Hai-Qing Lin

Entanglement and Quantum Phase Transition in the Extended Hubbard Model

We study quantum entanglement in a one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.

Exact solution of XXZ spin chain with unparallel boundary fields

By using a set of gauge transformations (face-vertex correspondence relations), the XXZ spin chain with both transverse and longitudinal magnetic boundary fields is studied. The corresponding reflection boundary matrices therefore have non-diagonal elements. The Bethe ansatz equations, the eigenvalues and the eigenstates of the transfer matrix and the Hamiltonian of the system are obtained in the framework of algebraic Bethe ansatz method. The ground states for different couplings are derived.

Angle- and energy-resolved plasmon coupling in gold nanorod dimers.

The plasmon coupling in the dimers of Au nanorods linked together at their ends with dithiol molecules has been studied. The plasmon coupling in the dimers composed of similarly sized nanorods gives antibonding and bonding plasmon modes. The plasmon wavelengths of the two modes have been found to remain approximately unchanged, with the scattering intensity ratio between the antibonding and bonding modes decaying rapidly as the angle between the nanorods is increased. This plasmon coupling behavior agrees with that obtained from both electrodynamic calculations and modeling on the basis of the dipole-dipole interaction. The electric field in the gap region is largely enhanced for the bonding mode, while that for the antibonding mode is even smaller than the far field, highlighting the importance of selecting appropriate plasmon modes for plasmon-enhanced spectroscopies. An anti-crossing-like behavior in the plasmon coupling energy diagram has further been revealed for linearly end-to-end assembled dimers composed of differently sized nanorods. This result will be useful for plasmonic applications where the plasmon wavelength is required to be controllable but without sacrificing the electric field enhancement.

Experimental Evidence of Plasmophores: Plasmon-Directed Polarized Emission from Gold Nanorod–Fluorophore Hybrid Nanostructures

We show that the fluorescence emission from individual hybrid nanostructures composed of Au nanorod cores and oxazine 725-embedded mesostructured silica shells is strongly polarized, with the degree of polarization being equal to that of the light scattered by the nanorod and varying from 0 to 1 as the longitudinal plasmon resonance wavelength is increased. Our analyses indicate that the interactions of the plasmon resonance of the nanorod with the excitation and emission processes of the fluorophores are temporally separated under unsaturated excitation conditions. The emission polarization is found through electrodynamic calculations to arise from the plasmon-coupled emission instead of the plasmon-enhanced excitation polarization. The emission carries the direction and polarization properties that are essentially determined by the dipolar plasmon of the nanorod antenna. Our results therefore provide direct and concrete evidence for the plasmophore that has been proposed recently for plasmon-enhanced fluorescence.

Universal Scaling and Fano Resonance in the Plasmon Coupling between Gold Nanorods

The plasmon coupling between metal nanocrystals can lead to large plasmon shifts, enormous electric field enhancements, and new plasmon modes. Metal nanorods, unlike spherical ones, possess a transverse and a longitudinal plasmon mode owing to their geometrical anisotropy. Consequently, the plasmon coupling between metal nanorods is much more complicated than that between nanospheres. For the latter, experimental approaches, simple scaling relationships, and exact analytic solutions have been developed for describing the plasmon coupling. In this study, we have carried out extensive finite-difference time-domain simulations to understand the plasmon coupling in the dimers of Au nanorods that are aligned along their length axes. The effects of the gap distance, longitudinal plasmon energy, and end shape of the nanorod monomers on the plasmon coupling have been scrutinized. The coupling energy diagrams show a general anticrossing behavior. All of them can be rescaled into one simple and universal hyperbolic formula. A theoretical model based on two interacting mechanical oscillators has been developed to understand the plasmon coupling between two arbitrarily varying Au nanorods. This model, together with the universal equation, allows for the determination of the coupled plasmon energies of Au nanorod dimers with high accuracies. Furthermore, the Fano interference has been observed in the nanorod heterodimers, with its behavior being dependent on the gap distance and plasmon energies of the nanorod monomers. Our results will be useful for predicting the coupled plasmon energies of metal nanorod dimers in a variety of plasmonic applications and understanding the Fano resonance in plasmonic nanostructures.

Observation of the Fano resonance in gold nanorods supported on high-dielectric-constant substrates.

