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

Chapter 3
Magic Wavelength
The concept of a magic wavelength is mostly discussed in connection with time and
frequency measurements. Today time and frequency standards are determined by
Cesium fountain clocks as NIST-F1, where transitions are induced in a microwave-
cavity [14]. Although frequency is already the most precisely measurable quantity,
frequency measurements would be greatly improved by exploiting optical instead of
microwave transitions.
For an optical clock, ultracold neutral atoms have to be trapped in order to
minimize Doppler-Shifts. Optical traps have the disadvantage of shifting the energy
levels, where the magnitude of the shift is proportional to the intensity of the beam
used to create the trap, as we have shown in the previous chapter. In general, these
shifts are different for different atomic levels, and the resonance frequency therefore
depends on the trapping potential, i.e. the exact position of the atom inside the trap.
Nevertheless, if the energy shifts are equal for the ground and the respective excited
state the resonance frequency gets insensitive to the intensity of the laser beam and
hence to the trapping potential. The wavelength with the above characteristics is called
the magic wavelength [15].
An attractive trap at the magic wavelength provides the same potential for the
ground and excited state. Hence the atoms held in this trap are not heated when a
resonant transition is induced. The fluorescence signal contains information not only
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