Searcharxiv⌕ Search

arXiv subjects

Fu-Lin Zhang

Publications and source records attributed to Fu-Lin Zhang.

At least 55 records · Page 3Linked to original sources
arXiv2013

Dirac equation with a magnetic field in 3D non-commutative phase space

For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the motion of the charged particle along the magnetic field has the effect to increase the magnetic field. In the classical limit, matrix elements of the velocity operator related to the probability give a clear physical picture: Along an effective magnetic field the mechanical momentum is conserved and the motion perpendicular to the effective magnetic field follows a round orbit. If using the velocity operator defined by the coordinate operators, the motion becomes complicated.

quant-ph↗
arXiv2013

Speed of disentanglement in multi-qubit systems under depolarizing channel

We investigate the speed of disentanglement in the multiqubit systems under the local depolarizing channel, in which each qubit is independently coupled to the environment. We focus on the bipartition entanglement between one qubit and the remaining qubits constituting the system, which is measured by the negativity. For the two-qubit system, the speed for the pure state completely depends on its entanglement. The upper and lower bounds of the speed for arbitrary two-qubit states, and the necessary conditions for a state achieving them, are obtained. For the three-qubit system, we study the speed for pure states, whose entanglement properties can be completely described by five local-unitary-transformation invariants. An analytical expression of the relation between the speed and the invariants is derived. The speed is enhanced by the the three-tangle which is the entanglement among the three qubits, but reduced by the the two-qubit correlations outside of the concurrence. The decay of the negativity can be restrained by the other two negativity with the coequal sense. The unbalance between two qubits can reduce speed of disentanglement of the remaining qubit in the system, even can retrieve the entanglement partially. For the k-qubit systems in an arbitrary superposition of GHZ state and W state, the speed depends almost entirely on the amount of the negativity when k increases to five or six. An alternative quantitative definition for the robustness of entanglement is presented based on the speed of disentanglement, with comparison to the widely studied robustness measured by the critical amount of noise parameter where the entanglement vanishes. In the limit of large number of particles, the alternative robustness of the GHZ-type states is inversely proportional to k, and the one of the W states approaches 1/\sqrt{k}.

quant-ph↗
arXiv2013

Most robust and fragile two-qubit entangled states under depolarizing channels

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad et al. [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region [1/2,1]. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

quant-ph↗
arXiv2012

Prepotential approach to systems with dynamical symmetries

A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have the symmetries which are similar to the corresponding ones, and can be solved by using the algebraic method.

quant-ph↗
arXiv2012

Higgs algebraic symmetry of screened system in a spherical geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(\dot{r}=0)$.

math-ph↗
arXiv2012

Berry phases for interacting spins in composite environments

Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.

quant-ph↗
arXiv2012

Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light

Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well.

quant-ph↗
arXiv2011

Local correlations of mixed two-qubit states

The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992)]. A lower bound of the local weight is proved being connected with the concurrence of the state $p_L^{\max}= 1-\mathcal{C}(ρ)$. The local probability distributions for two families of mixed states are constructed independently, which accord with the lower bound.

quant-ph↗
arXiv2011

Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States

Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party correlations in two families of $n$-qutrit Greenberger-Horne-Zeilinger type states. For the pure states in one of the families, the irreducible 2-party, $n$-party and $(n-m)$-party ($0< m < n-2$) correlations are nonzero, which is different from the $n$-qubit case. We also derive the correlation distributions in the $n$-qutrit maximal slice state, which can be uniquely determined by its $(n-1)$-qutrit reduced density matrices among pure states. It is proved that there is no irreducible $n$-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible $n$-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.

quant-ph↗
arXiv2011

Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants

Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|Ψ>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{iθ}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.

quant-ph↗
arXiv2011

Bounds of concurrence and their relation with fidelity and frontier states

The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically.

quant-ph↗
arXiv2011

Quantum Entanglement transfer between spin-pairs

We investigate the transfer of entanglement from source particles (SP) to target particles (TP) in the Heisenberg interaction $ H=\vec s_{1} \cdot \vec s_{2}$. In our research, TP are two qubits and SP are two qubits or qutrits. When TP are two qubits, we find that no matter what state the TP is initially prepared in, at the specific time $t=π$, the entanglement of TP can attain to 1 after interaction with SP which stay on the maximally entangled state. For the TP are two qutrits, we find that the maximal entanglement of TP after interaction is relative to the initial state of TP and always cannot attain to 1 to almost all of initial states of TP. But we discuss an iterated operation which can make the TP to the maximal entangled state.

quant-ph↗
arXiv2011

Virial Theorem and Hypervirial Theorem in a spherical geometry

The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman Theorem, these relations can be used to formulate a \emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method.

math-ph↗
arXiv2011

Geometric phase for nonlinear coherent and squeezed state

The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated respectively. Moreover, some of their common properties are discussed respectively, such as gauge invariance, non-locality and non-linear effects. The non-linear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r -> \infinity, the limiting value of the geometric phase is also determined by non-linear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states maybe regarded as a geometric criterion.

quant-ph↗
arXiv2009

Connection between Coulomb and harmonic oscillator potentials in relativistic quantum mechanics

The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita transformation. These connections lead to an approach to solve the Coulomb problems using the results of the harmonic oscillator potential in the above-mentioned relativistic systems.

quant-ph↗
arXiv2009

Higgs algebraic symmetry in the two-dimensional Dirac equation

The dynamical symmetry algebra of the two-dimensional Dirac Hamiltonian with equal scalar and vector Smorodinsky-Winternitz potentials is constructed. It is the Higgs algebra, a cubic polynomial generalization of SU(2). With the help of the Casimir operators, the energy levels are derived algebraically.

quant-ph↗
arXiv2009

Applications of Polynomial Algebras to Deformed Oscillator

The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different maximal order.

math-ph↗