We investigate the origin of coordinated two-electron ionization of atoms under irradiation by short, intense laser pulses. We introduce a wave-function masking technique that separates the wave function into multiple components, based on the location of the population at some preselected time. Propagating these components separately allows a semiclassical tracking of populations and recollision events, with the full wave function being obtainable at any time as the coherent sum of the masked components. This method reveals that for our model system the most significant pathway to coordinated double ionization involves a correlated recollision event in which the returning electron comes back to the core in opposition to the laser force.

We report heteronuclear photoassociation spectroscopy in a mixture of magneto-optically trapped ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}.$ The laser-induced decrease in the ${}^7\mathrm{Li}$ steady-state particle number, only appearing in the presence of ${}^6\mathrm{Li},$ gives clear evidence of photoassociation to form ${}^6{\mathrm{Li}}^7\mathrm{Li}.$ Hyperfine resolved spectra of the vibrational level $v=83\mathrm{}$ of the singlet state ${\mathrm{A}}^1{\Sigma }_u^{+}$ have been taken up to intensities of $1000{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The absolute resonance frequencies and the rotational constant have been measured. Saturation of the photoassociation rate has been observed for two hyperfine transitions, which can be shown to be due to saturation of the rate coefficient near the unitarity limit. Saturation intensities on the order of $40{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ can be determined.

Bright-soliton train creation and evolution in a Bose-Einstein condensate is simulated numerically using the experimental conditions of K. E. Strecker et al. [Nature 417, 150 (2002)] as a starting point. We identify the controlling factors that dictate soliton number, phase imprinting, and stability. Reliable production of multiple phase-engineered condensed-matter pulses can have practical applications to future nonlinear atom optics experiments, which we illustrate with an example of colinear scattering between repulsive solitons.

Suppose N parties describe the state of a quantum system by N possibly different density operators. These N state assignments represent the beliefs of the parties about the system. We examine conditions for determining whether the N state assignments are compatible. We distinguish two kinds of procedures for assessing compatibility, the first based on the compatibility of the prior beliefs on which the N state assignments are based and the second based on the compatibility of predictive measurement probabilities they define. The first procedure leads to a compatibility criterion proposed by Brun, Finkelstein, and Mermin [BFM, Phys. Rev. A 65, 032315 (2002)]. The second procedure leads to a hierarchy of measurement-based compatibility criteria which is fundamentally different from the corresponding classical situation. Quantum mechanically none of the measurement-based compatibility criteria is equivalent to the BFM criterion.

The energy of a fluctuating electromagnetic field is investigated for the thermal Casimir force acting between parallel plates made of a real metal. It is proved that for nondissipative media with temperature-independent dielectric permittivity the energy at nonzero temperature comprises the (renormalized) energies of the zero-point and thermal photons. In this manner photons can be considered as collective elementary excitations of the matter of plates and electromagnetic field. If the dielectric permittivity depends on temperature, the energy contains additional terms proportional to the derivatives of $\varepsilon$ with respect to temperature, and the quasiparticle interpretation of the fluctuating field is not possible. The correlation between energy and free energy is considered. Previous calculations of the Casimir energy in the framework of the Lifshitz formula at zero temperature and optical tabulated data supplemented by the Drude model at room temperature are analyzed. It is demonstrated that this quantity is not a good approximation either for the free energy or the energy. A physical interpretation of this hybrid quantity is suggested. The contradictory results in the recent literature on whether the zero-frequency term of the Lifshitz formula for the perpendicular polarized modes has any effective contribution to the physical quantities are discussed. Four main approaches to the resolution of this problem are specified. The precise expressions for entropy of the fluctuating field between plates made of a real metal are obtained, which helps to decide between the different approaches. The conclusion is that the Lifshitz formula supplemented by the plasma model and the surface impedance approach are best suited to describe the thermal Casimir force between real metals.

We discuss a restriction on relaxation times derived from the Lindblad-type master equations for two-level systems and show that none of the inverse relaxation times can be greater than the sum of the others. The relation is experimentally proved or disproved and can be considered to be a measure for or against the applicability of the Lindblad-type master equations, and therefore, of the so-called completely positive condition.

In this paper, we consider some frustrated spin models for which the ground states are known exactly. The concurrence, a measure of the amount of entanglement can be calculated exactly for entangled spin pairs. Quantum phase transitions involving macroscopic magnetization changes at critical values of the magnetic field are accompanied by macroscopic jumps in the $T=0\mathrm{}$ entanglement. A specific example is given in which magnetization plateaus give rise to a plateau structure in the amount of entanglement associated with nearest-neighbor bonds. We further show that macroscopic entanglement changes can occur in quantum phase transitions brought about by the tuning of exchange interaction strengths.

