Disorder-Induced Dephasing in Backscattering-Free Quantum Transport

We analyze the disorder-perturbed transport of quantum states in the absence of backscattering. This comprises, for instance, the propagation of edge-mode wave packets in topological insulators, or the propagation of photons in inhomogeneous media. We quantify the disorder-induced dephasing, which we show to be bound. Moreover, we identify a gap condition to remain in the backscattering-free regime despite disorder-induced momentum broadening. Our analysis comprises the full disorder-averaged quantum state, on the level of both populations and coherences, appreciating states as potential carriers of quantum information. The well-definedness of states is guaranteed by our treatment of the nonequilibrium dynamics with Lindblad master equations.

Figure 1

Disorder-induced dephasing in backscattering-free propagation. (a) Quasiclassical representation of skipping orbits in a quantum Hall sample in the presence of a strong magnetic field. Because of the directional Lorentz-force bending of the orbits, obstacles or impurities cannot reverse the direction of motion. (b) Generic band model of a topological insulator. Edge modes exist in the bulk band gap of width $\mathrm{\Delta }$. To propagate backscattering-free, edge mode wave packets must remain confined in the gap region. (c) and (d) Decoherence cone describing the spatiotemporal dephasing behavior of the disorder-averaged quantum state [cf. Eq. (3)]. Coherences within the cone remain unaffected, outside they decay. Values in (c) increase from 0 (violet).

Figure 2

(a) Impact of disorder on the functioning of a beam splitter. Optimal operation, based on constructive and destructive interference in the output ports, presupposes identical input states $|\psi ⟩$ and $|{\psi }^{\prime }⟩$. If, due to different disorder histories of the state components, the wave packets differ, interference in the output ports is corrupted, resulting in detrimental leakage between the ports. (b) Purity evolution in a closed loop of circumference $L=17\ell$. Shown is the time evolution of the purity $r(t)$ for a Gaussian wave packet with (i) $\sigma =\ell$, (ii) $\sigma =2\ell$, and (iii) $\sigma =10\ell /3$. We compare the numerically exact evolution of the state, averaged over 500 disorder realizations (black dots), the prediction of the solution (3) for periodic correlations (purple dashed curves), and the approximation (5) (red dotted lines). While in all cases the purity fully recovers when the state completes a full cycle, the intermediate purity loss scales with the wave packet extension. In case (iii), the purity decay is reversed before it reaches its saturation as predicted by Eq. (5).