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.
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.
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.
Nearest neighbor bosons possessing only on-site interactions do not form on-site bound pairs in their quantum walk due to fermionization. We obtain signatures of nontrivial on-site pairing in the quantum walk of strongly interacting two component bosons in a one dimensional lattice. By considering an initial state with particles from different components located at the nearest-neighbor sites in the central region of the lattice, we show that in the dynamical evolution of the system, competing intra- and intercomponent on-site repulsion leads to the formation of on-site intercomponent bound states. We find that when the total number of particles is three, an intercomponent pair is favored in the limit of equal intra- and intercomponent interaction strengths. However, when two bosons from each species are considered, intercomponent pairs and trimer are favored depending on the ratios of the intra- and intercomponent interactions. In both cases, we find that the quantum walks exhibit a reentrant behavior as a function of intercomponent interaction.
Quantum walks of interacting particles may display nontrivial features due to the interplay between the statistical nature and the many-body interactions associated with them. We analyze the quantum walk of interacting defects on top of a uniform bosonic Mott insulator at unit filling in a one-dimensional graph. While the quantum walk of a single-particle defect shows trivial features, the case of two particles exhibits the interesting phenomenon of quantum walk reversal as a function of additional on-site three-body attractive interactions. In the absence of a three-body interaction a quantum walk of pairs of particles is obtained, and as the strength of the three-body interaction becomes more and more attractive, independent-particle behavior appears in the quantum walk. Interestingly, further increase in the three-body interaction leads to the reappearance of the quantum walk associated with a pair of particles. This quantum walk reversal phenomenon is studied using the real-space density evolution, Bloch oscillation, and two-particle correlation functions.
We investigate the quantum walk in a system of two-component bosons in one dimensional lattice. By considering an initial state with particles from different components residing in the nearest-nieghbour sites, we show that the competing intra- and inter-component repulsion leads to the formation of onsite inter-component bound states in the dynamical evolution - a phenomenon which is not favourable in the case of indistinguishable bosons. We obtain that when the total number of particles is three, an inter-component pair is favoured for equal inter- and intra-component interaction strengths. However, when two atoms from each species are considered, apart from the intra-component pairs, the system tends to favour a three particle bound state when the strength of inter-component interaction is half of the intra-component one. Moreover, in the regime of equal interactions both inter- and intra-component pairs are formed. In all the cases, we find that the quantum walks exhibit a re-entrant behaviour as a function of inter-species interaction.
Abstract We study the quantum walk on the off-diagonal Aubry-André-Harper (AAH) lattice with periodic modulation using a digital quantum computer. We investigate various initial states at the single-particle level, considering different hopping modulation strengths and phase factors. Initiating the quantum walk with a particle at the lattice edge reveals the robustness of the edge state, attributed to the topological nature of the AAH model, and displays the influence of the phase factor on this edge state. On the other hand, when the quantum walk begins with a particle in the lattice bulk, we observe a repulsion of the bulk walker from the edge, especially under strong hopping modulation. Furthermore, we extend our investigation to the quantum walk of two particles with nearest-neighbour (NN) interaction. We show the repulsion effect in the quantum walk when two walkers originate from the edge and bulk of the lattice due to the interaction. Additionally, when two particles are positioned at nearest-neighbor sites with strong hopping modulation, they unexpectedly form a local bound state at very small interaction strength, highlighting the unique interplay between hopping modulation and interaction in our quantum walk setup. We analyze these phenomena by examining physical quantities such as density evolution, two-particle correlation, and participation entropy, and discuss their potential applications in quantum technologies.
The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range inter-particle interaction is studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site. Using exact diagonalization method, the continuous-time quantum walk is directly simulated. The numerical simulations show that the range of interaction (long-range or short-range), the strength of the inter-particle interaction, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk. Under the effect of strong long-range interaction, the particles initially located on the non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located on the neighboring lattice sites can exhibit co-walking. After introducing the isolated defect into the system with strong interaction, two particles residing on the same side of the isolated defect keep co-walking, while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect, the two particles keep stationary or co-walking near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.