Abstract
We consider two identical bosons propagating on a one-dimensional lattice and address the prob- lem of discriminating whether their mutual on-site interaction is attractive or repulsive. We suggest a probing scheme based on the properties of the corresponding two-particle quantum walks, and show that the sign of the interaction introduces specific and detectable features in the dynamics of quantum correlations, thus permitting to discriminate between the two cases. We also discuss how these features are connected to the band-structure of the Hubbard Hamiltonian, and prove that discrimination may be obtained only when the two walkers are initially prepared in a superposition of localized states.
Highlights
The Hubbard model (HM) [1,2,3] well describes, in simple and general terms, the physics of several systems of correlated particles, either fermions or bosons [4], e.g., Mott insulators, ultracold atomic lattices [5,6,7,8], spin chains [9,10], and nonlinear waveguides [11,12,13,14,15]
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
We address here the discrimination between attractive and repulsive interaction for two identical bosons propagating on a one-dimensional lattice according to the Hubbard model
Summary
The Hubbard model (HM) [1,2,3] well describes, in simple and general terms, the physics of several systems of correlated particles, either fermions or bosons [4], e.g., Mott insulators, ultracold atomic lattices [5,6,7,8], spin chains [9,10], and nonlinear waveguides [11,12,13,14,15]. Among the different criteria that have been proposed, the so-called entanglement of particles [52] is one of the most promising, due to its simple computability, and to the fact that it should be physically measurable in many experimental scenarios [53] It has been recently employed for estimating quantum correlations in spin chains [63,64]—where it is able to detect quantum phase transitions—and in model systems of QWs described by the Hubbard Hamiltonian [28,42,65]. VI closes the paper with some concluding remarks and Appendix A presents some further discussions about the symmetries of the system, in order to better appreciate the results presented in the body of the paper
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