Real-Time Decoherence of Landau and Levitov Quasiparticles in Quantum Hall Edge Channels

Quantum Hall edge channels at integer filling factor provide a unique test bench to understand the decoherence and relaxation of single-electron excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau)- and time (Levitov)-resolved single-electron excitations at filling factor $\nu =2$. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel-type experiments to probe specific signatures of these different scenarios.

Figure 1

A single-electron excitation prepared in a coherent wave packet ${\phi }_e$ enters a finite-length interaction region. The edge channel comes out entangled with the environmental degrees of freedom. In the case of two edge channels, the second channel plays the role of the environment.

Figure 2

Excess Wigner function $\mathrm{\Delta }{W}_{\text{out}}^{(e)}(t,\omega )$ at various propagation times for a Landau quasiparticle of lifetime ${\tau }_e$ emitted at energy $\hslash {\omega }_e=10\hslash {\tau }_e^{-1}$. The horizontal dashed line at $\omega =0$ is the Fermi level. Plots correspond to increasing propagating lengths expressed in terms of times of flight: ${\tau }_s$ for the slow mode and ${\tau }_c={\tau }_s/20$ corresponds to the fast mode. The time shift $\overline{\tau }=({\tau }_c+{\tau }_s)/2$ compensates for the global drift of the excitations. Panel (a) shows the initial excess Wigner function. Panels (b) to (f) shows the excess Wigner function for increasing slow mode times of flight.

Figure 3

Excess Wigner function $\mathrm{\Delta }{W}_{\text{out}}^{(e)}(t,\omega )$ of a single electronic leviton of width ${\tau }_0$ for various propagation times; ${\tau }_s$ (respectively ${\tau }_c$) denotes the time of flight of the spin (respectively charged) mode within the interaction region, and ${\tau }_c={\tau }_s/20$ and $\overline{\tau }=({\tau }_s+{\tau }_c)/2$. Panel (a) shows the initial excess Wigner function whereas panels (b) and (c) shows the same quantity for increasing slow mode times of flight.

Figure 4

The average current $⟨i(t)⟩$ in units of $-e/{\tau }_e$ [(a) and (b)] and the excess electron distribution function $\delta f_e(\omega )$ [(c) and (d)] corresponding to $\mathrm{\Delta }{W}_{\text{out}}^{(e)}(t,\omega )$ presented on Fig. 2. The initial $⟨i(t)⟩$ and $\delta f_e(\omega )$ values appear as solid line black curves.