Anisotropy and Magnetic Field Effects on the Entanglement of a Two Qubit Heisenberg \u3ci\u3eXY\u3c/i\u3e Chain

We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature Tc that is independent of the external B field

Fermionic concurrence in the extended Hubbard dimer

In this paper, we introduce and study the fermionic concurrence in a two-site extended Hubbard model. Its behaviors both at the ground state and finite temperatures as function of Coulomb interaction $U$ (on-site) and $V$ (nearest-neighbor) are obtained analytically and numerically. We also investigate the change of the concurrence under a nonuniform field, including local potential and magnetic field, and find that the concurrence can be modulated by these fields.Comment: 5 pages, 7 figure

Entanglement, quantum phase transition and scaling in XXZ chain

Motivated by recent development in quantum entanglement, we study relations among concurrence $C$, SU$_q$(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 possess the maximum concurrence. When the anisotropic parameter $\Delta$ is deformed, however, its value decreases. Its dependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ 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 $C=C_0-1/2\xi$ near the critical point. For different size of the system, we show that there exists a universal scaling function of $C$ with respect to the correlation length $\xi$.Comment: 4 pages, 3 figures. to appear in Phys. Rev.

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb sturmian functions of half integer angular momentum. We show that, in the case of H$^-$, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for $S\rightarrow P$ transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.Comment: 28 pages, 4 figure

Angular Distributions for Double Ionization of \u3ci\u3eLi\u3c/i\u3e\u3csup\u3e-\u3c/sup\u3e by an Ultrashort, Intense Laser Pulse

We predict photoelectron angular distributions for double ionization of Li- by both weak and intense ultrashort, linearly polarized laser pulses by direct numerical integration of the three-dimensional, time-dependent Schrödinger equation. Li- is treated as a two-active electron system. Near threshold, for low intensity we recover general features of angular distributions for one-photon double ionization. For the intense field (multiphoton) case, the photoelectron angular distribution changes significantly, particularly in directions parallel and perpendicular to the laser polarization axis

Two-active electron approach to multi-electron systems in intense ultrashort laser pulses: Application to Li\u3csup\u3e–\u3c/sup\u3e

The interaction of Li– with an ultrashort intense laser pulse is investigated by solving the time-dependent Schrödinger equation (TDSE) in the dipole approximation using a two-active electron approach. We describe the numerical solution of the TDSE and give a more detailed presentation of a technique for obtaining angular distributions for double ionization by intense ultrashort laser pulses. We show how selection rules observed in the angular distributions for double ionization by an intense laser field can be derived from the symmetry properties of the wave function. In an attempt to elucidate the mechanisms for double ionization in the multiphoton regime, we have performed numerical experiments for ionization by single cycle and double half-cycle pulses. Our preliminary results unveil the important contribution of the shake-off mechanism, in addition to the rescattering and sequential ionization mechanisms

Multielectron system in an ultrashort, intense laser field: A nonperturbative, time-dependent two-active-electron approach

We present a two-active-electron (TAE) approach for solving the time-dependent Schrödinger equation (TDSE) for the interaction of a multi-electron system with an ultrashort, intense, and linearly polarized laser pulse [Lagmago Kamta and Starace, Phys. Rev. Lett. 86, 5687 (2001)]. A technique for obtaining angular distributions for double ionization by such pulses is also described. The approach for solving the TDSE in the TAE approximation is full dimensional and accounts for correlations between the two electrons, as well as the polarization of the core. It is based on a configuration-interaction expansion of the time-dependent wave function in terms of one-electron atomic orbitals. Applying the method to the lithium negative ion (Li-), we display the time-dependent dynamics of the photodetachment process. For low intensities, our results for the detachment yield follow expectations from lowest-order perturbation theory and agree satisfactorily with R-matrix calculations. Our results for angular distributions indicate that following multiphoton double ionization by an intense laser field, electrons are predominantly ejected along the laser polarization axis; however, a significant number are ejected perpendicularly to this axis. An angular momentum-based analysis of these angular distributions indicates that, in the dipole approximation and for an initial 1Se state interacting with a linearly polarized laser field, double ejection of both electrons along the direction perpendicular to the laser polarization axis can only occur following absorption of an even number of photons, whereas multiphoton absorption of an odd number of photons does not lead to double ejection at these angles