dipole matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.3 Effective Raman-Rabi frequencies and final state probability . . . . . . . 41 6.4 Numerical results for Sodium atoms . . . . . . . . . . . . . . . . . . . . . 44 6.5 Experimental procedure to determine the transfer efficiency of stimulated Raman transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Appendix A Wigner-Eckart Theorem 51 Appendix B Properties of Sodium 53 B.1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 B.2 Sodium in an external magnetic field . . . . . . . . . . . . . . . . . . . . . 55 B.3 Dipole matrix elements for Sodium . . . . . . . . . . . . . . . . . . . . . . 59 Appendix C Einstein-coefficients for Rubidium 62 ix
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: Spatially resolved single atom dete
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
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Figure B.1: Grotrian diagram for So
Page 69 and 70:
Figure B.3: Schematic of the cyclin
Page 71 and 72:
Figure B.4: Sodium 3 2 S1/2 ground
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F’=2 F’=1 F’=0 mF = −1 mF =
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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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Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

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