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arXiv:1006.0061 · Physical Review A

Perfect coherent shift of bound pairs in strongly correlated systems

L. Jin, Z. Song

Published May 3, 2011• 8 citations
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Abstract

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.

DOI
10.1103/physreva.83.052102

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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 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.
We study the Bose-Hubbard and Fermi-Hubbard model in the limit of large coordination numbers Z (i.e., many tunnelling partners). Via a controlled expansion into powers of 1/Z, we establish a hierarchy of correlations, which facilitates an approximate analytic solution of the quantum evolution. For the Bose-Hubbard model, we derive the growth of phase coherence after a quench from the Mott to the superfluid phase. For a quench within the Mott phase, we find that various local observables approach a quasi-equilibrium state after a finite period of time. However, this state is not thermal, i.e., real thermalisation -- if it occurs -- requires much longer time scales. For a tilted lattice in the Mott state, we calculate the tunnelling probability and find a remarkable analogy to the Sauter-Schwinger effect (i.e., electron-positron pair creation out of the vacuum due to a strong electric field). These analytical results are compared to numerical simulations for finite lattices in one and two dimensions and we find qualitative agreement. Finally, we generalize these studies to the more involved case of the Fermi-Hubbard model.
We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.
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.