The ionization of ${\mathrm{H}}_2,$ leading to ${\mathrm{H}}_2^{+}$ recoil ions in nondissociative states, and the ionization of He by incident ${\mathrm{He}}^{+}$ ions were investigated in the 0.25–1.23-a.u. impact velocity range employing electron and target recoil-ion momentum-imaging techniques. Similarities as well as differences were observed in the electron velocity distributions from ${\mathrm{H}}_2$ and He targets. In both cases the data strongly suggest of the promotion of molecular orbitals formed between target and projectile within a rather well-defined projectile velocity window. In particular, the data support the promotion of the $2p\pi$ molecular orbital populated via rotational coupling. Outside this molecular promotion window, in particular at lower velocities, mechanisms of a different kind appear to dominate the ionization process, and electron momentum distributions are very dissimilar for He and ${\mathrm{H}}_2.$ Reduced projectile scattering cross sections, derived from measured target recoil-ion transverse momentum distributions, support these conclusions and point to the coexistence, at certain impact velocities, of different ionization mechanisms.

We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\Lambda$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\Lambda$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.

Just as it is possible to stabilize the frequency of an electromagnetic field to an atomic resonance between energy eigenstates, it is possible to stabilize the intensity or brightness of a field to an atomic Rabi resonance. For ease of reference, such a stabilized field is termed an “atomic candle.” Here, we describe a microwave atomic candle based on the $(F=2,$ $m_F=0)$–$(F=1,$ $m_F=0)$ ground-state hyperfine transition of ${}^{87}\mathrm{Rb}$ (6834.7 MHz) as observed in an optically pumped vapor. We discuss the atomic candle’s operation and the intensity stability of the field it produces (relative to the Rabi-resonance peak). We then discuss our use of the candle to investigate Rabi-resonance shifts. Specifically, we find that the Rabi resonance depends on the ac Stark shift of the hyperfine transition, the microwave field-atom detuning, and the alkali-metal vapor temperature.

For the process of intracavity second-harmonic generation in the region of unstable dynamics, the joint fluctuations of numbers of photons and phases of the fundamental mode and second harmonic are studied in positive P representation. It is shown that above the bifurcation point of the optical system the distribution functions of the phases of the fundamental mode and second harmonic have a two-component structure. The quantum trajectories of the phases of these modes are not localized in the components of their states, which demonstrates the presence of quantum-mechanical interference between these components. In both components of each state the same values of numbers of photons are realized. It is shown that in the case of coherent initial states of both modes the joint distribution functions of the numbers of photons and phases are in the oscillatory regime. With time, the modes pass from a two-component delocalized state to a one-component one and then back to the two-component state. The time of oscillation of the distribution function is of the order of the photon’s lifetime in the cavity volume. Self-matching of phases of interacting modes is investigated above the bifurcation point.

We give a detailed account of a recently introduced technique to suppress distinguishing information in the space-time component of the state vector of a pair of photons. The method works by creating interference between two possible ways for each photon to occupy any given space-time mode. Under certain conditions, this technique also allows the preparation of the two photons in a highly entangled space-time state.

We present detailed considerations on the achievable sensitivity in the measurement of birefringence using a high finesse optical cavity, emphasizing techniques based on frequency metrology. Alternative approaches of laser locking and cavity measurement techniques are discussed and demonstrated. High-precision measurements of the cavity mirror birefringence have led to the interesting observations of photorefractive activities on mirror surfaces.

In the density-functional formalism (DFF), the ground state of any electron system is described by a unique universal energy functional of the density. Thus the functional has to describe properly the dimensional crossover (DC), i.e., the functional for a system confined in $d-1$ spatial dimensions must result from the functional for the d-dimensional system when its density profile becomes a δ function along one of the coordinates. As a first step in the study of DC within DFF for electron systems, we present a study of the ability of density kinetic-energy functionals to behave correctly at the DC. We conclude that the weighted density approximation is the best suited to describe the strict DC, but it fails to describe systems with a small, but finite, width along the constrained coordinate. In contrast, the average density approximations, which diverge at the strict DC, are the best functionals to describe these highly inhomogeneous systems close to the DC.

We derive the classical threshold law for the breakup of three charged particles interacting via long-range Coulomb forces for the case of a charge ratio of $1/4$ between the particles involved. The Wannier exponent in canonical Wannier theory is known to diverge in this case. We find that the classical threshold law, which is proportional to $\exp (-\lambda /\sqrt{E}),$ shows exponential suppression of the ionization probability at threshold. We thus identify the possibility that exponential behavior in breakup processes, typically attributed to quantum-mechanical tunneling, can arise as a completely classical dynamical effect. We show that in the limit of zero energy, the behavior of the cross section is characterized by a classical to quantum transition. We discuss the regime of parameters in which this transition occurs and the possibility of an experimental observation of this transition.

