Relaxation of an electron wave packet at the quantum Hall edge at filling factor ν=2

We address the recent experiment (S. Tewari et al., Phys. Rev. B 93, 035420 (2016)) where the suppression of phase coherence of a single-electron wave packet created at the edge of a quantum Hall (QH) system at filling factor 2 has been investigated with the help of an electronic Mach-Zehnder (MZ) interferometer. The authors of the experiment have observed an unexpected behavior of phase coherence that saturates at high energies instead of vanishing, presumably suggesting the relaxation of a wave packet to the ground state before it arrives to the MZ interferometer. Here, we theoretically investigate this situation using the model of edge states [I.P. Levkivskyi and E. V. Sukhorukov, Phys. Rev. B 78, 045322 (2008)], which accounts for the strong Coulomb interaction between the two electron channels at the edge of a QH system. We conclude that the observed phenomenon cannot be explained within this model for the reason that under an assumption of linearity of the electron spectrum at low energies, the system remains integrable in terms of the collective charge excitations and therefore full relaxation to the ground state is not possible, despite strong interactions. As a result, the degree of the phase coherence decreases with the energy of the initial state in a power-law manner. Since this does not happen in the experiment, a different physical phenomenon may take place at the edge of a QH state, which deserves further investigation. We support our findings by calculating the energy distribution and the Wigner function of the outgoing nonequilibrium state of the single-electron wave packet.