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JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING

Quantum walks of two identical particles in one-dimensional lattices

Yunbo Zhang, Limin Wang, Li Wang

Published Jan 1, 2015• 0 citations
Publisher
DOI
10.3724/sp.j.1249.2015.01001

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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.
We address the discrimination between attractive and repulsive interaction in systems made of two identical bosons propagating on a one-dimensional lattice, and suggest a probing scheme exploiting the dynamical properties of the corresponding two-particle quantum walks. In particular, we show that the sign of the interaction leaves a clear signature in the dynamics of the two walkers, which is governed by the Hubbard model, and in their quantum correlations, thus permitting one to discriminate between the two cases. We also prove that these features are strictly connected to the band structure of the Hubbard Hamiltonian.