We describe the implementation of a quantum mechanical method to calculate state-to-state differential cross sections for atom-diatom reactive scattering processes. The key ingredient of this approach is the efficient and accurate propagation of a real scattering wave packet in the Chebyshev order domain, from which the $S$-matrix elements can be extracted. This approach is implemented with Open MP and applied to compute differential and integral cross sections for the direct $\mathrm{H}+{\mathrm{H}}_2$ abstraction reaction and the more challenging $\mathrm{N}\left({}^{2}D\right)+{\mathrm{H}}_2$ insertion reaction.

We question the conclusions reached by De Castro et al. [Phys. Rev. A 72, 023410 (2005)] regarding the theoretical analysis of experimental results by Laarman et al. [Phys. Rev. A 72, 023409 (2005)] on photoionization of He in the presence of a strong free-electron laser radiation pulse.

We cannot agree with the Comment by Maquet et al. [Phys. Rev. A. 74, 027401 (2006)]. It seems that Maquet et al. are thinking in terms of classical fields. In our recent paper we have presented a study of the two-photon rate of He making use of quantized fields. This approach becomes a natural choice if we have in mind processes at high photon energy. In this description of the problem the squared vector potential $\mathbf{A}\bullet \mathbf{A}$ term is essential.

We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically, we show that the effects of the low-dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high-temperature regime of the Caldeira-Leggett model.

We study the effects of losses on the entanglement created between two separate atomic gases by optical probing and homodyne detection of the transmitted light. The system is well-described in the Gaussian state formulation. Analytical results quantifying the degree of entanglement between the two gases are derived and compared with the entanglement in a pair of light pulses generated by an Einstein-Podolsky-Rosen (EPR) source. For low (high) transmission losses, the highest degree of entanglement is obtained by probing with squeezed (antisqueezed) light. In an asymmetric setup where light is only sent one way through the atomic samples, we find that the logarithmic negativity of entanglement attains a constant value $-{\log }_2\left(N\right)$ with $N=1∕3$, irrespective of the loss along the transmission line.

We calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbor coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of four spins.

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.

The formation of the $\left[1s2s\right]$ $S$ states in heliumlike uranium $\left({\mathrm{U}}^{90+}\right)$ has been studied in relativistic collisions of initially lithiumlike uranium $\left({\mathrm{U}}^{89+}\right)$ ions with ${\mathrm{N}}_2$ target molecules. By measuring projectile x-ray emission in coincidence with projectile ionization, a strong selectivity for the formation of the $\left[1s2s\right]$ $S$ states in heliumlike uranium is observed. This selectivity is found to be unaffected by the subsequent rearrangement of the atomic orbitals involved. By measuring the photon emission associated with the decay of the $\left[1s2s\right]$ ${}^{1}S_0$ and the $\left[1s2s\right]$ ${}^{3}S_1$ substates, we obtain for their relative population probabilities a ratio of close to 1. This finding deviates considerably from the assumption of a statistical distribution $2J+1$.

The photoionization cross sections of two even-parity excited states $5d6d{}^{3}D_1$ and $6s7d{}^{3}D_2$ of atomic Ba at the ionization-laser wavelength of $556.6\mathrm{nm}$ were measured. We found that the total cross section depends on the relative polarization of the atoms and the ionization-laser light. With density-matrix algebra, we show that, in general, there are at most three parameters in the photoionization cross section. Some of these parameters are determined in this work. We also present the measurement of the radiative lifetime of five even-parity excited states of barium.

Collision-induced properties of two interacting molecules $a$ and $b$ are derived by means of a general diagrammatic method involving $M$ molecule-molecule and $N$ photon-molecule couplings. The method is an extension of previous graphical treatments of nonlinear optics because it exhaustively determines interaction-induced polarization mechanisms in a trustworthy and handy fashion. Here we focus on long-range intermolecular interactions. Retardation effects are neglected. A fully quantum-mechanical treatment of the molecules is made whereas second quantization for the electromagnetic field, in the nonrelativistic approximation, is implicitly applied. The collision-induced absorption, Raman, and hyper-Raman processes are viewed and studied, through guiding examples, as specific cases $N=1$, 2, and 3, respectively. In Raman $(N=2)$, the standard first-order $(M=1)$ dipole-induced dipole term of the incremental polarizability, $\mathrm{\Delta }\widehat{\alpha }$, is the result of a coupling of the two photons with distinct molecules, $a$ and $b$, which perturb each other via a dipole-dipole mechanism. Rather, when the two photons interact with the same molecule, $a$ or $b$, the ($N=2$, $M=1$) graphs predict the occurrence of a nonlinear polarization mechanism. The latter is expected to contribute substantially to the collision-induced Raman bands by certain molecular gases.

