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Non-trivial pairing in the quantum walk of two-component Bose-Hubbard model

Mrinal Kanti Giri, Suman Mondal, Bhanu Pratap Das, Tapan Mishra

Published Sep 2, 2021• 0 citations
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Abstract

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.

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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.
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.
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.
Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an uniform bosonic Mott insulator at unit filling in an one dimensional graph. While the quantum walk of single particle defect shows trivial features, the case of two particles exhibits interesting phenomenon of quantum walk reversal as a function of additional onsite three-body attractive interactions. In the absence of the 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, the independent particle behavior in quantum walk appears. Interestingly, further increase in the three-body interaction leads to the re-appearance of the quantum walk associated to a pair of particles. This quantum-walk reversal or re-entrant phenomenon is studied using the real-space density evolution, Bloch oscillation as well as two-particle correlation functions.
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 ground state of one-dimensional few-atom Bose–Bose mixtures under harmonic confinement throughout the crossover from weak to strong inter-species attraction . The calculations are based on the numerically exact multi-configurational time-dependent Hartree method. For repulsive components, we detail the condition for the formation of a molecular Tonks–Girardeau gas in the regime of intermediate inter-species interactions, and the formation of a molecular condensate for stronger coupling. Beyond a critical inter-species attraction, the system collapses to an overall bound state. Different pathways emerge for unequal particle numbers and intra-species interactions. In particular, for mixtures with one attractive component, this species can be viewed as an effective potential dimple in the trap center for the other, repulsive component.
Dynamical formation of doublons or on-site repulsively bound pairs of particles on a lattice is a highly nontrivial phenomenon. In this work, we show the signatures of doublon formation in a quantum computer by simulating the continuous time quantum walk in the framework of the one-dimensional extended Fermi-Hubbard model. By considering two up-component and one down-component particles initially created at the three neighboring sites at the middle of the lattice and allowing intra- (inter-)component nearest-neighbor (on-site) interactions, we show the formation of a stable on-site doublon in the quantum walk. The probability of such doublon formation is more (less) if the hopping strength of the down particle is weaker (stronger) compared to the up particle. On the contrary, for an initial doublon along with a free up particle, the stability of the doublon is more prominent than the doublon dissociation in the dynamics irrespective of the hopping asymmetry between the two components. We first numerically obtain the signatures of the stable doublon formation in the dynamics and then observe them using noisy intermediate-scale quantum (NISQ) devices.