Quantum dynamics of low dimensional interacting systems using the continuous-time quantum walk

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The quantum walk (QW) is the quantum analog of the classical random walk where an initial state undergoes reversible, unitary time evolution leading to a dynamical evolution of the quantum states. The study of QW has attracted a great deal of attention in recent years, not only in the context of studying the dynamical properties of quantum systems but also due to its possible application in quantum technologies. Numerous studies have been performed theoretically and experimentally to investigate the QW of single and two interacting particles using various systems. In this thesis, we theoretically study the QW of interacting particles in the framework of the two-component Bose-Hubbard model in one-dimensional lattices. In the first part of the thesis, we explore the QW of two-component hardcore bosons / spinless fermions with hopping imbalance. We show that the hopping imbalance and interaction play an essential role in exhibiting exciting phenomena for different initial states, such as the formation of repulsively bound pairs, reflection and transmission of the wavefunction, etc . Further, we study the QW of interacting two-component bosons with hopping imbalance. In this case, we show the fascinating phenomenon of onsite bound pair formation of two different species which start their QW from the nearest neighbour sites. We also predict the existence of non-trivial threeparticle bound state and nearest neighbour pairs. In the final part of the thesis, we study the QW of interacting bosons in a Harper-Hofstadter ladder. We explore the chiral dynamics in the single- and two-particleQWby considering uniform and staggered flux threading the ladder. We show that the uniform flux facilitates a chiral motion which disappears in the presence of the staggered flux. On the other hand, we find that the staggered flux significantly affects the spreading of the particle’s wavefunction both for single and two-particle QW. We further analyse the effect of flux on the bound state formation. These studies are carried out using the exact diagonalization and the timeevolving block decimation methods.
Supervisor: Mishra, Tapan