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Physical Review A

Comment on “Coherent shift of localized bound pairs in the Bose-Hubbard model”

Manuel Valiente, David Petrosyan, Alejandro Sáenz

Published Jun 25, 2010• 3 citations
Publisher

Abstract

We consider scattering of a single particle from an interaction-bound pair of particles in the one-dimensional Bose-Hubbard model. We show that the transmission probability of the single particle is always significantly smaller than unity. This invalidates the main result of L. Jin et al. [Phys. Rev. A 79, 032108 (2009)], where it is claimed that a single-particle wave packet can pass with unit probability through a bound-particle pair and coherently shift its position by one lattice site.

DOI
10.1103/physreva.81.066101

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We consider scattering of a single particle from an interaction-bound pair of particles in the one-dimensional Bose-Hubbard model. We show that the transmission probability of the single particle is always significantly smaller than unity. This invalidates the main result of L. Jin et al. [Phys. Rev. A 79, 032108 (2009)], where it is claimed that a single-particle wave packet can pass with unit probability through a bound-particle pair and coherently shift its position by one lattice site.
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.
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.
We consider the Bose-Hubbard model with particle losses at one lattice site. For the noninteracting case, we find that half of the bosons of an initially homogeneous particle distribution are not affected by dissipation that only acts on one lattice site in the center of the lattice. A physical interpretation of this result is that the surviving particles interfere destructively when they tunnel to the location of the dissipative defect and therefore never reach it. Furthermore we find for a one-dimensional model that a fraction of the particles can propagate across the dissipative defect even if the rate of tunneling between adjacent lattice sites is much slower than the loss rate at the defect. We analyze the robustness of our findings with respect to small interactions and small deviations from the symmetric setting. A possible experimental realization of our setup is provided by ultracold bosonic atoms in an optical lattice, where an electron beam on a single lattice site ionizes atoms that are then extracted by an electrostatic field.
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 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.