Fano resonances in plasmonic nanostructures, characterized by their asymmetric resonance spectral profile, are currently attracting much interest due to their potential applications in biological sensing, metamaterials, photoswitching, and nonlinear optical devices. In this study, we report on the observation of the Fano resonance in Au nanorods induced by their coupling with the supporting substrate. For Au nanorods having a large size and deposited on a substrate with a large dielectric constant, the strong nanorod-substrate coupling gives rise to a Fano line shape on the far-field scattering spectrum. Electrodynamic calculations reveal that the Fano resonance originates from the interference of a broad octupolar and a narrow quadrupolar plasmon mode of the nanorod. Such an interaction is enabled by the strong image charges induced by substrates with high dielectric constants. Moreover, the Fano resonance is very sensitive to the nanorod-substrate spacing. When the spacing is experimentally increased to be larger than ∼8 nm, the Fano resonance disappears. These results will be important not only for understanding the interference of different plasmon modes in plasmonic systems but also for developing a number of plasmon-based optical and optoelectronic devices.

Distinct Plasmonic Manifestation on Gold Nanorods Induced by the Spatial Perturbation of Small Gold Nanospheres

The plasmon coupling between a Au nanorod and a small Au nanosphere has been studied with scattering measurements, electrodynamic simulations, and model analysis. The spatial perturbation of the nanosphere leads to distinct spectral changes of the heterodimer. The plasmonic responses, including Fano resonance, are remarkably sensitive to the nanosphere position on the nanorod, the gap distance, and the nanocrystal dimensions. The nanosphere dipole is intriguingly found to rotate around the nanorod dipole to achieve favorable attractive interaction for the bonding dipole-dipole mode. The sensitive spectral response of the heterodimer to the spatial perturbation of the nanosphere offers an approach to designing plasmon rulers of two spatial coordinates for sensing and high-resolution measurements of distance changes.

Plasmon coupling in clusters composed of two-dimensionally ordered gold nanocubes.

Gold nanocubes are assembled into clusters of varying numbers and ordering on indium tin oxide substrates. The plasmon coupling in the clusters is studied with both dark-field imaging and finite-difference time-domain calculations. Generally, as a cluster becomes larger and more asymmetric, it exhibits more scattering peaks towards longer wavelengths. The coupling of the vertically oriented dipole in the nanocube with its image dipole in the substrate generates two scattering peaks. One is fixed in energy and the other red-shifts with increasing cluster size. The coupling of horizontally oriented dipoles among different nanocubes produces multiple scattering peaks at lower energies. Their positions and intensities are highly dependent on the number and ordering of nanocubes in the cluster. Au nanocubes in the clusters are further welded together by thermal treatment. The scattering peaks of the thermally treated clusters generally become sharper. The lower-energy scattering peaks arising from dipolar oscillations are red-shifted.

Entanglement, quantum phase transition, and scaling in the XXZ chain

Motivated by recent development in quantum entanglement, we study relations among concurrence C, SU{sub q}(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possesses the maximum concurrence. When the anisotropic parameter {delta} is deformed, however, its value decreases. Its dependence on {delta} scales as C=C{sub 0}-C{sub 1}({delta}-1){sup 2} in the XY metallic phase and near the critical point (i.e., 1<{delta}<1.3) of the Ising-like insulating phase. We also study the dependence of C on the correlation length {xi}, and show that it satisfies C=C{sub 0}-1/2{xi} near the critical point. For different sizes of the system, we show that there exists a universal scaling function of C with respect to the correlation length {xi}.

Plasmonic Percolation: Plasmon-Manifested Dielectric-to-Metal Transition

Percolation generally refers to the phenomenon of abrupt variations in electrical, magnetic, or optical properties caused by gradual volume fraction changes of one component across a threshold in bicomponent systems. Percolation behaviors have usually been observed in macroscopic systems, with most studies devoted to electrical percolation. We report on our observation of plasmonic percolation in Au nanorod core-Pd shell nanostructures. When the Pd volume fraction in the shell consisting of palladium and water approaches the plasmonic percolation threshold, ~70%, the plasmon of the nanostructure transits from red to blue shifts with respect to that of the unshelled Au nanorod. This plasmonic percolation behavior is also confirmed by the scattering measurements on the individual core-shell nanostructures. Quasistatic theory and numerical simulations show that the plasmonic percolation originates from a positive-to-negative transition in the real part of the dielectric function of the shell as the Pd volume fraction is increased. The observed plasmonic percolation is found to be independent of the metal type in the shell. Moreover, compared to the unshelled Au nanorods with similar plasmon wavelengths, the Au nanorod core-Pd shell nanostructures exhibit larger refractive index sensitivities, which is ascribed to the expulsion of the electric field intensity from the Au nanorod core by the adsorbed Pd nanoparticles.