Disorder-dressed quantum evolution

Helical transport in coupled resonator waveguides

“…First, let us complement our numerical investigation by deriving an effective temporal evolution equation for the disorder-averaged field state, which is valid in the limit of weak disorder [43,55]. We begin with a recap of the general line of argument.…”

“…We remark that Eq. ( 15) can be manifestly formulated in Lindblad form [43,55]. Moreover, we stress that the time integral indicates the non-Markovian, i.e., time-nonlocal nature of the disorder impact, and thus cannot be simplified, e.g., by taking the limit t → ∞, without losing essential aspects of the disorder-induced evolution.…”

“…As an independent assessment of the disorder-induced backscattering of wavepackets, we now consider the purity evolution of the disorder-averaged state. The purity, which is defined as Tr[ρ 2 ] and measures the "mixedness" of a quantum state, indicates, when applied to the disorder-averaged state, to what extend states evolving under individual disorder realizations deviate from the unperturbed (disorder-free) evolving state [43]. In particular, in the case of backscattering-free, dispersionless propagation, as approximated by our master equation (22), it has been shown [42] that the purity evolves, due to unavoidable disorder-induced dephasing, into a characteristic plateau value given by…”

“…First, we calculate the scattering length under the Born approximation, obtaining an order of magnitude enhancement of the Anderson localization length around a critical energy due the spin-momentum locking. Second, we study the propagation dynamics, employing a recently-developed master equation framework [41][42][43] to quantify the preservation of phase information and spatial coherence of wavepackets propagating along the waveguide by calculating the purity of field, which provides the information about how much an evolving wavepacket deviates from the disorder-free state. We conclude that one-dimensional helical channels are promising way to achieve compact, disorder-resistant integrated photonic waveguides.…”