Untersuchung von Photonenzahlzustaenden mit dem Ein-Atom-Maser

The quantum mechanical description of the radiation field is based on field states that are characterized by the number of quanta of the radiation field, called photons. These states called photon number states or Fock states consist of a fixed, integer number of photons. They are eigenstates of the Hamiltonian of the radiation field and therefore of fundamental importance to the quantum theory of the electromagnetic field. Photon number states are those states of the electromagnetic field that can be considered to be maximally distant from classical field states. They show extreme sub-Poissonian statistics and vanishing intensity noise. Thus due to the uncertainty relation their phase is completely undefined. These properties are called "intensity squeezing". Since the foundation of the theory of quantum electrodynamics, photon number states have been used in many theories as base states of the electromagnetic field. Yet, so far there have been experimental difficulties in the preparation and detection of these states that could not be overcome. In consequence for a long time it has been an unachieved goal of experimental quantum optics to produce, maintain and detect such states. In this thesis the first experimental production and the unambiguous measurement of photon number states of an extremely long lived resonator field are described. Three different methods are discussed, all of them using the one-atom-maser apparatus, which examines the interaction of single atoms of a weak thermal atomic beam with a single mode of a microwave resonator with a quality factor of 4 discussed in this thesis, shows how such a deterministic source for single photons can be realized in a pulsed one-atom-maser experiment making use of the dynamics of trapping states. Following the detailed description of a theoretical model, a first experimental realization of the source is shown. Here we achieve a creation probability of at least 83% for the one-photon Fock state. In addition in this mode the maser can be considered as a source for single atoms in a certain state. An extension of the optics and laser system of the one-atom-maser that is currently under construction will allow for an even higher yield of one-photon Fock states and also for the deterministic production of higher order Fock states. This will allow for many new interesting experiments using the described methods