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

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a quadrupole field with a magnetic field gradient in radial (ρ-) and axial (z-) direction, where dBz dz = 2dBρ . (4.5) dρ In addition to the magnetic field gradient there are three pairs of counter-propagating beams, red-detuned from the resonance at zero magnetic field; a schematic of the alignment is shown in fig. 4.2. If a trapped atom moves out of the zero magnetic field at the center of the trap, the magnetic sublevels will split according to the magnitude Figure 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 of the magnetic field. Therefore the detuning decreases with an increasing distance from the center of the magnetic field. If the polarizations of the two opposing beams are aligned correctly, there will be more light scattered from one than from the other and the atom driven back towards the center of the trap, i.e. an atom moving to the right scatters more σ − -polarized light. In fig. 4.3 we have shown a schematic for the magnetic detuning in a 1-D-MOT, which can easily be extended to three dimensions. The beams in our setup are 20MHz red detuned from the 3 2 S1/2(F = 2) → 3 2 P3/2(F ′ = 3) transition; the magnetic field gradient in the axial direction is 15G/cm. 21
Figure 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]. 4.3 Experimental procedure After loading about 10 9 atoms into the MOT we collected the scattered light and focused it down onto an avalanche photo diode (APD). By introducing an AC-Stark shift with a YAG-laser (IPG Photonics YLD-10) at 1064nm the fluorescence signal of the MOT should change slightly. Since the desired signal is small compared to the background fluorescence we intended to use a lock-in amplifier (SRS 510) to extract the signal. We therefore pulsed the YAG-laser with frequencies between 1kHz and 10kHz. The first signal we got was due to light directly scattered from the YAG beam into the APD. We therefore put additional shielding around the APD and could remove scattered light at a wavelength of 1064nm. We created a MOT with a diameter of approximately 500µm and variied the beam waist of the YAG-laser between 190µm and 400µm. The predicted AC-Stark shift δ due to a 6W YAG-beam with a waist of 400µm is 49.4kHz in about 49% of the atoms, assuming the MOT to be spherical and of equal density. Using eq. 4.4 we can calculate 22
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: I Figure 4.1: Scattering Rate depen
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 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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