Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin -1/2 particles with one of particles driven by rotating magnetic field. The influences of coupling and precession frequency of the magnetic field on geometric phase are also discussed in detail.     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

Spin bath interaction effects on the geometric phase

We calculate the geometric phase of a spin-1/2 particle coupled to an external environment comprising N spin-1/2 particle in the framework of open quantum systems. We analyze the decoherence factor and the deviation of the geometric phase under a nonunitary evolution from the one gained under an unitary one. We show the dependence upon the system's and bath's parameter and analyze the range of validity of the perturbative approximation. Finally, we discuss the implications of our results.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously, and can also cause sudden change of the Berry phase for some weak magnetic field cases.     

Geometric phases and entanglement of two qubits with XY type interaction

It is shown that geometric phases and entanglement may fail to detect level crossings for two qubits with XY interaction. The rotating magnetic field produces a magnetic monopole sphere like conducting spheres in that only a ground state evolving adiabatically outside the sphere acquires a geometric phase.     

Interacting spin pairs in rotational magnetic fields and geometric phase

In virtue of the quantum invariant theory, we obtain the rigorous solution of the isotropic bipartite system in rotational magnetic fields, based on which the general expression of the noncyclic geometric phase is worked out and the entanglement dependence of the noncyclic geometric phase in this model is investigated. We show that the influence of the coupling on noncyclic geometric phase depends on the initial condition of the system. We also show that when the magnetic fields are stationary, there is a more general class of states existed of which the noncyclic geometric phase could be interpreted solely in terms of the solid angle enclosed by the geodesically closed curve on a two-sphere parameterized by the evolving Schmidt coefficients.     

Non-Adiabatic Geometric Phase in a Dispersive Interaction System

We investigate the geometric phase and dynamic phase of a two-level fermionic system with dispersive interaction, driven by a quantized bosonic field which is simultaneously subjected to parametric amplification. It is found that the geometric phase is induced by a counterpart of the Stark shift. This effect is due to distinct shifts in the field frequency induced by interaction between different states （｜e〉 and ｜g〉 ） and cavity field, and a simple geometric interpretation of this phenomenon is given, which is helpful to understand the natural origin of the geometric phase.     

Various Correlations in a Two-Qubit Heisenberg XXZ Spin System Both in Thermal Equilibrium and Under the Intrinsic Decoherence

In this paper we discuss various correlations measured by the concurrence (C), classical correlation (CC), quantum discord (QD), and geometric measure of discord (GMD) in a two-qubit Heisenberg XXZ spin system in the presence of external magnetic field and Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction. Based on the analytically derived expressions for the correlations for the cases of thermal equilibrium and the inclusion of intrinsic decoherence, we discuss and compare the effects of various system parameters on the correlations in both cases. We also found that there is not a definite ordering of these quantities in thermal equilibrium, whereas there is a descending order of the CC, C, GMD and QD under the intrinsic decoherence with a nonnull B when the initial state is $|\varPsi_{2}(0) \rangle = \frac{1}{\sqrt{2}} (|00 \rangle + |11 \rangle)$ .     

Spin geometry of entangled qubits under bilocal decoherence modes

The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states—the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a certain state. The question for which conditions the path traced out in the geometric picture depends only on the relative angle between the bilocal rotations is addressed.     

Pairwise entanglement of a three-qubit Heisenberg XY chain in a nonuniform magnetic field with intrinsic decoherence

Taking into account the intrinsic decoherence, the concurrence of the nearest and the next-to-nearest neighbor qubits in a three-qubit Heisenberg XY chain are investigated when a nonuniform magnetic field is included. We show that the effects of the external magnetic field, including the uniform and inhomogeneous magnetic fields, on the time evolution of entanglement between the nearest and the next-to-nearest neighbor qubits rely deeply on the initial states. We can moderate the destructive effect of intrinsic decoherence by controlling the uniform and inhomogeneous magnetic fields, so that a proper value of uniform and inhomogeneous magnetic fields can, to a great extent enhance the stationary entanglement.     

Non-hermitian quantum mechanics in non-commutative space

A recent investigation of the possibility of having a -symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a -symmetric deformation of this space. Specifically, a -symmetric harmonic oscillator together with an iC(x ₁+x ₂) interaction are discussed in this space, and solutions are obtained. We show that in the deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x ₁+x ₂) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not -symmetric. A complex interacting anisotropic oscillator system also is discussed.     

Quantum corrections of the Dzyaloshinskii-Moriya interaction on the spin-$\frac{1}{2}$ AF-Heisenberg chain in an uniform magnetic field

We have investigated the ground state phase diagram of the 1D AF spin- Heisenberg model with the staggered Dzyaloshinskii-Moriya (DM) interaction in an external uniform magnetic field H. We have used the exact diagonalization technique. In the absence of the uniform magnetic field (H=0), we have shown that the DM interaction induces a staggered chiral phase. The staggered chiral phase remains stable even in the presence of the uniform magnetic field. We have identified that the ground state phase diagram consists of four Luttinger liquid, staggered chiral, spin-flop, and ferromagnetic phases.     

Geometric phase in entangled bipartite systems

The geometric phase (GP) for bipartite systems in transverse external magnetic fields is investigated in this paper. Two different situations have been studied. We first consider two non-interacting particles. The results show that because of entanglement, the geometric phase is very different from that of the non-entangled case. When the initial state is a Werner state, the geometric phase is, in general, zero and moreover the singularity of the geometric phase may appear with a proper evolution time. We next study the geometric phase when intra-couplings appear and choose Werner states as the initial states to entail this discussion. The results show that unlike our first case, the absolute value of the GP is not zero, and attains its maximum when the rescaled coupling constant J is less than 1. The effect of inhomogeneity of the magnetic field is also discussed.     

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.     

Geometric phase induced by quantum nonlocality

By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior.     

The non-commutative oscillator, symmetry and the Landau problem

The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.     

Entanglement dynamics of a three-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a three-qubit system under a quantum spin environment at a finite temperature in the thermodynamics limit. For the case under study, we find the evolution of pairwise entanglement depends not only on the initial states but also on the parameters related to the system and the spin environment. In addition, an undesirable entanglement sudden death occurs in the process of entanglement evolution, and this effect can be controlled by the coupling constant between two qubits, external magnetic field, and the interaction between the system and the environment.     

Behavior of quantum coherence of Ξ-type four-level atom under bang-bang control

In this paper, we have studied the bang-bang (BB) decoupling scheme to suppress the phase decoherence, the amplitude decoherence and the general decoherence in a four-level Ξ-type atom system. The corresponding dynamical decoupling groups are given for designing the decoupling pulse sequences to suppress these three kinds of decoherence, respectively. Results show that in a proper time scale, the decoupling operations suppress the decoherence effectively. Especially in the ideal limits, it can suppress the decoherence completely. We also give the time scale in which the BB control works well. Numerical simulations show that, the larger cycle times N, the better effect of the BB decoupling operations under a fixed time scale.