The dynamics of recombination in ultrastrong laser fields is studied by numerical simulations for one-dimensional model atomic systems. A nonmonotonic behavior of the ground-state final population as a function of the laser field amplitude is demonstrated. It is attributed to both the slow drift of the electron wave packet and the nontrivial field dependence of the lifetime of the eigenstates of the Kramers-Henneberger well.

We propose two schemes for cooling bosonic and fermionic atoms that are trapped in a deep optical lattice. The first scheme is a quantum algorithm based on particle number filtering and state dependent lattice shifts. The second protocol alternates filtering with a redistribution of particles by means of quantum tunnelling. We provide a complete theoretical analysis of both schemes and characterize the cooling efficiency in terms of the entropy. Our schemes do not require addressing of single lattice sites and use a novel method, which is based on coherent laser control, to perform very fast filtering.

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.

Unidirectional half-cycle pulses (HCP) are ideally suitable for shaping, driving, and probing atomic wave packets in momentum space. The shortest HCP presently available have a width of about $500\mathrm{fs}$ restricting the manipulation of electronic wave packets to those in high-lying Rydberg states. The nonlinear harmonic response of atoms to strong two-color infrared laser pulses with frequencies $\omega$ and $2\omega$ opens up the opportunity to form trains of ultrafast HCP’s on an attosecond time scale. In the present contribution, we investigate the influence of macroscopic propagation effects onto the production of HCP and show that trains of unidirectional attosecond HCP’s could be produced under experimentally realistic conditions.

A highly compact four-parameter form for helium’s approximate nonrelativistic wave function is proposed and shown to yield an energy expectation value within $0.003\mathrm{a.u.}$ of the “exact” value. The wave function employs proper atomic-number-parametrized hydrogenic orbitals and a correlation function whose form is $[1+(1∕2)r_{12}{e}^{-\alpha r_{12}}]$, coupled with a variationally determined expansion in $r_1$, $r_2$, and $r_{12}$.

The photoelectron spectra (PES) excited by narrow bandwidth femtosecond x rays in the presence of a femtosecond laser were investigated. Two transfer equations were found which can be used to precisely reconstruct the detailed x-ray profile from the measured PES. The reconstruction is a direct procedure without any previous pulse-shape assumption. The method has high time resolution and broad temporal measurement range which depend on the laser and x-ray parameters.

It is shown that Smolin four-qubit bound entangled states [J. A. Smolin, Phys. Rev. A 63, 032306 (2001)] can maximally violate the simple two-setting Bell inequality similar to the standard Clauser-Horne-Shimony-Holt (CHSH) inequality. The simplicity of the setting and the robustness of the entanglement make it promising for current experimental technology. On the other hand, the entanglement does not allow for secure key distillation, so neither entanglement nor maximal violation of Bell inequalities implies directly the presence of a quantum secure key. As a result, one concludes that two tasks—reducing of communication complexity and cryptography—are not (even qualitatively) equivalent in a quantum multipartite scenario.

We investigate the theory of a few photons on demand from a single two-level emitter excited by a square laser pulse. Using the generalized optical Bloch equations, we find exact expressions for the probability of generating zero, one, two, and three photons, the average $⟨N⟩$, and Mandel’s $Q$ parameter, which exhibit rich physical behaviors. The exact solution is used to design control fields that yield an optimal single- or two-photon source, under the constraints of finite laser-field strength and finite interaction time.

We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. We show that the enhanced completely cross fifth-order nonlinearity generated in such a system can be used to produce efficient three-way entanglement and to realize a three-qubit quantum phase gate. We demonstrate that such phase gate can be transferred to an all-optical Toffoli gate, facilitating practical applications in quantum information and computation.