A development of the techniques for solving the quasirelativistic Hartree-Fock equations for quasirelativistic atomic calculations published earlier [Phys. Rev. A 74, 052501 (2006)] is presented. Trial calculations using these techniques revealed that the one-electron characteristics and spin-orbit splitting are less precise in the case of $p$ electrons. To overcome this problem, a different method of averaging the spin-orbit interaction within the quasirelativistic Hartree-Fock equation is proposed for $p$ electrons. The specific account of the contact interaction in the case of $p$ electrons is discussed. The technique for calculating the spin-orbit interaction constant while using the quasirelativistic radial orbitals is presented. Since the pecularities appear on the level of one-electron interactions, only hydrogenlike ions are investigated. Data revealing how the methods under discussion influence the results obtained are presented.

A study of the combined effects of correlation, confinement and relativistic effects on the photoionization of the outer $ns$ subshells of the alkaline-earth-metal atoms, Mg, Ca, Sr and Ba has been performed with particular emphasis on the Cooper minima using the relativistic-random-phase approximation (RRPA) methodology. It is found that the response of the Cooper minima to these various effects can be rather different behavior for the various atoms considered. On the other hand, relativistic effects were found to be essentially obliterated by confinement, in all cases. The situations are analyzed in detail and qualitative understanding of most of the phenomenology is presented.

We report cross sections for low-energy elastic electron collisions with the diazabenzene molecule pyrazine, obtained from first-principles calculations. The integral elastic cross section exhibits three sharp peaks that are nominally shape resonances associated with trapping in the vacant ${\pi }^{*}$ molecular orbitals. Although the two lowest-energy resonances do in fact prove to be nearly pure single-channel shape resonances, the third contains a considerable admixture of core-excited character, and accounting for this channel coupling effect is essential to obtaining an accurate resonance energy. Such resonant channel coupling has implications for electron interactions with the DNA bases, especially the pyrimidine bases for which pyrazine is a close analog. In the absence of data on pyrazine itself, we compare our elastic differential cross section to measurements on benzene and find close agreement.

We consider a spinor condensate of ${}^{87}\mathrm{Rb}$ atoms in its $F=1$ hyperfine state at finite temperatures. Putting initially all atoms in $m_F=0$ component we find that the system evolves into the state of thermal equilibrium. This state is approached in a steplike process and when established it manifests itself in distinguishable ways. The atoms in states $m_F=+1$ and $m_F=-1$ start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the $m_F=+1$ and $m_F=-1$ spinor condensate components periodically lose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.

Dilute Fermi systems with large $s$-wave scattering length $a_s$ exhibit universal properties if the interparticle spacing $r_0$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, $r_0$ is the only relevant length scale and observables such as the energy per particle depend only on $r_0$ (or, equivalently, the energy $E_{\mathrm{FG}}$ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum $l$ using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an $l$-dependent length scale ${\xi }_l$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite $l$. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.

We study Bose-Einstein condensation in a harmonic trap with a dimple potential. We specifically consider the case of a tight and deep dimple potential which is modeled by a Dirac $\delta$ function. This allows for simpler, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrödinger equation is used instead of the Gross-Pitaevski equation. Calculating the atomic density, chemical potential, critical temperature, and condensate fraction, the role of the relative depth of the dimple potential with respect to the harmonic trap in large condensate formation at enhanced temperatures is clearly revealed.

The atom diode is a laser device that lets the ground-state atom pass in one direction but not in the opposite direction. We examine three-dimensional effects of that device for arbitrary atomic incidence angles on flat laser sheets, and set breakdown limiting angles and velocities. It is found that a correct diodic behavior, independent of the incident angle, can be obtained with blue-detuned lasers.

Quaternionic quantum mechanics has been revealed to be a very useful framework to describe quantum phenomena. In the case of two qubit compound systems we show that the complex projection of quaternionic pure states and quaternionic unitary maps permits the description of interesting phenomena such as decoherence and optimal entanglement generation. The approach, however, presents severe limitations for the case of multipartite or higher dimensional bipartite quantum systems as we point out.

