Two component quantum walk in one-dimensional lattice with hopping imbalance

TL;DR

This paper explores how inter-component interactions and hopping imbalance influence the dynamics of a two-component quantum walk in a one-dimensional lattice, revealing phenomena like bound states, phase separation, and reflection effects.

Contribution

It introduces a detailed analysis of two-component quantum walks with hopping imbalance, highlighting the effects of interaction strength and initial states on walk dynamics.

Findings

Weak interactions allow independent quantum walks of particles.

Strong interactions lead to bound pair quantum walks.

Interaction causes spatial phase separation and reflection phenomena.

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.