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

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4.2 Schematic of the beam configuration in a magneto optical trap (MOT), the current in the Anti-Helmholtz-coils (red) flows opposite, the MOT beams are represented by the blue arrows . . . . . . . . . . . . . . . . . . 21 4.3 Sketch of the Zeeman-Shift in a 1-D MOT. The dashed line represents the red detuned MOT-beam frequency. The position dependant Zeeman- shift changes the detuning from the resonance frequency [8]. . . . . . . . 22 5.1 Simplified scheme of a resonant transition with spatial resolution; the resonance frequency ω0 is space-dependant, i.e. the resonance frequency ω0 at x0 is not in resonance at point x. For simplicity we have assumed that only the final state | f 〉 is dependant on the magnetic field. . . . . . . 25 5.2 Simplified scheme of a resonant Raman transition with spatial resolution;the resonance frequency is space-dependant. For simplicity we have assumed that only the final state | f 〉 is dependant on the magnetic field. The two frequencies ω1 and ω2 are off-resonance with an intermediate level |I〉. The detuning is given by ∆. . . . . . . . . . . . . . . . . . . . . . 26 5.3 Possible configurations of a three-level system driven by a two-photon process, from left to right: ladder-configuration, V-configuration, Λ- configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.4 Schematic of the frequencies and detunings in a stimulated Raman process in a three-level atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.5 Possible Raman transitions between two hyperfine states with J = 1/2. For simplicity we assume all atoms to start in the |F = 1, m = 0〉 state. The detuning of 1.772GHz belongs to the Sodium ground state 2 S1/2. The splitting of the magnetic sublevels is according to the anomalous Zeeman-effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.6 Definition of the quantization axis by an external magnetic field. The direction of the magnetic field is represented by the red arrow. Unprimed coordinates belong to the lab frame, coordinates in the atom frame are primed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 xii
6.1 Schematic of the possible Raman transitions leading to the effective Raman-Rabi frequency β0−1 . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.2 Dependance of the final state probability of pulse duration τ. . . . . . . 45 6.3 Dependance of the final state probability of the detuning δ from the Raman resonance frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.4 The final state probability as a function of the position. 0 belongs to the point of 0 magnetic field. The Raman detuning δ equals 0, the magnetic field gradient is 150G/cm. The angle θ equals 0, i.e. the magnetic field points along the z-axis (atom and lab frame coincide). . . . . . . . . . . . 47 6.5 Dependance of the final state probability of the position. O belongs to the point of 0 magnetic field. The Raman detuning δ equals 0, the magnetic field gradient is 150G/cm. The angle θ equals 0, i.e. the magnetic field points along the z-axis (atom and lab frame coincide). All atoms start in the F=1 M=-1 state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 B.1 Grotrian diagram for Sodium, neglecting fine and hyperfine structure splittings. Allowed transitions are indicated. The spectroscopic notation and the atomic configuration are presented. Energy is not to scale. . . . 54 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. . . . . . . . . . . . . . . . . . 55 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. . . . 56 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 xiii
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: List of Figures 2.1 Schematic of th
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
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The product of the two rotation mat
Page 67 and 68:
Figure B.1: Grotrian diagram for So
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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
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Bibliography [1] J. V. Prodan, W. D
Page 79 and 80:
[24] K. D. Stokes, C. Schnurr, J. R
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