We have produced and cooled the molecular ions ${\mathrm{MgH}}^{+}$ and ${\mathrm{MgD}}^{+}$ in a linear Paul trap. These ions were generated by the photochemical reactions ${\mathrm{Mg}}^{+}{(3p}^2{P}_{3/2})+{\mathrm{H}}_2\hspace{0.5em}({\mathrm{D}}_2)\to {\mathrm{MgH}}^{+}\hspace{0.5em}({\mathrm{MgD}}^{+})+\mathrm{H}\hspace{0.5em}(\mathrm{D}),$ and identified by the radial separation in the trap of ions with different charge-to-mass ratios. The molecular translational motion was cooled sympathetically by Coulomb interaction with laser-cooled ${\mathrm{Mg}}^{+}$ ions to a temperature estimated to be below 100 mK. Ordered structures (ion crystals) containing more than 1000 ions, with more than $95\%$ being molecular ions, were obtained. Such translationally cold and well-localized samples of molecular ions could become very useful for molecular physics and chemistry.

We present an ac heterodyne technique in cavity ringdown spectroscopy that permits $1\times {10}^{-10}$ absorption sensitivity with microwatt-level light power. Two cavity modes, one probing the empty cavity and the other probing intracavity absorption, are excited simultaneously but with their intensities temporally out of phase, with one mode decaying and the other rising. Heterodyne detection between the two modes reveals the dynamic time constants associated with the empty cavity and the additional intracavity gas absorption. The method offers a quick comparison between the on- and off-resonance information, a prerequisite to reaching the fundamental shot-noise limit. This simple and yet important improvement of cavity ringdown spectroscopy should lead to the enhanced performance of a wide range of applications.

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated, accounting for the finite conductivity of the metals. A simple formalism of surface modes is briefly presented which makes it possible to obtain a generalization of the Lifshitz results for the case of two semispaces covered by thin layers. Additional clarification of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate, both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using tabulated optical data for the complex refractive index of these metals. The computations turn out to be in agreement with perturbation theory up to fourth order in the relative penetration depth of electromagnetic zero-point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by thin Au layers is computed, and the possibility of neglecting spatial dispersion effects is discussed as a function of the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure nonretarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2–4) nm. More exact values of the Hamaker constant for Al and Au are determined.

We consider a general proposal for generating a train of entangled single-photon wavepackets. The photons are created inside a resonator via an interaction with an active medium. In the course of the generation process photons are transferred to the continuum outside the resonator through cavity loss. We show that wave packets generated in this way can be regarded as independent logical qubits. This and the possibility of producing strong entanglement between the qubits suggests many applications in quantum communication. We give a specific example in the context of cavity QED and show that undesired decoherence effects can be efficiently reduced in the considered scheme.

We exhibit a two-parameter family of bipartite mixed states ${\rho }_{\mathrm{bc}},$ in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes 2$ can be distilled by local quantum operations and classical communication (LQ+CC). Evidence for this undistillability is provided by the result that, for certain states in this family, we cannot extract entanglement from any arbitrarily large number of copies of ${\rho }_{\mathrm{bc}}$ using a projection on $2\otimes 2.$ These states are canonical NPT states in the sense that any bipartite mixed state in any dimension with NPT can be reduced by LQ+CC operations to a NPT state of the ${\rho }_{\mathrm{bc}}$ form. We show that the main question about the distillability of mixed states can be formulated as an open mathematical question about the properties of composed positive linear maps.

We study the distillability of a certain class of bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that nonpositivity of the partial transpose of a density operator is not a sufficient condition for distillability, when the dimension of both subsystems is higher than 2.

Landauer’s principle states that in erasing one bit of information, on average, at least $k_{B}T\ln \mathrm{}\left(2\right)\mathrm{}$ energy is dissipated into the environment (where $k_B$ is Boltzmann’s constant and $T$ is the temperature of the environment at which one erases). Here, Landauer’s principle is microscopically derived without direct reference to the second law of thermodynamics. This is done for a classical system with continuous space and time, with discrete space and time, and for a quantum system. The assumption made in all three cases is that during erasure the bit is in contact with a thermal reservoir.

