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arXiv:1004.4770 · New Journal of Physics

Fast transfer and efficient coherent separation of a bound cluster in the extended Hubbard model

L Jin, Z Song

Published Jun 9, 2011• 8 citations
arXivHTMLPDF

Abstract

We study the formation and dynamics of the bound pair (BP) in a strongly correlated extended Hubbard model for both the Bose and the Fermi system. The bound triple (BT) for the Bose system is also investigated. We find that the bandwidths of the BP and BT gain significantly when the on-site and nearest-neighbor interaction strengths reach the corresponding resonant points. This allows fast transfer and efficient coherent separation of the BP and BT. The exact result shows that the success probability of the coherent separation is unity in the optimal system. In the Fermi system, this finding can be applied to create distant entanglement without the need for temporal control and the measurement process.

DOI
10.1088/1367-2630/13/6/063009

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We study the formation and dynamics of the bound pair (BP) in a strongly correlated extended Hubbard model for both the Bose and the Fermi system. The bound triple (BT) for the Bose system is also investigated. We find that the bandwidths of the BP and BT gain significantly when the on-site and nearest-neighbor interaction strengths reach the corresponding resonant points. This allows fast transfer and efficient coherent separation of the BP and BT. The exact result shows that the success probability of the coherent separation is unity in the optimal system. In the Fermi system, this finding can be applied to create distant entanglement without the need for temporal control and the measurement process.
In the present work we extend the concept of coherent shift for the extended Bose-Hubbard model and Fermi-Hubbard model. We present two types of local bound pairs (BPs) for the Bose system and one type for the Fermi system. It is shown exactly that the perfect coherent shift can be achieved in such models in the large binding-energy limit. We find that for a Bose on-site BP, the perfect coherent shift condition depends on the nearest-neighbor interaction strength and the momentum of the incident single-particle wave packet, while for the other two types of BPs, it is independent of the initial state in the proposed systems. Numerical simulation of the scattering process between a single particle and a BP in a finite-size system is conducted and the computational results are shown to confirm the analytical investigation.
Based on the exact results obtained by Bethe ansatz, we demonstrate the existence of stable bound-pair (BP) wave packet in Bose-Hubbard model with arbitrary on-site interaction UUU. In large-UUU regime, it is found that an incoming single-particle can coherently pass through a BP wave packet and leave a coherent shift in the position of it. This suggests a simple scheme for constructing a BP charge qubit to realize a quantum switch, which is capable of controlling the coherent transport of one and only one photon in a one-dimensional waveguide.
We investigate the dynamics of bound pairs in an extended Hubbard model at resonance. We show that a single fermion and a singlet bound pair possess identical dispersion relations and scatter off each other. In contrast, a neighboring doublon pair is dynamically pinned in the strong-interaction regime. Remarkably, a single fermion and a singlet bound pair exhibit fundamentally different scattering behaviors when encountering a pinned doublon pair acting as a scattering center. While the singlet bound pair undergoes perfect transmission, the single fermion is completely reflected. These results demonstrate that a neighboring doublon pair functions as an efficient filter that separates bound pairs from single particles. Numerical simulations fully support the analytical predictions. Our findings provide a dynamical mechanism for generating and manipulating bound-pair states.
We study the one-dimensional Bose-Hubbard model under the resonant condition, where the nearest-neighbor and on-site interaction strengths are equal. In the strong interaction limit, nnn bosons occupied in a single site can transfer to neighboring sites in a complete manner, which is referred to as quantum slinky motion. It can be shown that quantum slinky motions can be described by a set of effective noninteracting Hamiltonians. These Hamiltonians are sets of generalized Su-Schrieffer-Heeger chains with an nnn-site unit cell in an auxiliary space, referred to as trimerization, tetramerization, pentamerization, etc., possessing nontrivial Zak phases. The corresponding edge states are demonstrated by the nnn-boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.
We study the temporal expansion of an ultracold Bose gas in two-dimensional, square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical (BEC) part and quantum mechanical fluctuations. After a quench, i.e. after a sudden switch of the lattice nearest-neighbor hopping, the expanding, bosonic cloud separates spatially into a fast, ballistic forerunner and a slowly expanding central part controlled by selftrapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.