The exponential speedup of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that quantum mechanics can also lead, through the phenomenon of localization, to exponential suppression of motion on these graphs (even in the absence of decoherence). In fact, for physical embodiments of graphs, this will be the generic behavior. It also has implications for proposals for using spin networks, including spin chains, as quantum communication channels.

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength $J$ (in units of Hz), significantly faster than ${\left(2J\right)}^{-1}$ per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing.

Transferring quantum information between two qubits is a basic requirement for many applications in quantum communication and quantum-information processing. In the iterative quantum-state transfer proposed by Burgarth et al. [Phys. Rev. A 75, 062327 (2007)], this is achieved by a static spin chain and a sequence of gate operations applied only to the receiving end of the chain. The only requirement on the spin chain is that it transfers a finite part of the input amplitude to the end of the chain, where the gate operations accumulate the information. For an appropriate sequence of evolutions and gate operations, the fidelity of the transfer can asymptotically approach unity. We demonstrate the principle of operation of this transfer scheme by implementing it in a nuclear magnetic resonance quantum-information processor.

We numerically study protocols consisting of repeated applications of two qubit gates used for generating random pure states. A necessary number of steps needed in order to generate states displaying bipartite entanglement typical of random states is considered. Numerics indicates that for a generic two qubit entangling gate the decay of purity is exponential with the decay time scaling as $\sim n$, implying that of order $\sim n^2$ steps are needed to reach random bipartite entanglement. We also numerically identify the optimal two qubit gate for which the convergence is the fastest. Perhaps surprisingly, applying the same good two qubit gate in addition to a random single qubit rotations at each step leads to a faster generation of entanglement than applying a random two qubit transformation at each step.

We have measured the vibrationally resolved partial cross sections ${\sigma }_{(v_1^{\prime },v_2^{\prime },v_3^{\prime })}$ and asymmetry parameters ${\beta }_{(v_1^{\prime },v_2^{\prime },v_3^{\prime })}$ for ${\mathrm{N}}_{\mathrm{c}}$ and ${\mathrm{N}}_{\mathrm{t}}$ $K$-shell photoionization of the ${\mathrm{N}}_2\mathrm{O}$ molecule in the ${\sigma }^{*}$ shape resonance region above the ${\mathrm{N}}_{\mathrm{t}}$ and ${\mathrm{N}}_{\mathrm{c}}$ $K$-shell ionization thresholds. ${\mathrm{N}}_{\mathrm{c}}$ $K$-shell photoionization of the ${\mathrm{N}}_2\mathrm{O}$ molecule predominantly causes the excitation of the quasisymmetric vibrations $\left(v_1^{\prime }\right)$, whereas ${\mathrm{N}}_{\mathrm{t}}$ $K$-shell photoionization causes both quasisymmetric and quasiantisymmetric vibrations ($v_1^{\prime }$ and $v_3^{\prime }$) to be excited. The shape resonance energy in the ${\mathrm{N}}_{\mathrm{c}}$ $K$-shell photoionization increases with an increase in $v_1^{\prime }$. The ${\beta }_{(v_1^{\prime },0,0)}$ curves for the ${\mathrm{N}}_{\mathrm{c}}$ $K$-shell photoionization exhibit maxima at energies close to the shape resonance energies for the individual values of $v_1^{\prime }$. The shape resonance energy in the ${\mathrm{N}}_{\mathrm{t}}$ $K$-shell photoionization decreases with an increase in $v_1^{\prime }$ and slightly increases with an increase in $v_3^{\prime }$. The ${\beta }_{(v_1^{\prime },0,0)}$ curves show a significant state dependence in the region of the shape resonance, with the curves shifting to lower energy as $v_1^{\prime }$ increases. The vibrational state dependence of the cross sections ${\sigma }_{(v_1^{\prime },v_2^{\prime },v_3^{\prime })}$ and asymmetry parameters ${\beta }_{(v_1^{\prime },v_2^{\prime },v_3^{\prime })}$ are well reproduced by the theoretical calculations using the multichannel Schwinger configuration interaction (MCSCI) method, including both the ${\mathrm{N}}_{\mathrm{c}}$ and ${\mathrm{N}}_{\mathrm{t}}$ ion states.

