Seitenbandkühlung von gespeicherten Ytterbium-Ionen im Mikrowellenregime

Trapped ions in a Paul trap are at present one of the most promising candidates for
Quantum Information Processing (QIP). The technique that is used for this purpose in
this experiment was introduced in 2001 by F. Mintert and Ch. Wunderlich. The core
of this method is the use of atomic transitions in the radio- or microwave region, while
a magnetic field gradient along the trap axis (where the ion chain is situated) lifts
the degeneracy of the transition frequencies, such that the ions can be distinguished
in frequency space; it also serves for the coupling of internal and external degrees of
freedom of the ion chain. This method is called MAGIC (MAgnetic Gradient Induced
Coupling).
The performance of the measurements required that the apparatus of the experiment,
which consists of laser sources, lambdameter, vacuum- and microwave system
as well as imaging- and detection-units, had to be assembled and tested, which was
an important prerequisite for the successful performance of the here described experiments.
For the experiments it is advantageous to prepare the ions in an energetic state
close to the motional ground state, which contributes to a reduction of the dephasing
of the system while manipulating it with microwaves. By using the sideband-cooling
technique to the sub-Doppler regime it is taken advantage of the fact, that ions in a linear
trap are in good approximation situated in a harmonic oscillator potential and can
therefore only populate discrete vibrational energy levels, whose frequency difference
is given by the axial trap frequency. If the system is excited by a microwave, which
frequency is detuned from resonance to lower energies by a vibrational quantum,
the ion looses one such phonon within each cooling-cycle. When this cycle is driven
several times, the average phonon number and thus the temperature of the ion can be
reduced efficiently and the ion can be initialized in a state close to the motional ground
state. As sideband-cooling-transition two hyperfine-levels of 171Yb+ were used, addressed
with a microwave at about 12.6 GHz. In principle microwave photons do not
carry enough momentum to cool down the ions but due to the MAGIC-technique, this
is even possible.
In this work the parameters relevant for the sideband-cooling process were characterized,
including the heatrate that counteracts the cooling. With this, the average
phonon number was reduced from about 100 to 4(4), which is compatible with
the motional ground state. For the verification of the successful cooling process two
different methods for analysis were used while the results agreed. The work is to the
knowledge of the author the first detailed description of sideband-cooling of trapped
ions in a static magnetic field gradient in the microwave regime.