Erzeugung verschränkter Zustände im Zwei-Moden-Jaynes-Cummings-Modell

The basic model in Quantum Optics describing the interaction of radiation
with matter is the one-mode Jaynes-Cummings Model (JCM). In this thesis
a compact solution is presented for a two-mode extension of the JCM,
where the radiation is treated by two quantized field-modes of a resonator
interacting with two quantized levels of an atom or molecule.
When radiation and matter are described quantum mechanically new
unexpected non-classical e®ects occur. In particular, the phenomenon of entanglement
can be investigated. Entanglement is at the heart of quantum
mechanics and more recently became a basic building block of quantum cryptographic
devices as well as for quantum computers. Therefore the algebraic
formalism developed is applied to show how entanglement can be generated
in the framework of the two-mode JCM.
First, three generation schemes are presented to entangle the two quantized
field-modes of a resonator. It is shown that entanglement may be
generated starting from an initial field and an atom in one defined state in a
single step. It is also shown that entanglement may be built up in the case
of an empty cavity and excited atoms whose final states are detected, as well
as in the case when the final states of the initially excited atoms are not detected.
To investigate the time evolution of the two field-modes, probability
distributions are calculated analytically.
It is also shown that an atom and the two field-modes can form an entangled
state. This phenomenon already known from the one-mode JCM is
further investigated for the two-mode case. Finally, atomic observables like
the inversion and polarization are calculated analytically and discussed in
detail.