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arXiv:1605.07513 · Physical Review A

Probing the sign of the Hubbard interaction by two-particle quantum walks

Andrea Beggi, Luca Razzoli, Paolo Bordone, Matteo G. A. Paris

Published Jan 12, 2018• 12 citations
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Abstract

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.

DOI
10.1103/physreva.97.013610

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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.
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We investigate the quantum walk of two interacting particles of different mass in a one dimensional lattice. We show that the inter-particle interaction together with the mass imbalance exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the heavy and light particles perform independent particle quantum walks for small interaction. However, stronger interactions lead to the quantum walk of the repulsively bound pair. For a different initial states when the walkers are on different sites initially, the heavy particle performs quantum walk almost independently and the light particle shows reflected and transmitted components across the heavy particle for small interactions. After a critical interaction strength, the light particle wave function ceases to penetrate through the heavy particle. However, when the quantum walkers are initially kept at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both heavy and light particles from each other. We analyze these features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.