In recent years a significant amount of research in quantum optics has been devoted to the analysis of atomic three-level systems and for many physical quantities the same effects have been predicted for different configurations. These configurations can be split into essentially two classes. One for which the system contains a metastable state and another where the system has two close-lying levels and coherence effects become important. We demonstrate when and why for a wide range of parameters these two classes are, in fact, equivalent for many important physical quantities. A unified picture underlying a large body of work on these categories of atomic three-level systems is presented and applied to some examples.

Cross sections for radiative electron capture (REC) by 33-TeV ${\mathrm{Pb}}^{82+}$ ions in Be and C targets have been extracted from an analysis of measurements of total electron capture by these ions in Be, C, Al, Cu, Sn, and Au targets. The REC cross sections in the Be and C targets, where REC is significant, were obtained by subtracting cross sections for electron capture from pair production (ECPP), the only other significant capture process at these energies. The ECPP contributions in Be and C were determined from extrapolations of measured cross sections in the heavier targets where the ECPP process dominates, with suitable accounting for slightly decreased screening effects for the light targets. We obtain an experimental $K-\mathrm{REC}$ cross section $(0.010\mathrm{}\pm 0.002\mathrm{b}$ per electron per Pb K vacancy), which agrees with a calculation of REC made by applying detailed balance to the corresponding process of radiative recombination and using tabulated photoelectric effect cross sections. A comparison is also presented of the present experimental result with other heavy-ion measurements made at lower energies, and with nonrelativistic and relativistic calculations, which differ considerably in this energy regime.

We present an alternative method for laser cooling of atoms close to the one-dimensional recoil limit. This method is particularly suited for atoms not accessible to conventional sub-Doppler cooling methods. It is based on the repeated selection and accumulation of slow atoms from a precooled atomic cloud and on the repeated rethermalization of the remaining atoms. The prepared ensemble is used to measure atom interferences with increased visibility.

We propose a single optical photon source for quantum cryptography based on the acoustoelectric effect. Surface acoustic waves (SAWs) propagating through a quasi-one-dimensional channel have been shown to produce packets of electrons that reside in the SAW minima and travel at the velocity of sound. In our scheme, the electron packets are injected into a p-type region, resulting in photon emission. Since the number of electrons in each packet can be controlled down to a single electron, a stream of single- (or N-) photon states, with a creation time strongly correlated with the driving acoustic field, should be generated.

Recently, people have calculated tunneling’s characteristic times within Bohmian mechanics. Contrary to some characteristic times defined within the framework of the standard interpretation of quantum mechanics, these have reasonable values. Here, we introduce one of the available definitions for tunneling’s characteristic times within the standard interpretation as the best definition that can be accepted for the tunneling times. We show that, due to experimental limitations, Bohmian mechanics leads to the same tunneling times.

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian diffusion, thus providing a measure of robustness. The joint nonclassicality of position and momentum observables is shown to be complementary to their joint robustness in an exact sense.

We have revisited the Ghirardi-Rimini-Weber-Pearle (GRWP) approach for continuous dynamical evolution of the state vector for a macroscopic object. Our main concern is to recover the decoupling of the state vector dynamics for the center-of-mass (CM) and internal motion, as in the GRWP model, but within the framework of the standard cosmology. In this connection we have taken the opposite direction of the GRWP argument that the cosmic background radiation (CBR) has originated from a fundamental stochastic hitting process. We assume the CBR to be a clue of the Big Bang, playing a main role in the decoupling of the state vector dynamics of the CM and internal motion. In our model, instead of describing a continuous spontaneous localization (CSL) of a system of massive particles as proposed by Ghirardi, Pearle, and Rimini [Phys. Rev. A 42, 78 (1990)] the Itô stochastic equation accounts for the intervention of the CBR on the system of particles. Essentially, this approach leads to a precursor of the master equation for both the CBR and particle degrees of freedom. The violation of the principle of energy conservation characteristic of the CSL model is avoided as well as the additional assumption on the size of the GRWP’s localization width necessary to reach the decoupling between the collective and internal motions. Moreover, realistic estimation for the decoherence time, exhibiting an interesting dependence on the CBR temperature, is obtained. From the formula for the decoherence time it is possible to analyze the transition from micro- to macrodynamics in both the early hot universe and the nowadays cold one. The entropy of the system under decoherence is analyzed and the emergent “pointer basis” is discussed. In spite of not having imposed a privileged basis, in our model the position still emerges as the preferred observable as in the CSL model.

