Quantum tomography of an electron

Sizhuo Yu, Jean‐Michel Gillet

Pascal Degiovanni, Charles Grenier, Erwann Bocquillon +4 more

Giacomo Mauro D’Ariano, Matteo G. A. Paris, Massimiliano Federico Sacchi

This is the draft version of a review paper which is going to appear in Advances in Imaging and Electron Physics

Amir H. Tavabi, Alessio D'Errico, Paolo Rosi +10 more

The physical properties of a quantum system, whether pure or mixed, are described fully by its density matrix. Recovery of the density matrix through projective measurements -- referred to as quantum state tomography -- is a cornerstone of quantum optics and metrology. The implementation of this approach in transmission electron microscopy, in particular for the characterisation of an electron beam after inelastic scattering, has remained a longstanding challenge as a result of the complexity of scanning high-dimensional phase spaces, with the number of required measurements growing quadratically with space dimensionality. Here, we introduce a simplified approach by restricting tomography to the electron orbital angular momentum (OAM) subspace. By using an electron optical device known as an OAM sorter, we discretise the phase space into a finite set of measurable states, thus significantly reducing the experimental and computational burden. The resulting measurements suffice to probe essential features of inelastic scattering. We demonstrate the technique by studying the inelastic scattering of a structured electron probe exciting volume plasmons in a carbon film. The combined use of a structured beams and OAM-resolved quantum tomography reveals symmetry-breaking effects and offers insight into the coherence and evolution of the scattered quantum states. Analysis of the diagonalised density matrices further reveals the nature of the induced state transitions, demonstrating the power of the approach for quantum tomography of electron scattering.

Charles Grenier, RÉMY HERVÉ, Erwann Bocquillon +5 more

We propose a quantum tomography protocol to measure single-electron coherence in quantum Hall edge channels, and therefore access for the first time the wavefunction of single-electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single-electron decoherence and would provide a quantitative tool for analyzing single- to few-electron sources. We show how this protocol could be implemented using ultrahigh-sensitivity noise measurement schemes.

Jeff S. Lundeen, Alejandro Feito, Hendrik B. Coldenstrodt-Ronge +6 more