The radiative lifetime of the ${2s}^2{2p}^4$ ${}^1{S}_0$ level in ${\mathrm{F}}^{+}$ has been measured by time-resolved observations of both strong (though electric-dipole forbidden) decay branches: the electric quadrupole $\mathrm{}\left(E2\mathrm{}\right)\mathrm{}$ transition $(\approx 80\%$ branch) to the ${2s}^2{2p}^4$ ${}^1{D}_2$ level and the magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ transition $(\approx 20\%$ branch) to the ${2s}^2{2p}^4$ ${}^3{P}_1$ level. We observed the fluorescence associated with both transitions from a population of ${\mathrm{F}}^{+}$ ions circulating in a heavy-ion storage ring. Our result for the ${\mathrm{F}}^{+}$ ${2s}^2{2p}^4$ ${}^1{S}_0$ level lifetime of $420\pm 12$ ms provides a benchmark for theory. Moreover, although the calculated lifetimes vary by more than 20%, the calculated branching fractions vary by less than 4% and 7% for the ${}^1{\overrightarrow{S_0}}^1{D}_2$ $E2\mathrm{}$ and ${}^1{\overrightarrow{S_0}}^3{P}_1$ $M1\mathrm{}$ transitions, respectively. Using our measured lifetime and the calculated branching fractions, we report semiempirical transition probabilities for the ${}^1{\overrightarrow{S_0}}^1{D}_2$ $E2\mathrm{}$ and ${}^1{\overrightarrow{S_0}}^3{P}_1$ M1 transitions of 1.90 ${\mathrm{s}}^{-1}\pm 7\%$ and 0.50 ${\mathrm{s}}^{-1}\pm 9\%,$ respectively.

Parity (P) and time (T) invariance violating effects in the Ra atom are strongly enhanced due to close states of opposite parity, the large nuclear charge Z and the collective nature of $\mathrm{}(P,T)\mathrm{}$-odd nuclear moments. We have performed calculations of the atomic electric dipole moments (EDM) produced by the electron EDM and the nuclear magnetic quadrupole and Schiff moments. We have also calculated the effects of parity nonconservation produced by the nuclear anapole moment and the weak charge. Our results show that as a rule the values of these effects are much larger than those considered so far in other atoms (enhancement is up to ${10}^5$ times).

A formulation of the valence-universal coupled-cluster (VU-CC) method for atoms is presented. The method is based on Lindgren’s normal-ordered exponential expansion, in which the cluster operator is restricted to its one- and two-body components represented in terms of radial amplitudes defined by the configurational excitations. The approach employs an intermediate Hamiltonian technique which replaces the effective Hamiltonian formalism used in the standard VU-CC formulation. The modified version introduces many simplifications in comparison with the standard one and, in particular, offers an efficient way of solving coupled-cluster equations. The advantages of the approach are illustrated in a calculation for the Be atom, representing one of the basic yet very challenging applications for VU-CC methods.

We briefly review the description of electron propagation in the field of ultrarelativistic colliding nuclei. The crossing symmetry of the resulting amplitude is discussed. We show that the amplitude loses crossing invariance in the high-energy limit so that the conventional formalism to derive the pair production amplitude cannot be applied. Consequently, former calculations of the pair production amplitude using the solution of the two-center Dirac equation are incorrect. On the basis of bremsstrahlung and $e^{+}{e}^{-}$ pair production, conclusions about the Coulomb corrections in electron scattering and pair production in ultrarelativistic heavy-ion collisions are drawn.

We study the collinear chaotic scattering between an electron and a one-electron ion (e.g., ${\mathrm{He}}^{+})$ with negative total energy. The global dynamics of the unbounded motion in phase space can be illustrated by introducing two submanifolds of critical injecting and critical escaping. We find a type of bifurcation of chaotic scattering resulted from the tangency between these two submanifolds, which explains the emergence or disappearance of an extra zeroth-order chaotic band in the scattering functions as the nuclear charge Z is changed.

The ionization and excitation cross sections of atomic hydrogen with antiprotons are calculated using the close-coupling method, where the wave function is expanded by atomic states only on protons. The resulting total cross sections are in good convergence and in agreement with other calculations based on the close-coupling method with considerably large basis set. The angular distribution of ionized electrons is calculated by substituting the obtained wave function in the close-coupling method into the integral form of the transition amplitude. Above 100 keV, the angular distributions of ionized electrons are compared for proton- and antiproton impacts.

