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

are therefore useful tools. A tweezer at the magic wavelength would allow to trap
atoms in the ground state as well as in an excited state without heating them. Thus
transitions between these two states can be induced and fluorescence imaging can
be used to determine the atom number. Spatially resolved Raman transitions allow
to measure spatial distributions where the achievable resolution is smaller than the
wavelength.
As this work deals with the manipulation of atomic states with light we will
review the semi-classical description of atoms with non-resonant light (chapter 2) and
apply it to calculations of the AC-Stark shift in Sodium and Rubidium. Knowing the
respective energy shifts for the ground and the excited states we can determine the
magic wavelength, where the relative shift between the ground and a specific excited
state vanishes (chapter 3). Our efforts to determine the magic wavelength in Sodium
are summarized in chapter 4, together with a brief discussion of the experimental
environment.
In chapter 5 we expand the theory of the interaction of electro-magnetic radiation
with atoms to the case with two monochromatic light sources and introduce stimulated
Raman transitions in the presence of an external magnetic field. Chapter 6 summarizes
our calculations of stimulated Raman transitions for Sodium atoms, and outlines the
spatial resolution that is prospectively achievable using a magnetic field gradient.
A relevant parameter in all our calculations is the dipole matrix element between
two states. A convenient way to determine these is the Wigner-Eckart Theorem which
is briefly discussed in appendix A. Appendix B summarizes some physical properties
of Sodium atoms and describes the influence of an external magnetic field on the
energy level structure. The Einstein-coefficients we calculated to determine the magic
wavelength in Rubidium are tabulated in appendix C.
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