This thesis deals with dephasing, i.e. loss of coherence and properties due to external parameters, of a electronic Mach-Zehnder interferometer, and how these properties are changed by quantum noise. Thus the work is devided into two parts. The first chapter, chapter 5, shows experiments that display the transport properties of an electronic Mach-Zehnder interferometer itself, e.g. its behavior as a function of QPC transmission. The (almost) exponential dephasing with temperature and interferometer size L reveals a characteristic thermal energy "kB T0" that is proportional to the coherence length "l_phi", which can be estimated to be ~10 µm in the samples measured for this thesis. Another important property is the dephasing as a function of a dc bias voltage. Here, three different regimes could be identified. One is the case for filling factors close to 1, where only one edge channel is present throughout the sample. In this regime a lobe structure with single side lobes, next to a high central one, is observed, that is well described by the phenomenological model including Gaussian noise. This introduces an energy "epsilon0" describing the Gaussian decay. Possible microscopic explanations are intra-channel interactions along the interferometer arms of the collective modes of the Luttinger liquid. The other regimes appear close to filling factor two. When only one of the two incoming edge channels (the outer, which is used for the interference) is biased by "V_dc" a lobe structure with multiple side lobes of equal widths arises. Two energy scales can be extracted from this behavior. One is the period of the oscillations vs. "V_dc", "epsilon_L", the second is an energy that describes the decaying envelope, "epsilon_0". This overall dephasing with bias can be equally well approximated with an exponential and a Gaussian envelope and both give similar energies "epsilon_0". These two energy scales, "epsilon_L" and "epsilon_0", are approximately equal. The third regime is when both edge channels at filling factor two are biased with "V_dc". Here, depending on the transmission of QPC1, either an increase of visibility at low bias voltages is observed, accompanied with a slow decay at large bias voltages, or a lobe structure with a central lobe of increased width is seen. The increase of visibility with bias could be explained by expanding a phenomenological model for single side lobes, with a term considering a second biased, capacitive coupled edge channel.
The coherence of the Mach-Zehnder interferometer is governed by the filling factor in the range from 2 to 1. The zero bias visibility is zero for larger and smaller filling factors, with a smooth evolution in between, exhibiting a maximum at filling factor 1.5. All the characteristic energy scales, show the same characteristic, minimum values close to integer filling factors and a maximum at 1.5. And energy scales of the lobe structure, "epsilon_0" and "epsilon_L", are approximately equal and the characteristic thermal energy is proportional to this energy with a factor ~2pi².
At the end of this chapter it is shown, that the versatile coherence properties are best explained with the theory by Levkivskyi et al., where the long-range Coulomb interaction between co-propagating edge channels leads to the charge and dipole mode u and v. Especially, the lobe structure with multiple side lobes close to filling factor two originates from the dynamical phase factors of the plasmon modes and their oscillation of phase information between adjacent channels. Additionally the proportionallity to "kB T0" with the factor 2pi² is predicted in this theory, and its connection to the coherence length "l_phi". Furthermore, the expected evolution of the plasmon modes with filling factor fits with the expacted characteristic of the energy scales.
In the second chapter, chapter 6, of the experimental part, a novel non-equilibrium phase transition, which is induced by the non-Gaussian noise of a QPC and was predicted by Levkivskyi et al., is demonstrated. In this experiment the Mach-Zehnder interferometer is used as a phase sensitive detector to the noise produced by an upstream placed QPC0. For this purpose two samples are investigated. The order parameter of this phase transition is proportional to the normalized inverse of the lobe periodicity. It is shown, that it stays almost constantly one for t0>0.5, drops rapidly to zero at t0~0.5 and is zero below. This represents a transition, from a lobe pattern with multiple side lobes, i.e. a finite periodicity, to one with only a single side lobe, i.e. an infinite period. A second attribute of the transition that is verified is an almost diverging dephasing for large bias at t0=0.5. Additionally, lobe structures are directly compared to numerical calculations of this model with the non-Gaussian noise, i.e. all current cumulants, and Gaussian noise, where higher order cumulants are truncated. These numerical calculations are provided by Ivan Levkivskyi in the group of Eugene Sukhorukov in Geneva. One sample shows almost perfect overall agreement to the theory. The second sample exhibits only qualitative aggreement, but the discrepancies are well explained and can be mainly addressed to strong nonlinearities of the differential conductance of the QPC0.
Summing up, dephasing in a Mach-Zehnder interferometer is investigated in detail, especially at finite bias voltages. An explanation for a majority of the observed effects is given either with phenomenological models, or in terms of the theory of plasmonic excitations of co-propagating channels of Luttinger liquid, coupled by long-range Coulomb interaction. Furthermore, a formerly predicted noise-induced phase transition is demonstrated
