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

More documents

Recommendations

Info

d dt ρgg = iΩ 2 ( ˜ρge − ˜ρeg) + Γρee d dt ρee = − iΩ 2 ( ˜ρge − ˜ρeg) − Γρee (4.1) (4.2) d dt ρge = − iΩ 2 (ρee − ρgg) − ( Γ 2 + i∆) ˜ρge, (4.3) where ρij are the matrix elements of the density operator, Ω = µ·E is the resonant Rabi frequency, µ the dipole operator, E the electric field, Γ the natural decay rate of the excited state e and ˜ρge ≡ ρgeexp(−i∆t), ˜ρge = ˜ρ ∗ eg. The total steady-state photon scattering rate is then given by Γρee [20] Rsc = Γ 2 I/Isat 1 + (2 ∆ Γ )2 + I Isat , (4.4) where I Isat = 2 Ω 2 Γ . This approximation is valid if the detuning ∆ from the optical resonance is large, ∆ ≫ Γ. An additional light field causing an AC-Stark shift, corresponding to a detuning from resonance, should therefore decrease the scattering rate and consequently the amount of scattered light. Fig. 4.1 shows the scattering rate as a function of the detuning ∆ for several values of I . The natural decay rate Γ is taken to be 2π·9.795MHz, Isat corresponding to the Sodium D2-line, which we use to trap and cool the atoms. 4.2 Experimental Setup 4.2.1 Oven and Zeeman-slower Because of the low vapor pressure of Sodium (Pv = 2.2 · 10 −11 torr [20]) it is necessary to heat the Sodium in an oven to about 500K. Our oven is not recirculating and therefore it has to be refilled after a few hundred hours of operation [21]. In order to be able to trap the atoms in a magneto-optical trap (MOT) (see section 4.2.2) the atoms in the effusive beam have to be decelerated to a few meters per second. 19
I Figure 4.1: Scattering Rate dependance on the detuning δ for several values of . The Isat natural decay rate Γ is 2π · 9.795MHz for the D2-line in Sodium. This can be achieved by scattering a sufficient number of photons from a counter- propagating beam. Atoms with different velocities have different Doppler-shifts, so the optical transition will be out of resonance after a certain number of scattering events. A resonant transition can be maintained by changing the magnetic hyperfine splittings using an external magnetic field, tuned to compensate for the decreasing Doppler-shift of the decelerating atoms. In a low magnetic field the magnetic energy levels split proportionally to the magnitude of the field. This is called the anomalous Zeeman- effect and is used in a Zeeman-slower to maintain a resonant transition between the ground and the respective excited state. The slowing transition in our setup is the |F = 2, M = 2〉 → |F = 3, M = 3〉 transition and is excited by a dye laser (Coherent 899-21). 4.2.2 Magneto-Optical Trap After leaving the Zeeman-slower the atoms that are sufficiently slowed are trapped in a magneto-optical trap (MOT). Two coils in an Anti-Helmholtz-configuration provide 20
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: Chapter 4 Experiments on the magic
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
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

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

Create successful ePaper yourself

Delete template?

Save as template?