Incoherent effects in single-electron quantum optics

Ph. D. Thesis.Dynamic quantum dots as sources of single electrons open up new avenues to explore fundamental issues of solid-state physics. These types of single electron source allow for injection of electrons at energies high above the Fermi level. These high energies increase the spatial separation between bulk and injected electrons, reducing electron-electron interactions which are the dominant source of decoherence for cold electrons. Unfortunately, although these high energies reduce one source of decoherence, they introduce the potential for others to become dominant. In this thesis, we investigate two of these sources of decoherence on electrons which reduce their ability to act quantum mechanically, and explore the conditions required to mitigate these effects. First we investigate the effect of phase averaging, which is caused by the uncertainty in the injection energy of an electron. We calculate the phase contributions from beamsplitters, path lengths and the AharonovBohm phase, as well as the energy dependence of the transmission and reflection coefficients of the beamsplitters. We find that optimum conditions such that visibility can be maximised are obtained not at zero path length difference as in optics, but with an offset in the length of the interferometer arms. At the higher energies in hot-electron quantum optics, longitudinal-optical (LO)-phonon emission becomes the dominant source of decoherence. In this thesis we derive a complete quantum master equation to describe the rate of emission of LO-phonons and the behaviour of electrons undergoing this emission. The findings in this thesis are vital to the successful implementation of quantum optics-like experiments with hot electrons. These results can be used as input into both experimental architectures and dynamical simulations, and combined with previous results provide a complete quantum picture of the incoherent effects in hot electron quantum-optic