Single electron quantum tomography in quantum Hall edge channels

Abstract : Electron quantum optics aims at the controlled manipulation and measurement of the quantum state of a single to few electrons in metallic nanostructures comparable to recent achievements with microwave photons, light or cold atoms. Mach-Zenhder interference experiments in integer quantum Hall edge channels as well as the demonstration of an on-demand single electron source have risen the hope for electron quantum optics experiments in ballistic conductors. However the wavefunction of a coherent single electron excitation has never been imaged. Here, we propose a quantum tomography protocol to measure single electron coherence in quantum Hall edge channels analogous to homodyne tomography in quantum optics. Single electron quantum tomography would be a major step in electron quantum optics with applications ranging from characterization of single to few electron sources to quantitative studies of single electron decoherence in nanostructures. We discuss how this proposal could be implemented using recently developed ultrahigh sensitivity noise measurement schemes.