The and transitions in the oxygen isoelectronic sequence

Multiconfiguration Dirac-Fock results are reported for the and transitions in the oxygen-like sequence for Z =9,...,18. Both transition energies and transition rates are included. Received: 29 June 1998 / Accepted: 1st July 1998     

A classification of entanglement in three-qubit systems

We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence classes under local unitary operations. For mixed states characterization of full tripartite entanglement is not yet solved in general; some partial results will be presented here.     

Periodic orbits of the hydrogen molecular ion

Based on our previous work [Yiwu Duan, J.M. Yuan, C.G. Bao, Phys. Rev. A 52, 3497 (1995)], we study deeply the periodic orbits of the hydrogen molecular ion within the Born-Oppenheimer approximation (BOA). The Thiele-Burrau's transformation is introduced to regularize the singularities associated with the Coulomb potential terms and to transform the problem into a direct product of a pendulum and an anharmonic oscillator. This facilitates the analysis of the bifurcation properties of the periodic orbits. Some more details are also given about the calculation of the semiclassical density-of-state distribution using the Berry-Tabor formula. Received: 5 February 1999     

Controlling entanglement sudden death in cavity QED by classical driving fields

We investigate the entanglement dynamics of a quantum system consisting of two-level atoms interacting with vacuum or thermal fields with classical driving fields. We find that the entanglement of the system can be improved by adjusting the classical driving field. The influence of the classical field and the purity of the initial state on the entanglement sudden death is also studied. It is shown that the time of entanglement sudden death can be controlled by the classical driving fields. Particularly, the entanglement sudden death phenomenon will disappear if the classical driving fields are strong enough.     

Thermal entanglement of two interacting qubits in a static magnetic field

We study systematically the entanglement of a two-qubit Heisenberg XY model in thermal equilibrium in the presence of an external arbitrarily-directed static magnetic field, thereby generalizing our prior work [G. Lagmago Kamta, A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002)]. We show that a magnetic field having a component in the xy-plane containing the spin-spin interaction components produces different entanglement for ferromagnetic (FM) and antiferromagnetic (AFM) couplings. In particular, quantum phase transitions induced by the magnetic field-driven level crossings always occur for the AFM-coupled qubits, but only occur in FM-coupled qubits when the coupling is of Ising type or when the magnetic field has a component perpendicular to the xy-plane. When the magnetic field has a component in the xy-plane, the cut-off temperature above which the entanglement of both the FM- and AFM-coupled qubits vanishes can always be controlled using the magnetic field for any value of the XY coupling anisotropy parameter. Thus, by adjusting the magnetic field, an entangled state of two spins can be produced at any finite temperature. Finally, we find that a higher level of entanglement is achieved when the in-plane component of the magnetic field is parallel to the direction in which the XY exchange coupling is smaller.     

Nonclassical correlations from dissociation-time entanglement

We discuss a strongly entangled two-particle state of motion that emerges naturally from the double-pulse dissociation of a diatomic molecule. This state, which may be called dissociation-time entangled, permits the unambiguous demonstration of nonclassical correlations by violating a Bell inequality based on switched single-particle interferometry and only position measurements. We apply time-dependent scattering theory to determine the detrimental effect of dispersion. The proposed setup brings into reach the possibility of establishing nonclassical correlations with respect to system properties that are truly macroscopically distinct.     

Molecular orientation entanglement and temporal Bell-type inequalities

We make a detailed study of Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We show that, in general, when an observable has a continuous spectrum which is bounded, one is able to construct non-locality tests sharing common properties with those for two-level systems. The specific observable studied here is molecular spatial orientation, and it can be experimentally measured for single molecules, as required in our protocol. We also provide some useful general properties of the derived inequalities and study their robustness to noise. Finally, we detail possible experimental scenarios and analyse the role played by different experimental parameters.     

Symplectic transformations and entanglement in multipartite finite systems

Symplectic Sp(2l, ℤ_p) transformations in l-partite finite systems are explicitly constructed. The general method is applied to bi-partite and tri-partite systems. The effect of these transformations on the correlations and entanglement between the subsystems is discussed.     

Discussion of the entanglement classification of a 4-qubit pure state

We classify 4-qubit pure states under the stochastic local operation and classical communication (SLOCC). There exist twenty three essentially different classes of states, giving rise to a four-graded partially ordered structure. We also give the criterion to judge which class an arbitrary 4-qubit state belongs to. We re-classify the 4-qubit pure state into 2×2×4, 4×4 aspects. Finally, we give our analysis of the classification difference of methods for the 3-qubit pure state.     