The origin and the mechanisms responsible for an ultranonlocal field-counteracting term in the Kohn-Sham exchange-correlation potential ${\nu }_{\mathrm{xc}}$ of molecular chains in an external electric field are established for prototype systems. Using various analysis tools—conditional probability amplitude analysis, construction of the (nearly) exact ${\nu }_{\mathrm{xc}},$ one-electron perturbation theory, and Krieger-Li-Iafrate (KLI) calculations—it is shown that a field-counteracting term emerges in the “response” part ${\nu }_{\mathrm{resp}}$ of ${\nu }_{\mathrm{xc}}.$ For systems $A_2$ of two open-shell units A, with ${\mathrm{H}}_2$ as a prototype, the left-right electron Coulomb correlation generates a step in ${\nu }_{\mathrm{resp}},$ which effectively compensates for an electric field in the limit of large interatomic distances. For systems $A_n$ of closed-shell units A, with ${\mathrm{He}}_2$ and ${\mathrm{H}}_2{+\mathrm{H}}_2$ as prototypes, a field-counteracting term is generated in ${\nu }_{\mathrm{resp}}$ by the Pauli repulsion of electrons in the occupied Kohn-Sham orbitals. An analytical estimate of the field-counteracting step is obtained for ${\mathrm{He}}_2$ with the exchange-only KLI model of ${\nu }_{\mathrm{resp}},$ and the existence of an ultranonlocal linear term in ${\nu }_{\mathrm{resp}}$ is established with KLI calculations on the prototype molecular chain ${\mathrm{H}}_{18}.$

We present a numerical evaluation of the loop-after-loop contribution to the second-order self-energy for the ground state of hydrogenlike atoms with low nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie gauge and without an expansion in $Z\alpha .$ Our calculation confirms the results of Mallampalli and Sapirstein and disagrees with the calculation by Goidenko and co-workers. A discrepancy between different calculations is investigated. An accurate fitting of the numerical results provides a detailed comparison with analytic calculations based on an expansion in the parameter $Z\alpha .$ We confirm the analytic results of order ${\alpha }^2(Z\alpha {)}^5$ but disagree with Karshenboim’s calculation of the ${\alpha }^2\left(Z\alpha {)}^6{\ln }^3\right(Z\alpha {)}^{-2}$ contribution.

At the ultracold temperatures which occur in cold atom traps and Bose-Einstein condensates, only a few partial waves contribute to the scattering of ground-state alkali-metal atoms, and cross sections are extremely sensitive to threshold effects. We present an analysis of these threshold effects, using a generalized multichannel quantum defect theory (GMQDT) to construct a close-coupled scattering wave function which is analytic in energy across thresholds. We illustrate the theory using the hyperfine transitions in $\mathrm{N}\mathrm{a}+\mathrm{N}\mathrm{a}$ collisions, and show that it gives results completely equivalent to the usual close-coupled cross sections. The virtue of the GMQDT is that it treats both open and closed channels on an equal footing, and all interchannel dynamics is summarized in a single real symmetric matrix $\mathbf{Y}\mathrm{}\left(E\right)\mathrm{}$ which is essentially constant across thresholds (and often over excursions of energy which exceed the hyperfine splittings). The multichannel threshold energy behavior can then be related to calculable properties of the individual channels that are being closed. Many of the smaller spin depolarization cross sections are determined by very long-range ${\alpha }^2{/R}^3$ spin-spin interactions which are not well treated by GMQDT, and we correct these specific elements with a perturbative distorted-wave approximation which yields the observed threshold dependences and brings the GMQDT into perfect agreement with the exact close-coupled results.

Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for $\mathrm{Na}+{\mathrm{Na}}^{+}$ have been carried out with the best available ${}^2{\Sigma }_g^{+}$ and ${}^2{\Sigma }_u^{+}$ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.

This paper investigates the influence of experimentally nonuniform spatial laser profiles on controlling quantum dynamics. The influence of Gaussian $\left({\mathrm{TEM}}_{00}\right),$ donut $\left({\mathrm{TEM}}_{01}^{*}\right),$ and uniform laser profiles upon quantum control yield is considered. Nonuniform laser profiles can reduce the control yield, but it is shown that this effect can be diminished, by designing optimized laser pulses explicitly taking into account the spatial laser profile. These laser pulses are of significantly different structure than the ones for uniform profiles. This result suggests that an analysis of experimental laser fields to gain information on the resultant physical processes will be more difficult for pulses with nonuniform profiles. The simulations indicate that direct closed loop control in the laboratory can learn to operate effectively with nonuniform profiles.