We propose a method for direct calculation of the multiply differential cross section of the single and double ionization of two-electron atomic and molecular systems, which involves the reduction of the initial nine-dimensional Schrödinger equation to an evolution problem followed by the modeling of the wave packet dynamics. The cross section is obtained by the method of a time-scaled coordinate system. This approach, which describes well the behavior of two slow ejected electrons, avoids the use of rather uncertain cumbersome complex final-state functions of the continuous spectrum. Our results agree with those obtained by the convergent-close-coupling approach which is the object of some reserve because of ambiguity about its asymptotic behavior.

The doubly differential cross sections (DDCS) of double electron capture in collisions of slow ${\mathrm{C}}^{4+}$ with He were measured in the energy range of 240, 320, and $440\mathrm{eV}$ (in laboratory frame) using a crossed-beam apparatus and represented as a two-dimensional contour map. The double-electron capture into the ${\mathrm{C}}^{2+}\left(1s^{2}2s^2{}^{1}S\right)$ state was found to be dominant in the present energy range. The Stückelberg oscillation structures, which result from interference among two different paths on the interaction potential curves, were clearly observed in the DDCS at the present low impact energies. The differential cross sections were also calculated in an ab initio molecular orbital framework for ${\left(\mathrm{C}\mathrm{He}\right)}^{4+}$, and show a good agreement with the present experimental results.

We present a theoretical approach to the problem of subthreshold plasmon excitation in proton-aluminum collisions. Based both on recent experimental results by Ritzau et al. [Phys. Rev. B 59, 15506 (1999)] and on previous calculations by two of the authors, we solve the master equations and obtain the probability of both plasmon excitation and nearly free electron excitation due to plasmon decay as functions of the projectile initial velocity. The mechanism considered for subthreshold plasmon excitation involves an intermediary fast electron as suggested by Ritzau et al.

We developed a method to determine the relaxation time of the innermost vacancies for highly ionized heavy ions moving through the bulk. The method compares the intensities of photons emitted through the front and back sides of a thin metal foil. Using foils with known thickness and x-ray absorption cross sections, we directly obtained the mean x-ray emission depth, and thereafter the mean relaxation time. We present data for the emission depth of highly charged $8.5q$ keV and $23.5q$ keV ${\mathrm{Pb}}^{q+}$ ions $(q=53–58)$ impacting on thin Ta foils. The mean relaxation time of $M$-shell vacancies is estimated to be between 22 and $68\mathrm{fs}$, depending on charge state of the projectile, which is about five times longer relaxation time than reported by Hattas et al. [Phys. Rev. Lett. 82, 4795 (1999)]. The experimental results are supported by a model calculation that combines molecular-orbital calculation for the ${\mathrm{Pb}}^{54+}\text{−}\mathrm{Ta}$ interaction system with a rate-equation model for inner-shell relaxation.

An inhomogeneous electric field is used to study the deflection of a supersonic beam of water molecules. The deflection profiles show strong broadening accompanied by a small net displacement towards higher electric fields. The profiles are in excellent agreement with a calculation of rotational Stark shifts. The molecular rotational temperature being the only adjustable parameter, beam deflection is found to offer an accurate and practical means of determining this quantity. A pair of especially strongly responding rotational sublevels, adding up to $\approx 25\%$ of the total beam intensity, are readily separated by deflection, making them potentially useful for further electrostatic manipulation.

Four-level atom dynamics is studied in a ladder system in the nine parameter space consisting of driving field strengths, detunings and decay constants, $\{{\Omega }_1,{\Omega }_2,{\Omega }_3,{\Delta }_1,{\Delta }_2,{\Delta }_3,{\Gamma }_2,{\Gamma }_3,{\Gamma }_4\}$. One can selectively excite or induce two-level behavior between particular levels of ones choice by appropriately tuning the driving field strengths at three-photon resonance. The dynamics may be classified into two main regions of interest (i) small ${\Omega }_2$ coupling the ∣2⟩-∣3⟩ transition and (ii) large ${\Omega }_2$. In case (i) one sees two-level behavior consisting of adjacent levels and in a particular region in the parameter space, there is an intermittent shelving of the electrons in one of the two subsystems. In case (ii) the levels consist of the ground state and the upper most level. Emission statistics is studied using the delay function approach in both the cases. In case (i), the behavior of the second order correlation function $g^2\left(t\right)$, is similar to that of two-level emission for low ${\Omega }_1$ coupling the ∣1⟩-∣2⟩ transition, and the correlation increases with ${\Omega }_1$ for smaller time delays. While, in case (ii) when, in addition, ${\Omega }_3$ coupling the ∣3⟩-∣4⟩ transitionis kept low, $g^2\left(t\right)$ shows superpoissonian distribution, which may be attributed to three-photon processes.

