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

Chapter 6
Raman transitions of Sodium atoms
The following chapter uses the theory for stimulated Raman transitions we described
previously to calculate the ideal pulse duration needed to ensure a complete population
transfer from the |F = 1〉 to the |F = 2〉 ground state in Sodium. Furthermore, we
determine the spatial resolution achieved by applying a magnetic field gradient and
propose an experimental method to determine the pulse duration and the magnetic
field dependance.
6.1 Magnetic detuning from Raman Resonance
In section 5.5 we already introduced the detuning δB m f ,mi (r) = γm f ,m µB i
B(r) due to the
magnetic field. We will now calculate this detuning for Sodium atoms. Knowing the
Landé-g-factors for the ground state of Sodium, gi = −1/2 (F=1) and g f = +1/2 (F=2),
we can calculate γm f ,mi . The numerical values are shown in table 6.1. With these values
we can now calculate δB m f ,mi (r) for some particular initial and final state combination.
6.2 Dipole matrix elements
Before we can calculate the effective Raman-Rabi frequencies we need to determine
the transition dipole matrix elements 〈J = 1/2||µ||J = 3/2〉 and 〈J = 1/2||µ||J = 1/2〉. In
40