Two-mode squeezed vacuum state coupled to the common thermal reservoir

Entangled states play a crucial role in quantum information protocols, thus the dynamical behavior of entanglement is of a great importance. In this paper we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres-Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reservoir. Moreover for the case of interaction with vacuum as an environment we show that a state of interest after intinitely long interaction is not only entangled, but also pure. For comparison we also consider a model in which each of both modes is coupled to its own reservoir.Comment: replaced with version published in J. Phys.

Non-sequential double ionization of molecules in a strong laser field

We consider the final stage of double ionization of $\rm O_2$ molecules by short linearly polarized laser pulses. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons from a molecule takes place are identified. The analysis of the saddles and numerical simulations of the ionization indicate that to observe clear signatures of simultaneous electron escape in double ionization of $\rm O_2$ molecules stronger and much shorter laser pulses than those used in the recent experiment [E. Eremina, {\it et al}, Phys. Rev. Lett. {\bf 92}, 173001 (2004)] should be applied.Comment: 5 pages, 3 figures, Conference proceedings from 13th International Laser Physics Workshop, Triest, Italy, July 12-16, 200

Non-sequential double ionization of molecules

Double ionization of diatomic molecules by short linearly polarized laser pulses is analyzed. We consider the final stage of the ionization process, that is the decay of a highly excited two electron molecule, which is formed after re-scattering. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons takes place are identified. Numerical simulations of the ionization of molecules show that the process can be dominated by either sequential or non-sequential events. In order to increase the ratio of non-sequential to sequential ionizations very short laser pulses should be applied.Comment: 7 pages, 7 figures, submitted to PR

Strong-field triple ionisation of atoms with p3p^{3} valence shell

The interaction of strong pulsed femtosecond laser field with atoms having three equivalent electrons in the outer shell ($p^3$ configuration, e.g. nitrogen) is studied via numerical integration of a time-dependent Schr\"{o}dinger equation on a grid approach. Single, double and triple ionization yields originating from a completely antisymmetric wave function are calculated and extracted using a restricted-geometry model with the soft-core potential and three active electrons. The direct triple ionization channel is found to produce a larger yield than the channel connected with single and then direct double ionization. Compared against earlier results investigating the $n s^ 2 n p^1$ configuration, we propose that the differences found here might in fact be accessible through electron's momentum distribution.Comment: 5 pages, 3 figure

Strong-field ionization of atoms with p3p^3 valence shell: Two versus three active electrons

For a model atom with the $p^3$ valence shell we construct consistent three- and two-active electrons models enabling their direct comparison. Within these models, we study the influence of the third active electron on the double ionization yield in strong femtosecond laser fields. We reveal proportionality between double ionization signals obtained with both models in the field intensity region where non-sequential ionization dominates. We derive analytically a correspondence rule connecting the double ionization yields obtained within the three- and two-active electrons models.Comment: version accepted for Phys. Rev.

Nonsequential double ionization of atoms in strong laser pulses

It is now possible to produce laser pulses with reproducible pulse shape and controlled carrier envelope phase. It is discussed how that can be explored in double ionisation studies. To this end we solve numerically the Schr¨odinger equation for a limited dimensionality model which nevertheless treats electron repulsion qualitatively correctly and allows to study correlation effects due to the Coulomb repulsion

Double ionization of a three-electron atom: Spin correlation effects

We study the effects of spin degrees of freedom and wave function symmetries on double ionization in three-electron systems. Each electron is assigned one spatial degree of freedom. The resulting three-dimensional Schr\"odinger equation is integrated numerically using grid-based Fourier transforms. We reveal three-electron effects on the double ionization yield by comparing signals for different ionization channels. We explain our findings by the existence of fundamental differences between three-electronic and truly two-electronic spin-resolved ionization schemes. We find, for instance, that double ionization from a three-electron system is dominated by electrons that have the opposite spin

Strong-Field Double Ionization in a Three-Electron System: Momentum Distribution Analysis

We study strong-field double ionization in a three-electron system by applying a simplified, reduced-dimensionality model with three active electrons. The influence of the spin-induced symmetry of the spatial part of the wavefunction on the final two-photoectron momentum distribution is discussed. We identify partial momentum distributions originating from different sets of spins of outgoing electrons providing in this way a quantum support connection between V-structure and direct ionization typically explained classically. Changes in the momentum distribution with increasing field amplitude obtained in our simplified model are shown to be well-correlated with experimental data known from the literature. The possible relation between the observed dependencies and different ionization mechanisms is discussed.Comment: 9 pages, 4 figure

Quantum model for double ionization of atoms in strong laser fields

We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines that point towards the two-particle Stark saddle in the presence of a field. The resulting effective two dimensional model is similar to the aligned electron model, but it enables correlated escape of electrons with equal momenta, as observed experimentally. The time-dependent solution of the Schr\"odinger equation allows us to discuss in detail the time dynamics of the ionization process, the formation of electronic wave packets and the development of the momentum distribution of the outgoing electrons. In particular, we are able to identify the rescattering process, simultaneous direct double ionization during the same field cycle, as well as other double ionization processes. We also use the model to study the phase dependence of the ionization process.Comment: 14 pages, 16 figures, version accepted for publication in Phys. Rev.

Restricted space ab initio models for double ionization by strong laser pulses

Double electron ionisation process occurs when an intense laser pulse interacts with atoms or molecules. Exact {\it ab initio} numerical simulation of such a situation is extremely computer resources demanding, thus often one is forced to apply reduced dimensionality models to get insight into the physics of the process. The performance of several algorithms for simulating double electron ionization by strong femtosecond laser pulses are studied. The obtained ionization yields and the momentum distributions of the released electrons are compared, and the effects of the model dimensionality on the ionization dynamics discussed