Storing and release of a quantum light pulse in a medium of atoms in the tripod configuration are studied. Each of these operations is realized by switching on and off two sets of properly chosen control fields. The system constitutes a kind of a flexible beam splitter in which the input and output ports concern photons of the same direction but well separated in time. A version of Hong-Ou-Mandel interference is discussed. It is also shown that a stored nonclassical light is split into two nonclassical beams, with their statistical properties being steered by a choice of the control fields.

In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.

We have studied the role of degenerate Zeeman states in the storage and retrieval of light pulses in the three-level $\Lambda$-type system of electromagnetically induced transparency. A probe pulse with the ${\sigma }_{+}$ polarization is stored in the medium and subsequently released with the ${\sigma }_{-}$ polarization. However, the manipulation of the retrieved polarization causes an energy loss. Our study shows that the incompatibility between the stored ground-state coherence and the ratio of the probe and coupling Clebsch-Gordan coefficients is responsible for the energy loss. Such energy loss can be avoided as long as all population accumulates in a single Zeeman state. We provide the useful knowledge for the light-storage technique and demonstrate that the degenerate Zeeman states should be considered in the relevant applications.

We propose a scheme for the measurement of the $s$-wave scattering length $a$ of an atom or molecule with significant dipole-dipole interaction with an accuracy at the percent level. The frequencies of the collective oscillations of a Bose-Einstein condensate are shifted by the magnetic dipole interaction. The shift is polarization dependent and proportional to the ratio ${\epsilon }_{\mathrm{dd}}$ of dipolar and $s$-wave coupling constants. Measuring the differences in the frequencies for different polarization we can extract the value of ${\epsilon }_{\mathrm{dd}}$ and thus measure $a$. We calculate the frequency shifts for a large variety of nonaxisymmetric harmonic traps in the Thomas-Fermi limit and find optimal trapping geometries to maximize the shifts.

We consider the van der Waals interaction between two ground-state atoms embedded in adjacent semi-infinite magnetodielectric media, with emphasis on medium effects on it. We demonstrate that, in this case, at small atom-atom distances the van der Waals interaction is screened by the surrounding media in the same way as in an effective (single) medium. At larger atomic distances, however, its dependence on the material parameters of the system and the positions of the atoms is more complex. We also calculate the Casimir-Polder potential of an atom $A$ arising from a uniform distribution of atoms $B$ in the medium across the interface. Comparison of this potential with the corresponding result deduced from the Casimir force on a thin composite slab in front of a composite semi-infinite medium, both obeying the Clausius-Mossotti relation, suggests a hint on how to improve a well-known formula for the van der Waals potential with respect to the local-field effects.

We consider treating the usual probabilistic cloning, state separation, unambiguous state discrimination, etc., in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive trace-nonincreasing maps on a finite number of input states. From the system-ancilla model we construct the corresponding unitary implementation of $\text{pure}\to \text{pure}$, $\text{pure}\to \text{mixed}$, $\text{mixed}\to \text{pure}$, and $\text{mixed}\to \text{mixed}$ state transformations in the whole system and obtain the necessary and sufficient conditions for the existence of the desired maps. We expect our work will be helpful to explore physically accessible transormations on a finite set of input states.

