Controlled information transfer in continuous-time chiral quantum walks

Abstract

In this paper we investigate properties of continuous time chiral quantum walks, which possess complex valued edge weights in the underlying graph structure, together with an initial Gaussian wavefunction spread over a number of vertices. We demonstrate that, for certain graph topology and phase matching conditions, we are able to direct the flow of probability amplitudes in a specific direction inside the graph network. We design a quantum walk graph analogue of an optical circulator which is a combination of a cycle and semi-infinite chain graphs. Excitations input into the circulator from a semi-infinite chain are routed in a directionally biased fashion to output to a different semi-infinite chain. We examine in detail a two port circulator graph which spatially separates excitations flowing back in forth between the two semi-finite chains to directionally occupy the top or bottom half of the cycle portion of the circulator. This setup can be used, for example, to detect non-Markovian processes, which leads to information and energy back-flow from the bath back into the system.

Controlled transport in chiral quantum walks on graphs

“…The deformation is absent at p = k 0 = −π/2, where the second derivative ϵ ′ ′ = 0. This is precisely the physical reason for the high fidelity of wave package transport numerically studied in [21].…”

“…In the absence of time-reversal symmetry (θ nm ̸ = 0, π), a walker can move in a preferred direction, while its movement in other directions is suppressed, which makes the transport time-asymmetric or chiral. We first consider the chiral quantum walk on a chain which was studied in [21]. By choosing phases that scale linearly with the coordinate of sites, it was showed numerically that a directed transport, instead of expansion or asymmetric transport, of a Gaussian wave package with initial zero momentum can be achieved.…”

“…Here, we give an analytical explanation of the counter-intuitive phenomenon. The adjacency matrix of chain (matrix representation of the Hamiltonian in Wannier basis) can be written as [21]…”

“…The Y-junction graph, in which the phases on the edge-weights cannot be gauged away as in section 2 due to the loop nature, can bring novel phenomena in quantum walks such as directed currents [38], non-reciprocal transmission [35], and quantum transport enhancement [39]. It was paid close attention recently both in theories [16,21,27,39] and experiments [36,[40][41][42][43]. The Y-junction graph can be realized in experiments by high-dimensional photonic quantum states, multiple concatenated interferometers, or dimension-dependent losses [37].…”

“…Consequently, from ( 23) we obtain n 1 = |(e i•2π/3 + e i•0 + e −i•2π/3 )/3| 2 = 0, which means that the superposition leads to complete destruction of the reflected wave package on the first chain. (b) After one scattering the phases of the decomposed wave functions varies differently on each chain according to (21), and they compose a wave function that locates at chain-2 only. (c) Similarly, after two scatterings, the wave package which is the superposition of the three wave packages, locates at chain-3 only.…”