Zhang Hong-Biao

Fidelity Susceptibility in the SU(2) and SU(1,1) Algebraic Structure Models

We mainly explore the fidelity susceptibility based on the Lie algebraic method. On physical grounds, the exact expressions of fidelity susceptibilities can be respectively obtained in SU(2) and SU(1,1) algebraic structure models, which are applied to one-body system and many-body systems, such as the single spin model, the single-mode squeeze harmonic oscillator model and the BCS model. In terms of the double-time Green-function method, our general conclusions are illustrated with two models which exhibit the fidelity susceptibilities at the finite temperature and T = 0.

Entanglement of Two-Superconducting-Qubit System Coupled with a Fixed Capacitor

We study thermal entanglement in a two-superconducting-qubit system in two cases, either identical or distinct. By calculating the concurrence of system, we find that the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits and our result is in a good agreement with the experimental data.

Fidelity susceptibility and geometric phase in critical phenomenon

Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).Motivated by recent developments in quantum fidelity and fidelity susceptibility,we study relations among Lie algebra,fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1,1) algebraic structure models. From this relation,the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time,we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition,the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC).Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin—Meshkov—Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1, 1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC).

Reduced Properties and Applications of Y(sl(2)) Algebra for a Two-Spin System

By taking a special constraint for a general realization of Y(sl(2)), two sets of sl(2) algebras are presented, in which a u(1) algebra is hidden. With the help of this constraint, the block-diagonal form can be written to the generator J of Yangian algebras, and especially it is a rotational transformation of a spin in the elementary quantum mechanics. This sheds new light on the physical meaning of Y(sl(2)).

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model: an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2) squeezed number states respectively. Some statistical properties of these states are also discussed.

SO(3,2) Structure and Distributions of Two-Component Bose-Einstein Condensates with Lower Excitations*

The eigenstates describing two-component Bose–Einstein condensates (BEC) with weakly excitations have been found, by using the SO(3,2) algebraic mean-field approximation. We show that the two-component modified BEC (see Eq.(26)) possesses uniquely super-Poissonian distribution in a fixed magnetic field along direction. The distribution will be uncertain, if B = 0.The wave function describing two-component Bose-Einstein condensate with weakly excitations has been found, by using the SO(3,2) algebraic mean-field approximation. We show that the two-component modified BEC (see eq.(\ref{ga})) possesses uniquely super-Poissonian distribution in a fixed magnetic field along z-direction. The distribution will be uncertain, if B=0.

Sudden birth and sudden death of thermal fidelity in a two-qubit system

We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field. With the help of contour plots, we clearly identify the ground states of the system in different regions of parameter space, and discuss the corresponding energy level crossing. The fidelity between the ground state of the system and the state of the system at temperature T is calculated. The result shows that the fidelity is very sensitive to the magnetic field anisotropic factor, indicating that this factor may be used as a controller of the fidelity. The influence of the Yangian transition operators on the fidelity of the system is discussed. We find that the Yangian operators can change the fidelity dramatically and give rise to sudden birth and sudden death phenomena of the thermal fidelity. This makes the corresponding Yangian operators possible candidates for switchers to turn the fidelity on and off.

Application of Y(sl(2)) Algebra for Entanglement of Two-Qubit System

We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y(sl(2)) in quantum information.

A Realization and Truncation of Yangian Algebra in the Generalized Hydrogen Atom with a U(1) Monopole

We establish an extended hydrogen atom associated with a U(1) monopole in which a realization of Yangian Y(sl(2)) is proposed and the energy spectrum is also given. By solving the RTT relation R(u?v)[T(u)?T(v)] = [T(v)?T(u)]R(u?v) for the truncation T(3) = 0, the obtained model is shown to be related to the truncated Yangian.

Explicit Analysis of Creating Maximally Entangled State in the Mott Insulator State

We clarify the essence of the method proposed by You (Phys. Rev. Lett. 90 (2004) 030402) to create the maximally entangled atomic N-GHZ state in the Mott insulator state. Based on the time-independent perturbation theory, we find that the validity of the method can be summarized as that the Hamiltonian governing the evolution is approximately equivalent to the type aJx2+bJx, which is the well known form used to create the maximally entangled state.