We consider the time-delayed coincidence counting of two photons emitted in a cascade by a single particle (atom, molecule, nucleus, etc.). The time-dependence of the probability amplitude of the second photon in the cascade has a sharply rising leading edge due to the detection of the first photon, as results from causality. If a macroscopic ensemble of resonant two-level absorbers is placed in the path of the second photon between the radiation source and the detector, the photon absorption does not follow Beer’s law due to the time-asymmetric shape of the photon. For very short delay times almost no absorption takes place, even in an optically dense medium. We analyze the propagation of such a second photon in a thick resonant three-level absorber if a narrow electromagnetically induced transparency (EIT) window is present at the center of the absorption line. It is shown that the EIT medium can change the asymmetric time dependence of the photon probability amplitude to a bell shape (EIT filtering). This bell-shaped photon interacts much more efficiently with another ensemble of two-level absorbers chosen, for example, to store this photon and the information it carries. Ideally a photon wave packet with a Gaussian time-envelope is most effectively stored.

We demonstrate loading of ${}^{88}\mathrm{Sr}^{+}$ ions into a $0.5\text{−}\mathrm{mm}$-scale printed circuit board surface-electrode ion trap. We then characterize the trap by measuring the secular frequencies and comparing them to a three-dimensional simulation of the trap, and by measuring the stray electric fields along two of the trap’s principal axes. Cancelling these fields by applying additional voltages enables a hundredfold increase in the trap lifetime to greater than ten minutes at a vacuum of ${10}^{-9}\text{torr}$.

We investigate the effect of an external periodic driving to the self-trapping transitions of two weakly coupled Bose-Einstein condensates in a double-well potential. It is shown that the self-trapping can be effectively controlled by modulating the double-well with a high frequency driving and thus renormalizing the transition parameters. In particular, an exact solution is constructed under the balance condition between the external field and the nonlinear interaction among particles, which allows one to precisely control theself-trapping states.

We have investigated the characteristics of quasibound states of a quadrupole-deformed microcavity both experimentally and theoretically. Five distinct single-mode groups are observed in the cavity emission spectra with their cavity quality factors varied by several orders of magnitude. Although the corresponding mode wave functions show qualitatively different geometrical shapes, these single modes exhibit almost identical far-field emission patterns, which contradicts a common understanding that the emission direction is usually associated with the geometry of the mode wave functions. The observed universal directionality is explained by a subtle manifestation of unstable manifolds of classical chaos in the formation of quasibound states.

We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.

We examine the maximum entanglement reached by an initially fully aligned state evolving in an $XY$ Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of $[n∕2]$ peaks in the global entanglement for an $n$-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite $n$-spin chains obtained through the Jordan-Wigner mapping, are discussed.

Using data from atomic Hartree-Fock calculations, we examine whether it is easier to predict the ionization potential of a system using its shape function or using its electron density. A simple linear combination of two moments of the shape function capably predicts the periodic trends in the ionization potential, while a similar expansion in terms of the electron density does not. While it is known that the shape function determines all the properties of an electronic system, this suggests that the shape function is actually more useful than the electron density for predicting periodic properties, where the dependence of the electron density on the number of electrons only obscures the essential phenomenon. We present a theoretical argument as to why this might be true. Generalizing our results, one suspects the shape function will be more useful than the electron density when examining molecules’ chemical properties.

A correction term to the hyperspherical hidden crossing method (HHCM) was previously derived for large hyperradius $R$ using the one-Sturmian theory. With the correction term, the HHCM potentials agree asymptotically with close-coupling channel potentials through order $1∕R^2$. Here, we present an optimal pair of paths in the complex $R$ plane for the inclusion of the correction term. With this new pair of paths, the correction term can be treated in a consistent way for the two levels associated with a transition. Using the new paths, we apply the HHCM with the correction term to calculate $s$-, $p$-, $d$-, and $f$-partial wave cross sections for Ps formation in $e^{+}\text{−}\mathrm{Li}$ collisions in the energy range $0–1.8\mathrm{eV}$. The comparison of the total Ps formation cross section, with both an accurate hyperspherical close-coupling calculation and experimental measurements, shows that the HHCM with the correction term is a reliable method to describe collisions involving three charged particles. A systematic study of the Stückelberg phase with respect to orbital angular momentum and momentum of the incident positron provides interesting insights into the scattering process.