Path integral treatment of the Hanbury Brown-Twiss effect for pulsed electron matter wave

Hanbury Brown-Twiss (HBT) anticorrelations for a continuous beam of free electrons were claimed to be observed in 2002 [1]. The recent advent of femtosecond electron pulses has motivated us to pursue the HBT effect for pulsed electron beams with unprecedentedly higher phase space degeneracies. To provide a rigorous theoretical description of this problem, the quantum decoherence of a two-electron pulsed beam upon entanglement with a two-state emitter will be considered first. The two-particle state will then be propagated in space and time toward a detector using Feynman's path integral formalism. Effects of the partial temporal coherence in this system will also be taken into account which is an improvement built on an earlier work published in our group [2]. The method can ultimately be extended to include the Coulomb repulsion along with the Pauli exclusion principle. [1] H. Kiesel, A. Renz, and F. Hasselbach, Nature \textbf{418}, 392 (2002). [2] P. Lougovski, and H. Batelaan, Phys. Rev. A \textbf{84}, 023417 (2011).