Coherent wave-particle quantum walks

Salvador Godoy, Francisco Espinosa‐Magaña

With the help of quantum-scattering-theory methods and the approximation of the stationary phase, we propose a one-dimensional quantum-random-walk (QRW) model, which describes for both tunneling and scattering above the potential, the coherent diffusion of independent particles described by wave packets in a periodic one-dimensional lattice. The QRW model describes for each lattice cell the time evolution of modulating amplitudes of two opposite-moving wave packets as they are scattered by periodic potential barriers. Since the QRW model is a coherent process, interference contributions in the probabilities bring about strong departures from classical results. For many identical free particles we obtain the theoretical and graphical Bose and Fermi two-body QRW probability distribution. The result is generalized to N identical free particles and we obtain the N-body Bose and Fermi QRW probability distribution.

Jamie Smith

Tianli Feng, Yong-Sheng Zhang, Guangming Zhao +2 more

The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum walks of waves. Firstly, we show the behaviors of the quantum walks of plane wave, which are largely different from the counterparts of either the classical or the quantum walks of particles. Two situations - with and without intermediate time measurements of the walks are considered. At last, it is shown that the quantum walks of plane wave can be used to calculate the evolution of the general wave packets, e.g., Gaussian wave packet.

Timothy P. Spiller, Terrence D. Clark, Robert J. Prance +2 more

Zi-Yong Ge, Heng Fan

The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent state space has been proposed theoretically and realized experimentally. However, due to the inherent characteristics of coherent states, it is challenging to control the number of photons when we need the coherent space to be a nearly orthogonal space in practice. Here, we demonstrate that the nonorthogonality of coherent sates, on the one hand can be cancelled by multiple measurement, on the other hand, it is useful resource to characterize the nature of the system. Thus the number of photons of the system is controllable. We first present a feasible scheme to measure the wave function of quantum walks. Then we show that the expected number of photons of the coherent space is good observable to represent topological properties of the system, which reflected the advantage of coherent state space quantum walks. In addition, we propose an experimental protocol in a circuit quantum electrodynamics architecture, where a superconducting qubit is a coin while the cavity mode is used for quantum walk.