Additional symmetry for the electronic shell in its ground state and many-electron effects

The additional symmetry for the properties related to the ground state of the atom is considered taking into account many-electron effects. Calculations of the I _4f, I _3d,I _2p,I _3p binding energies, 4f ^N-15d - 4f^N system differences and 2p, 3p electron affinities in the second order of perturbation theory and in the configuration interaction approximation have been performed for the ground configurations with one open shell. The analysis of separate many-electron corrections for these quantities and their variation along the sequences of atoms and ions shows that the main corrections maintain the considered symmetry. Received 18 January 1999 and Received in final form 17 July 1999     

Global entanglement and coherent states in an {\sf N}-partite system

We consider a quantum system consisting of N parts, each of which is a “quKit” described by a K dimensional Hilbert space. We prove that in the symmetric subspace, , a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement all states are globally entangled.     

Dynamics of entanglement in one-dimensional Ising chains with two- and three-body interactions

The evolution of entanglement in a one-dimensional Ising chain with both two-body and three-body interactions, under two types of initial states, is numerically simulated. We analyse three problems concerning the dynamics of pairwise entanglement: (i) the possibility of generating large entanglement from an initial separable state by the use of a selective irradiation scheme; (ii) the effect of three-body interaction on the generation of entanglement from an initial separable state; (iii) the effect of three-body interaction on the decay of the entanglement from a state with only (m,n)-pair maximal entangled, and the rest in product form. It is shown that a large pairwise concurrence C_mn can be obtained when the resonant, transverse radio-frequency fields are selectively switched on from the mth to nth spins. Three-body interaction will decrease the oscillation amplitude of the nearest neighbour concurrence, while the oscillation amplitude of remote pairwise concurrence will be greatly increased with the consideration of three-body interactions. For an initial (m,n)-pair maximal entangled state, a slow decay of the pairwise concurrence C_mn is found with the introduction of three-body interactions.     

The theoretical calculation of transition probabilities for some excited p-d transitions in atomic nitrogen

The atomic transition probabilities are calculated for individual lines between some quartet terms of 3p↦4d and 3p↦5d transition arrays using weakest bound electron potential model theory (WBEPMT). In the determination of relevant parameters which are needed for calculation of transition probabilities, we employed numerical non-relativistic Hartree-Fock wave functions for expectation values of radius in both ground and excited states unlike to NCA method used on traditional WBEPMT procedure. We have obtained very good agreement between our results and the accepted values taken from NIST.     

Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system

The generation of continuous variable entanglement via atomic coherence in a two-mode three-level cascade atomic system is discussed according to the entanglement criterion proposed by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]. Atomic coherence between the top and bottom levels is induced with two photons of a strong external pump field. It shows that entanglement for the two-mode field in the cavity can be generated under certain conditions. Moreover, by means of the input-output theory, we show that the two-mode entanglement could also be approached at the output.     

Multilevel atomic entanglement induced by spontaneous emission in free space

We investigate two identical Λ-type atoms in free space, and focus on the entanglement between the two atoms. We derive a master equation for the atomic subspace and solve it analytically to show how the spontaneous emission from the two atoms system induces entanglement. The magnitude of the entanglement and the steady state entanglement are found to be strongly dependent on the initial states and the orientation of the dipoles of the two atoms.     

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.     

Comparative study of linear entropy and negativity in molecular vibrations

The dynamical comparison of entanglement, measured by linear entropy and negativity, is carried out for initial pure separable states in vibrations of H₂O and SO₂. It is shown that both measures of an initial state with local-mode character have the same period for H₂O, while those of an initial state with normal-mode character are no longer identical in period. When the total quantum number of the initial state is one, both measures rise and lower together with the period for H₂O being larger than that for SO₂. For a suitable state in H₂O, both measures exhibit a beat phenomenon with a long period.     

Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger (GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon, where the projection of the feasible region to some two dimensional planes has lead to better visualization. To reveal the PPT entangled regions of these density matrices, we manipulate some appropriate optimal non-decomposable linear entanglement witnesses (EWs) as the envelope of family of linear optimal non-decomposable EWs. These nonlinear EWs are nonlinear functional of MUB diagonal states, so that they are nonnegative valued over all separable, but they are negative valued over some PPT entangled MUB diagonal states. Even though, these nonlinear EWs can not separate completely, the PPT entanglement region from separable one, but however in special cases they lead to necessary and sufficient condition for separability. To support the evidence, we study three categories for special choices of parameters in density matrices, and using the nonlinear EWs we can distinguish the region of PPT entangled states and separable states, completely. At the end some numerical simulations are provided to show the practical applicability of these nonlinear EWs in detecting some PPT entangled MUB diagonal states.     

Bounds on bipartitely shared entanglement reduced from superposed tripartite quantum states

For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite (2 ⊗ 2 ⊗ n)-dimensional cases.     

Maximum-entropy technique with logarithmic constraints: Estimation of atomic radial densities

Maximum-entropy (ME) approximations to density functions involving logarithmic constraints are studied. It is proved the existence and uniqueness of the ME approximation constrained by the normalization, the geometric mean and (i) a moment of arbitrary order, or (ii) the logarithmic uncertainty. A numerical analysis of the accuracy of these ME approximations is carried out for the radial electron densities of neutral atoms in both position and momentum spaces. Received 23 November 1998 and Received in final form 20 May 1999