We derive the first terms in the amplitude of lepton pair production in the Coulomb fields of two relativistic heavy ions. Using the Sudakov technique, which simplifies the calculations in momentum space for the processes at high energies, we get compact analytical expressions for the differential cross section of the process under consideration in the lowest order in the fine-structure constant (Born approximation) valid for any momentum transfer and in a wide kinematic region for produced particles. Exploiting the same technique, we consider the next terms of the perturbation series (up to the fourth order in the fine-structure constant) and investigate their energy dependence and limiting cases. It has been shown that taking into account all relevant terms in the corresponding order, one obtains expressions that are gauge invariant and finite. We estimate the contribution of the Coulomb corrections to the total cross section and discuss the cancellations of the different terms in the total cross section.

We present a theory of van der Waals (vdW) atom-surface attraction in which the second order vdW energy is explicitly exhibited as a correlation–self-energy of atomic electrons generated by a dynamic, nonlocal image potential due to polarization of the electrons of the bounded metal-semiconductor surface system in the electrostatic limit. This formulation is applied to a metal-semiconductor plasma in a magnetic field perpendicular to its bounding surface. The dependence of the atom-surface vdW energy on magnetic field strength provides an adjustable parametrization of the underlying zero-point photon energy (represented in terms of the nonretarded longitudinal plasmon-photons of the Coulomb interaction), opening the possibility of analyzing the concomitant fundamental quantum phenomenology in detail with material parameters that can be examined experimentally. The determination of the image potential, including its nonlocal and dynamic magnetic field effects, involves the construction of a “surface dielectric function,” which is carried out using a Green’s function joining procedure for nonlocal dynamic electrostatics. In this aspect of our second-order vdW energy calculation, we take account of the role of the magnetic field by means of a hydrodynamic model of magnetoplasma nonlocality in dynamic longitudinal dielectric response. Both local and nonlocal magnetic field effects in vdW energy are analyzed within the framework of a multipole expansion, and are also discussed, respectively, in expansions in powers of ${\omega }_c^2$ $({\omega }_c$ is the cyclotron frequency). Furthermore, we determine the role of Landau quantization magnetic field effects in the skewing of the surface electron charge distribution from its uniform positive background, exhibiting de Haas–van Alphen oscillatory (and “staircase”) behavior.

The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the possibility of probing the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean-field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.

Quantum depletion from an atomic quasi-one-dimensional Bose-Einstein condensate with a dark soliton is studied in a framework of the Bogoliubov theory. Depletion is dominated by an anomalous mode localized in a notch of the condensate wave function. Depletion in an anomalous mode requires a different treatment than depletion without anomalous modes. In particular, quantum depletion in the Bogoliubov vacuum of the anomalous mode is experimentally irrelevant. A dark soliton is initially prepared in a state with minimal depletion, which is not a stationary state of the Bogoliubov theory. The notch fills up with incoherent atoms depleted from the condensate. For realistic parameters the filling time can be as short as 10 ms.

We consider a collection of atoms prepared in a Bose-Einstein condensate which interact via two-body elastic collisions. A resonant driving field couples two internal states which together constitute an effective spin 1/2 system for each atom, and from which a total spin for the gas can be defined. It is shown that in the limit of strong driving, the system dynamics reduces to a mechanism for spin squeezing similar to that of a recent proposal for undriven condensates. However, we find that the conditions for spatial stability in our driven system are complementary to those of the undriven system. Reasons for this difference, associated with the physics of dressed atom collisions, are discussed along with conditions for preparing and observing the spin squeezed state.

The tunneling rate of a skyrmion in ferromagnetic spin-1/2 Bose-Einstein condensates through an off-centered potential barrier is calculated exactly with the periodic instanton method. The prefactor is shown to depend on the chemical potential of the core atoms, the level at which the atom tunnels. Our results can be readily extended to estimate the lifetime of other topological excitations in the condensate, such as vortices and monopoles.

Extended phase-matching conditions for spontaneous parametric down-conversion are examined. By augmenting the conventional phase-matching conditions, they permit the creation of a class of frequency-entangled states that generalizes the usual twin-beam biphoton state. An experimental characterization of these states is possible through interferometric coincidence counting.

