Abstract

We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the slow and fast particles perform independent particle quantum walks when the interaction between them is weak. However, stronger inter-particle interactions result in quantum walks by the repulsively bound pair formed between the two particles. For different initial states when the walkers are on different sites initially, the quantum walk performed by the slow particle is almost independent of that of the fast particle, which exhibits reflected and transmitted components across the particle with large hopping strength for weak interactions. Beyond a critical value of the interaction strength, the wave function of the fast particle ceases to penetrate through the slow particle signalling a spatial phase separation. However, when the two particles are initially at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both of them from each other. We analyze the above mentioned features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.

Highlights

  • We investigate the two-component quantum walk in one-dimensional lattice

  • We have studied the quantum walk (QW) of a two-component system in the presence of interaction and hopping imbalance in a one-dimensional lattice

  • By considering different initial states depending on the positions of the particles (↑ and ↓ where the ↑ particle has higher hopping strength), we have analyzed the combined effect of hopping imbalance and inter-component interaction on the two particle QW

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Summary

Introduction

We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. We study the effect of hopping imbalance and interaction on the QW of two particles initially located at two different sites.

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