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Static properties of two connected Bose-Hubbard rings

Albert Escrivà, Bruno Juliá-Díaz, M. Guilleumas

Published Jul 10, 2018• 0 citations
OpenAlex

Abstract

We consider two coupled Bose-Hubbard rings populated with ultra-cold bosons with repulsive interactions. The atoms can either tunnel between the sites of the same ring, with a given inter-ring coupling, or between the sites of different rings coupled by an intra-ring coupling. By solving the corresponding Bose-Hubbard Hamiltonian we obtain the many-body ground state for different values of the interaction and tunneling strengths. We characterize the static many-body properties of the ground state by means of coherence, correlations and entanglement.

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We consider two coupled Bose-Hubbard rings populated with ultra-cold bosons with repulsive interactions. The atoms can either tunnel between the sites of the same ring, with a given inter-ring coupling, or between the sites of different rings coupled by an intra-ring coupling. By solving the corresponding Bose-Hubbard Hamiltonian we obtain the many-body ground state for different values of the interaction and tunneling strengths. We characterize the static many-body properties of the ground state by means of coherence, correlations and entanglement.
Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow for a viable implementation of cold-atom based devices and qubit systems. In this work, we exhaustively investigate the ground state properties and the low-lying energy spectrum of two linearly coupled Bose-Hubbard rings. We show that the competition among interactions, intra- and inter-ring hopping processes gives place to a rather rich physical scenario, where Mott-like states and (different kinds of) superfluid-like states emerge. The latter ones depend also on the (in)commensurate filling of the atoms. Our analysis, carried out within a simple analytical framework and by means of the exact numerical diagonalization of the system Hamiltonian, provides one with a rather complete characterization of the static properties of the two-ring ladder, including, but not limited to, coherence, fragmentation, correlations, and entanglement. We complement our investigation by studying how these indicators depend on the commensurability of the total number of bosons with respect to the total number of sites and show that the two stacked rings are always entangled for an odd number of atoms.
Abstract Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow for a viable implementation of cold-atom based devices and qubit systems. In this work, we exhaustively investigate the ground state properties and the low-lying energy spectrum of two linearly coupled Bose–Hubbard rings. We show that the competition among interactions, intra- and inter-ring hopping processes gives place to a rather rich physical scenario, where Mott-like states and (different kinds of) superfluid-like states emerge. The latter ones depend also on the (in)commensurate filling of the atoms. Our analysis, carried out within a simple analytical framework and by means of the exact numerical diagonalization of the system Hamiltonian, provides one with a rather complete characterization of the static properties of the two-ring ladder, including, but not limited to, coherence, fragmentation, correlations, and entanglement. We complement our investigation by studying how these indicators depend on the commensurability of the total number of bosons with respect to the total number of sites and show that the two stacked rings are always entangled for an odd number of atoms.
The tunneling phenomena of cold atoms in double-well with different interaction (U) and tunnel coupling (J) were studied. Experiments cannot be interpreted completely by a two-site Bose-Hubbard model. Thus, a new model was introduced, in which the ground state and the first excited state of the double-well were used as state bases. The expression of Hamiltonian was derived under the new model, which explains the reason why the parameter isnot consistent with the experiment from a two-site Bose-Hubbard model. Furthermore, we figured out the fluctuation of entanglement degree of the atoms in the double-well, and directly described the whole process of tunneling with the population of particles in the three states.
We investigate a three-site ring system with a small number of quantum degenerate bosons and fermions. By means of the exact diagonalization of the Bose-Fermi-Hubbard Hamiltonian, we show that the symmetry of the ground state configuration is a function of both the boson-boson and the inter-species interaction in the system. The phase diagram of the system, constructed by computing the exact two-body spatial correlations, reveals nontrivial insulating phases that exist even in the strong bosonic tunneling limit and for incommensurate filling of bosons. These insulating phases are due to the inter-species interactions in the system and are not necessarily accompanied by the suppression of the particle number fluctuations.
We study the system of multibody interacting bosons on a two-dimensional optical lattice and analyze the formation of bound bosonic pairs in the context of the Bose-Hubbard model. Assuming a repulsive two-body interaction we obtain the signatures of pair formation in the regions between the Mott insulator lobes of the phase diagram for different choices of higher-order local interactions. Considering the most general Bose-Hubbard model involving local multibody interactions we investigate the ground state properties utilizing the cluster mean-field theory approach and further confirm the results by means of sophisticated infinite projected entangled pair states calculations. By using various order parameters, we show that the choice of higher-order interaction can lead to pair superfluid phase in the system between two different Mott lobes. We also analyze the effect of temperature and density-dependent tunneling to establish the stability of the PSF phase.
The quantum dynamics of population-balanced fractional vortices and population-imbalanced vortices in an effective two-state bosonic system, made of two coupled discrete circuits with few sites, is addressed within the Bose-Hubbard model. We show that, for low on-site interaction, the tunneling of quantized vortices between the rings performs a coherent, oscillating dynamics connecting current states with chiral symmetry. The vortex-flux transfer dually follows the usual sinusoidal particle current of the Josephson effect, in good agreement with a mean-field approximation. Within such a regime, the switch of persistent currents in the rings resembles flux-qubit features and is feasible for experimental realization. On the contrary, strong interatomic interactions suppress the chiral current and lead the system into fragmented condensation.