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

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Figure 6.2: Dependance of the final state probability of pulse duration τ. In a future experimental setup, the detuning between the two Raman beams will be created by an Acousto-Optic Frequency Shifter (Brimrose TEF-1700-350-589) with an optical threshold of 100W/mm 2 and a diffraction efficiency of 14.8% at a wavelength of 532nm. The time development of the final state probability depends critically on the intensities of the two Raman beams. So it is important to note that the following calcu- lations are based on beams with 7.6 mW with a beam waist of 50µm. The large beam waist guarantees that the intensity in the Raman resonance region is approximately constant. A plot of the time dependance is shown in fig. 6.2. After a pulse duration of 337.3µs the population transfer reaches 98.8%. With a pulse of length 337.3µs, less than 20kHz detuning from the Raman resonance frequency will reduce the population transfer significantly, as can be seen in fig. 6.3. This results in a spectral resolution of less than 250nm if we take the magnetic field gradient to be 150G/cm. Nevertheless, the spatial resolution is severely limited due to the initial velocity of the atoms and their acceleration during the Raman pulse. 45
Figure 6.3: Dependance of the final state probability of the detuning δ from the Raman resonance frequency By confining the atoms in an optical lattice it is possible to circumvent the resolution limits due to the atoms velocity and acceleration. We can then use a long pulse duration time, to ensure an efficient population transfer and to gain a good spectral resolution. But this also means that the resolution is ultimately limited by the size of each individual lattice site, i.e. 266nm for a beam with a wavelength of 532nm. The center of the resonant Raman region should coincide with the center of the lattice site to avoid a population transfer in the two neighbouring sites. A magnetic field gradient of 150G/cm means a splitting of the magnetic levels according to the anomalous Zeeman effect. Fig. 6.4 represents the case where the quantization axis of the atoms coincides with the z-direction in the lab frame (magnetic field along the direction of beam propagation). In this case eq. 6.7 reduces to 46
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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
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: With the calculation of the detunin
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 and 70: Figure B.3: Schematic of the cyclin
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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