We have performed extensive close-coupling calculations to obtain total impact ionization cross sections of He atoms by antiprotons at energies from 1 keV to 300 keV by expanding the time-dependent two-electron wave functions in terms of helium eigenstates. The stability of the calculated ionization probabilities and total ionization cross sections with respect to the choice of basis functions has been examined. Our total ionization cross sections are only slightly higher than the results from the forced-impulse approximation of Reading et al. [J. Phys. B 30, L189 (1997)] but they disagree with the existing experimental data below 40 keV [Hvelplund et al., J. Phys. B 27, 925 (1994)]. We conclude that new measurements for the ionization of He by antiprotons are needed in the low-energy region.

Several recent experiments on liquid and solid samples containing protons or deuterons have shown an interesting anomaly, which is apparently absent when the hydrogen isotopes are replaced by heavier particles. The anomaly is a shortfall in the intensity of energetic neutrons scattered by the samples; specifically, the intensity per hydrogen isotope in bulk samples is smaller than the intensity for total scattering by an isolated hydrogen isotope. Short-lived correlations in the spatial and spin degrees of freedom of the hydrogen isotopes have been proposed as an explanation of the anomaly. The correlations involve entanglements of the degrees of freedom created by the requirements of quantum mechanics applied to identical particles. By using energetic neutrons to perform Compton scattering experiments on the hydrogen isotopes, the time scale of the experimental probe covers the region of ${10}^{-16}–{10}^{-15}\mathrm{s}$ where entangled states might still be expected to survive. The proposed explanation is pursued here by reporting the cross section for Compton scattering, also known as deep inelastic scattering, by two identical nuclei occupying nonequivalent states. The model reproduces the observed dependence of the cross section on energy transfer, in which intensity accumulates at the recoil energy of a single nucleus. Several features of the model demand that the intensity at the recoil energy is indeed less than the intensity for total scattering by an isolated nucleus. Although the pair approximation used here is unquestionably a first approximation to real many-body entanglements, it is a compelling explanation of all the observations, including the restoration of the normal cross section at longer observation times achieved by moving to longer scattering times.

A method for quantum interferometry and phase control of degenerate Rydberg states has been proposed and realized experimentally. Phase control was carried out by a pulse of a weak dc electric field which caused a Stark splitting of degenerate Rydberg sublevels for a short time. A strong interference dependence of the probability of the microwave transition ${37P}_{3/2}\to {37S}_{1/2}$ in sodium Rydberg atoms on a phase difference between the Stark sublevels of the ${37P}_{3/2}$ state has been detected. Changes in the probability were measured directly by a pulsed resonant microwave radiation applied after the electric-field pulse. Records of the quantum interference signals and Stark spectra of the microwave transition are presented and discussed. An influence of the laboratory magnetic field has been analyzed.

We address high-order harmonic generation with linearly polarized bichromatic fields, concentrating on a modulation in the harmonic yield as a function of the relative phase between the two field components, and on an offset phase shift of this modulation for neighboring cutoff harmonics. These effects have been recently observed in experiments where the relative phase between the two driving fields was controlled. Using the three-step model and the fully numerical solution of the time-dependent Schrödinger equation, we discuss the phase-dependent modulation and show that the offset phase is inherent to a particular set of semiclassical trajectories for the returning electron. These trajectories are identified using classical arguments and isolated by means of the saddle-point method, which allows a detailed investigation of their interference. Thus, by adding a second driving field whose amplitude lies within an adequate parameter range, one is able to single out a set of trajectories according to its behavior with respect to the relative phase. This effect is already present at the the single-atom-response level.

We calculate the energy-level shifts of a tightly confined trapped alkali-metal atom in the presence of a second trapped atom. A complete microscopic description of the interaction energy between the two atoms is used. This allows us to study tightly confined atoms near a Feshbach resonance and to evaluate the usefulness of the regularized $\delta$-function potential approximation. We present results for sodium and cesium when confined in a spherically symmetric harmonic optical trap. Possible implications of the level shifts and collisional decoherence for quantum computing with atomic systems are given.

We consider electron-atom scattering in a circularly polarized laser field at sufficiently high electron energies, permitting us to describe the scattering process by a first-order Born approximation. Assuming the radiation field has sufficiently moderate intensities, the laser dressing of the hydrogen target atom in its ground state will be treated in second-order perturbation theory. Within this approximation scheme, it is shown that the nonlinear differential cross sections of free-free transitions do not depend on the dynamical phase $\phi$ of the radiative process nor on the helicity of the circularly polarized laser light. Relations to the corresponding results for linear laser polarization are established.

We have investigated motional heating of laser-cooled ${}^9{\mathrm{Be}}^{+}$ ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes. The results show that heating is due to electric-field noise from the trap electrodes that exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.