A nonlocal unitary transformation of two-qubits occurs when some Hamiltonian interaction couples them. Here we characterize the amount, as measured by time, of interaction required to perform two-qubit gates, when also arbitrarily fast, local unitary transformations can be applied on each qubit. The minimal required time of interaction, or interaction cost, defines an operational notion of the degree of nonlocality of gates. We characterize a partial order structure based on this notion. We also investigate the interaction cost of several communication tasks, and determine which gates are able to accomplish them. This classifies two-qubit gates into four categories, differing in their capability to transmit classical, as well as quantum, bits of information.

Schemes of experimental realization of the main two-qubit processors for quantum computers and the Deutsch-Jozsa algorithm are derived in virtual spin representation. The results are applicable for every four quantum states allowing the required properties for quantum processor implementation if for qubit encoding, virtual spin representation is used. A four-dimensional Hilbert space of nuclear spin $3/2$ is considered in detail for this aim.

Two-photon $E1M1\mathrm{}$ transition rates are evaluated for heliumlike ions with nuclear charges in the range $Z=50\mathrm{}–94.$ The two-photon rates modify previously published lifetimes/transition rates of $2^3{P}_0$ states. For isotopes with nuclear spin $I\ne 0,$ where hyperfine quenching dominates the $2^3{P}_0$ decay, two-photon contributions are significant; for example, in heliumlike ${}^{187}$Os the two-photon correction is 3% of the total rate. For isotopes with $I=0,$ where the $2^3{P}_0$ decay is unquenched, the $E1M1\mathrm{}$ corrections are even more important reaching 60% for $Z=94.\mathrm{}$ Therefore, to aid in the interpretation of experiments on hyperfine quenching in heliumlike ions and to provide a more complete database for unquenched transitions, a knowledge of $E1M1\mathrm{}$ rates is important.

It is usually assumed that the first-Born approximation for electron-atom ionization becomes valid for the fully differential cross section at sufficiently high impact energies, at least for asymmetric collisions where the projectile suffers only a small energy loss and is scattered by a small angle. Here we investigate this assumption quantitatively for ionization of hydrogen atoms. We find that convergence of the Born approximation to the correct nonrelativistic result is generally achieved only at energies where relativistic effects start to become important. Consequently, the assumption that the Born approximation becomes valid for high energy is inaccurate, since by the time it converges, nonrelativistic scattering theory is not valid.

Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, require some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities that may hide important physical aspects of the problem. In this work we present a method to calculate the exact Green functions for general point interactions in one dimension. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients R and T to construct G. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of N general point interactions, on a line, on a half-line, under periodic boundary conditions, and confined in a box.

The mechanism of transverse radiation viscosity acting on free charges, atomic, and small macroscopic particles in uniform electromagnetic fields is analyzed. It is shown that in the process of light scattering by these particles, besides the force accelerating them in the direction of propagation of the radiation, there is a force in the transverse direction slowing them down. The general expression for this force is obtained. It is considered how this force can influence: (i) the motion of ultrarelativistic electrons in transverse photon fluxes; (ii) the behavior of a beam of nonrelativistic electrons moving in a copropagating uniform electromagnetic field; (iii) the transverse motion of atoms under the action of resonant radiation and (iv) the motion of small macroscopic particles.

Single-atom high-order harmonic generation is considered in the strong-field approximation, as formulated in the Lewenstein model, and analyzed in terms of quantum orbits. Orbits are classified according to the solutions of the saddle-point equations. The results of a numerical integration are compared with the saddle-point approximation and the uniform approximation. Approximate analytical solutions for long orbits are presented. The formalism developed is used to analyze the enhancement of high-order harmonic generation near channel closings. The enhancements exactly at the channel closings are extremely narrow and built up by the constructive interference of a very large number of quantum orbits. Additional broader enhancements occur slightly below channel closings. They are generated by the interplay of a medium number of orbits.