The dynamics of an initially sharp-boundary wave packet in the presence of an arbitrary potential barrier is investigated. It is shown that the penetration through the barrier is universal in the sense that it depends only on the values of the wave function and its derivatives at the boundary. The dependence on the derivatives vanishes at long distances from the barrier, where the dynamics is governed solely by the initial value of the wave function at the boundary.

We report a theoretical study of elastic electron collisions on three isoelectronic free radicals, namely, $\mathrm{SiNN}$, $\mathrm{SiCO}$, and $\mathrm{CSiO}$. More specifically, differential, integral, and momentum-transfer cross sections are calculated and reported in the $(1–100)\mathrm{eV}$ energy range. Calculations are performed at the static-exchange-polarization-absorption level of approximation. A combination of the iterative Schwinger variational method and the distorted-wave approximation is used to solve the scattering equations. Our study reveals that the calculated cross sections for the $e^{-}\text{−}\mathrm{SiNN}$ and $e^{-}\text{−}\mathrm{SiCO}$ collisions are very similar even at incident energies as low as $3\mathrm{eV}$. Strong isomeric effects are also observed in the calculated cross sections for $e^{-}\text{−}\mathrm{CSiO}$ and $e^{-}\text{−}\mathrm{SiCO}$ collisions, particularly at incident energies below $20\mathrm{eV}$. It is believed that the position of the silicon atom being at the center or extremity of the molecules may exert important influence on the calculated cross sections.

This paper presents an investigation of the charge-state and energy dependences of transfer-ionization (TI) and single-electron-capture (SC) processes for fluorine ions ($q=4+$ to $9+$) incident on a supersonic He jet target. The measurements were made for beam energies between 0.5 and $2.5\mathrm{MeV}∕\mathrm{u}$. A recoil ion momentum spectrometer was used to separate TI and SC based on the longitudinal momentum transfer and time of flight of the recoil ions. The cross-section ratios for TI to SC, $R={\sigma }_{\mathit{TI}}∕{\sigma }_{\mathit{SC}}$, were determined and observed to decrease monotonically with velocity. The values of $R$ were combined with measured total transfer cross sections to deduce the cross sections for both SC and TI. Coupled-channel calculations of the energy dependence of TI and SC for ${\mathrm{F}}^{9+}+\mathrm{He}$ were compared to the experimental cross sections as well as the values of $R$. The calculated cross sections were found to be slightly lower and the $R$ values slightly higher than the measured values, but with approximately the same energy dependences. A $q^2$ scaling of the ${\mathrm{He}}^{2+}+\mathrm{He}$ data was also compared to the present data and was found to give unexpected good agreement.

The temporal evolution of populations has been directly measured for a three-level ladder system undergoing coherent excitation by stimulated Raman adiabatic passage (STIRAP). The measurement technique makes use of charge transfer as diagnostic. The method is model independent and has a temporal resolution of a few nanoseconds. The temporal evolution is measured for several values of the delay between the pump and Stokes laser pulses that are part of the STIRAP excitation scheme. The corresponding quantum Liouville equations are solved and the results of the calculations are compared with experiment.

Using the alternative representation of time-dependent Hamiltonians that describe laser-driven systems [I. Gilary and N. Moiseyev, Phys. Rev. A 66, 063415 (2002)], we have performed calculations for the stability of ${\text{He}}^{-}$ in a superintense linearly polarized laser field. We estimated the laser parameters, amplitude, and frequency needed to stabilize ${\text{He}}^{-}$. If we choose the laser frequency $\omega =5\text{eV}$, the laser intensity needed for stabilization is $I^{\text{critical}}=9.0\times {10}^{15}\text{W}∕{\text{cm}}^2$ and the maximal detachment energy is 1.0 eV. Our results show that high frequencies and large intensities are preferred for stabilizing multiply negative atomic ions in superintense laser fields.

The coherent control of scattering processes is considered, with electron impact dissociation of used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies.