Repelling, binding, and oscillating of two-particle discrete-time quantum walks

Xiaoyu Sun, Qinghao Wang, Zhi-Jian Li

Siyong Jia, Delong Jia, Ziteng Song +1 more

Pablo Arnault, Benjamin Pepper, Armando Pérez

Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs) [C. Cedzich et al., Phys. Rev. Lett. 111, 160601 (2013);] this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended, initial condition, one numerically observes semiclassical oscillations, i.e., oscillations of a localized particle, for both the electric TBH and the electric DQW. More precisely, the numerical simulations strongly suggest that the semiclassical DQW Bloch oscillations correspond to two counterpropagating semiclassical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counterpropagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)].

Sayumi Takei, Akira Ishikawa, Kiyoshi Kobayashi

Yevhen Gerasimenko, Brian Tarasinski, C. W. J. Beenakker

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero modes) at boundaries or domain walls. Here we show that a topological zero mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.

Scott M. Berry, Jingbo B. Wang

We study discrete-time quantum walks on the line and on general undirected graphs with two interacting or noninteracting particles. We introduce two simple interaction schemes and show that they both lead to a diverse range of probability distributions that depend on the correlations and relative phases between the initial coin states of the two particles. We investigate the characteristics of these quantum walks and the time evolution of the entanglement between the two particles from both separable and entangled initial states. We also test the capability of two-particle discrete-time quantum walks to distinguish nonisomorphic graphs. For strongly regular graphs, we show that noninteracting discrete-time quantum walks can distinguish some but not all nonisomorphic graphs with the same family parameters. By incorporating an interaction between the two particles, all nonisomorphic strongly regular graphs tested are successfully distinguished.