We extend to more than one spatial dimension the semiclassical full-wave vector Maxwell-Bloch equations for the purpose of achieving an adequate and rigorous description of ultrashort pulse propagation in optical waveguides containing resonant nonlinearities. Our considerations are based on the generalized pseudospin formalism introduced by Hioe and Eberly [Phys. Rev. Lett. 47, 838 (1981)] for treatment of the resonant coherent interactions of ultrashort light pulses with discrete-multilevel systems. A self-consistent set of coupled curl Maxwell-pseudospin equations in two spatial dimensions and time for the special case of a degenerate three-level system of quantum absorbers is originally derived. Maxwell’s curl equations are considered to be coupled via macroscopic medium polarization to the three-level atom model for the resonant medium. Two distinct sets of pseudospin equations are obtained corresponding to the TE- and TM-polarized optical waves. For the case of TM polarization, the electromagnetic wave is polarized in a general direction in the plane of incidence inducing two dipole transitions in a degenerate three-level system by each E-field component along the propagation axis and in transverse direction. We introduce a dipole-coupling interaction Hamiltonian allowing Rabi flopping of the population difference along and perpendicular to the propagation axis with frequencies depending on the corresponding field components. The relationship between the induced polarization and the state vector components that describe the evolution of the discrete-level system is derived in order to couple the quantum system equations to the Maxwell’s curl equations. The pseudospin equations are phenomenologically extended to include relaxation effects by introducing nonuniform decay times corresponding to the various dipole transitions occurring in a three-level system. The system has been discretized using finite differences on a Yee grid and solved numerically by an iterative predictor-corrector finite-difference time-domain method. Self-induced transparency soliton propagation through a degenerate three-level quantum system of absorbers in two spatial dimensions and time is demonstrated in planar parallel-mirror waveguide geometries.

A two-loop perfect-crystal neutron interferometer was used for the quantitative determination of which-way (WW) information and the verification of the duality relation between predictability and visibility. Our interferometer has two remarkable features, it allows the absorption-free tuning of WW information and it enables the simultaneous measurement of the duality relation without changing the interferometer setup. In addition, the duality relation of three interfering beams is a good demonstration that WW information should not be misused as particle property because one interferometer beam remains in a coherent superposition of two path alternatives, which is not consistent with the particle picture. The coherent WW tuning was performed without changing the neutron’s momentum and without dephasing.

The dynamics of head-on collisions of gravitationally bound Bose-Einstein condensates is studied. A fully consistent Schrödinger-Poisson system is solved numerically assuming axial symmetry about the axis of collision. Here, the investigation is focused on the regime where the head-on collisions of binary condensates exhibit solitonic nature of the condensates, inelastic collision properties, collision-induced collapse instability (in the case of attractive atomic interaction), and characteristic interference patterns that depend on the phase information (speed) of the colliding condensates.

The Bose-Einstein condensation in trapped gases of ${}^{85}\mathrm{Rb}$ at densities beyond the dilute regime can now be realized taking advantage of Feshbach resonances. The gas density may be characterized by the parameter ${\mathrm{na}}^3,$ where $n=N/V$ is the number density and a is the scattering length which is tuned using Feshbach resonance. We explore the properties of interacting trapped bosons in the density range $5\times {10}^{-3}<~{\mathrm{na}}^3<~5\times {10}^{-2}$ using Monte Carlo methods to compare with experiments. We find that there is a significant depletion of the condensate at $T=0\mathrm{}\mathrm{K},$ for example, $25\%$ at ${\mathrm{na}}^3{=10\mathrm{}}^{-2}.$ The condensate is not concentrated at the center of the trap but is spread out over four or five trap lengths. The condensate density distributions and the total density distributions within the trap are very similar and the condensate fraction is $100\%$ at the edges of the trap.

We present a comparative theoretical analysis of five different atomic schemes with respect to their performance as negative (anomalous) dispersive transparent media. The schemes discussed are the strongly driven and the degenerate two-level system, two closely spaced gain lines, and two slightly different double-$\Lambda$ schemes with incoherent pumping. The analysis shows that the degenerate two-level scheme is best suited for applications for which only modest negative dispersion but strongly reduced absorption is required, and dissipation and loss of the optical fields have to be avoided. Two closely spaced gain lines and one of the double-$\Lambda$ schemes are the best choice for applications which rely on large negative dispersion, but are not too sensitive to residual absorption and dissipation.

A time-dependent theory for conical emission during near-resonant propagation of laser light in an atomic vapor, which includes full propagation for the laser and frequency sidebands in a nonlinear two-level medium is presented. The density-matrix equations for the dipole moment and population are solved in the dressed atomic frame. The polarization source terms are accurate to order γ/R, where γ is a damping constant and R is the generalized Rabi frequency. Analytical plane-wave solutions and numerical, cylindrically symmetric propagation simulations including diffraction are presented. It is shown that the calculations with cylindrically symmetric fields and atomic excitation profiles are incapable of accounting for the high levels of optical gain that are responsible for the intense conical emission observed in experiments. This result is at first surprising, since the model accounts rigorously for all of the physical phenomena that have been previously proposed as being responsible for generating large gains, and the calculation matches the symmetry of the observations. The lack of large calculated gain seems to imply the existence of higher-order $\mathrm{}(m>\mathrm{}0\mathrm{})\mathrm{}$ radial modes in the field for the experimental conditions that give rise to cone emission. In the simulations, however, the cylindrically symmetric fields do produce weak red-detuned cones with angular-frequency distributions similar to those seen in experiments.