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arXiv:2001.08527 · Physical Review A

Quantum walks of interacting Mott-insulator defects with three-body interactions

Suman Mondal, Tapan Mishra

Published May 28, 2020• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.101.052341

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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.
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.
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.
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.
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.
Recent experiments on quantum walks (QWs) demonstrated a full control over the statistics-dependent walks of single particles and two particles in one-dimensional lattices. However, little is known about the general characterization of QWs at the many-body level. Here, we rigorously study QWs, Bloch oscillations, and the quantum Fisher information for three indistinguishable bosons and fermions in one-dimensional lattices using a time-evolving block decimation algorithm and many-body perturbation theory. We show that such strongly correlated QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states and of two- and three-body bound states but also allow a quantum enhanced precision measurement of the gravitational force. In contrast to the QWs of the fermions, the QWs of three bosons exhibit strongly correlated Bloch oscillations, which present a surprising time scaling t^{3} of the Fisher information below a characteristic time t_{0} and saturate to the fundamental limit of t^{2} for t>t_{0}.