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

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In all the calculations done above we have assumed the Raman detuning δ to be zero, i.e. the difference frequency equals the hyperfine splitting of the Sodium ground states in absence of a magnetic field (1.772GHz). By changing the detuning we can vary the position of the resonant Raman region in space. A detuning of 1MHz corresponds to a spatial shift of the resonant region by 7.55 µm. 6.5 Experimental procedure to determine the transfer efficiency of stimulated Raman transitions The experimental procedure used to test the efficiency of the Raman pulse is rather simple. After loading the MOT and cooling the trapped atoms, the repump beam is turned off. Therefore atoms that fall into the |F = 1〉 state remain there and are separated from the |F = 2〉 → |F ′ = 3〉 cycling transition. Eventually all atoms will fall into this dark state. The atoms can then be transferred into the magnetic trap. In the future, the trap will be in an Anti-Helmholtz configuration with an optical plug [31]. In this trap only the atoms with the magnetic sublevel M=-1 will be trapped. An evaporation cooling technique is then used to create a Bose Einstein Condensate. The optical lattice is created next and the atoms are confined to individual lattice sites. A Raman pulse is then applied and the corresponding number of atoms make the transition to the |F = 2〉 state. The resonant light is turned on. Although the resonant light forms a closed transition all atoms will eventually fall in the |F = 1〉 state again after a certain number of cycling transitions. During this process they gain energy and a time-of-flight measurement could separate the two atom groups and the atom number of those that made the Raman transition can be determined. Knowledge of the initial number of atoms is a crucial element of determining the Raman transition efficiency. One therefore must be certain that the initial number of atoms does not vary by more than a few percent. Knowing the ideal pulse duration one can study the population transfer efficiency as a function of a magnetic bias field. The relation between those two can then be 49
used to determine the necessary magnetic field gradient to achieve the desired spatial resolution. Instead of using a time-of-flight measurement one could also think of lowering the depth of the optical lattice. The atoms that underwent the Raman transition and therefore the cycling transition will leave the trap before the other atoms do which did not make the Raman transition. It is then possible to determine the atom number of the remaining atoms. In the proposed configuration for spatially resolved Raman imaging the magnetic field gradient is along the propagation axis of the two co-propagating Raman beams which are linearly polarized in ˆx- and ˆy-direction respectively. By preparing all atoms to be in the |F = 1, M = −1〉 state and confining them in an optical lattice a spatial resolution of one lattice site seems achievable applying a magnetic field gradient of 150 G/cm. A change in the Raman detuning can be used to vary the resonant Raman region in space. The resonant Raman region is at the point of zero magnetic field if the difference frequency equals the hyperfine splitting in absence of a magnetic field (1.772GHz). 50
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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
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: In the absence of a magnetic field,
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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Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

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