We show that a nondegenerate multifrequency parametric oscillator has different properties compared with the usual three-wave parametric oscillator. We consider, as an example, a scheme for a resonant cw monolithic microwave-optical parametric oscillator based on high-$Q$ whispering gallery modes excited in a nonlinear dielectric cavity. Such an oscillator may have an extremely low threshold and stable operation, and may be used in spectroscopy and metrology. The oscillator mimics devices based on resonant ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity and can be utilized for efficient four-wave mixing and optical comb generation. Moreover, the oscillator properties are important to better understand the stability conditions of long-baseline interferometers with movable mirrors that are currently used for gravity wave detection.

When linearly polarized light propagates through a medium in which elliptically polarized light would undergo self-rotation, squeezed vacuum can appear in the orthogonal polarization. A simple relationship between self-rotation and the degree of vacuum squeezing is developed. Taking into account absorption, we find the optimum conditions for squeezing in any medium that can produce self-rotation. We then find analytic expressions for the amount of vacuum squeezing produced by an atomic vapor when light is near-resonant with a transition between various low-angular-momentum states. Finally, we consider a gas of multilevel Rb atoms, and analyze squeezing for light tuned near the D lines under realistic conditions.

Laser and microwave fields can be mixed in paramagnetic samples in a coherent Raman process. The radiation scattered in the forward direction contains frequency components at the sum and difference frequency. We consider the details of this scattering process in a static magnetic field, where two types of signals appear: magnetic-resonance transitions give rise to signals at fixed magnetic fields, independent of the laser frequency. Another set of resonances is determined by the optical transition frequencies. These resonances are particularly prominent in samples with narrow optical absorption lines. We derive a comprehensive theory that describes both contributions and compare it with experimental data from the R lines of ruby.

We propose a scheme to implement a quantum controlled phase gate for trapped ions in thermal motion with one standing-wave laser pulse. Instead of applying the rotating-wave approximation, this scheme makes use of the counter-rotating terms of the operators. We also demonstrate that the same scheme can be used to generate maximally entangled states of N trapped ions by a single laser pulse.

By designing a proper unitary operator U, we synthesize nuclear-magnetic-resonance (NMR) analogs of Einstein-Podolsky-Rosen (EPR) states (pseudo-EPR states) using the generalized Grover’s algorithm on a NMR quantum computer. Experiments also demonstrate the generalized Grover’s algorithm for the case in which there are multiple marked states.

We investigate the transfer of a two-mode squeezed vacuum state through lossy transmission lines. It is shown that the state can violate Bell’s inequalities, and consequently, excludes a local hidden variable model at pronouncedly larger transmission lengths in comparison with previous claims. This can be important for security of continuous-variable quantum cryptography employing entangled states.

In the framework of the Lindblad theory for open quantum systems, we derive closed analytical expressions of the Heisenberg and Schrödinger generalized uncertainty functions for a particle moving in a harmonic-oscillator potential. The particle is initially in an arbitrary correlated coherent state, and interacts with an environment at finite temperature. We describe how the quantum and thermal fluctuations contribute to the uncertainties in the canonical variables of the system and analyze the relative importance of these fluctuations in the evolution of the system. We show that upon contact with the bath, the system evolves from a quantum-dominated to a thermal-dominated state in a time that is of the same order as the decoherence time calculated in other models in the context of transitions from quantum to classical physics.

Using the nonperturbative method of dressed states introduced in a previous publication [N. P. Andion, A. P. C. Malbouisson, and A. Mattos Neto, J. Phys. A 34, 3735 (2001)], we study effects of the environment on a quantum-mechanical system, in the case in which the environment is modeled by an ensemble of noninteracting harmonic oscillators. This method makes it possible to separate the whole system into the dressed mechanical system and the dressed environment, in terms of which a nonperturbative approach is possible. When applied to the Brownian motion, we give explicit nonperturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to studying atomic behaviors in cavities, the method accounts for experimentally observed inhibition of atomic decay in small cavities.

The nonadiabatic geometric quantum computation may be achieved using coupled low-capacitance Josephson junctions. We show that the nonadiabatic effects as well as the adiabatic condition are very important for these systems. Moreover, we find that it may be hard to detect the adiabatic Berry’s phase in this kind of superconducting nanocircuits; but the nonadiabatic phase may be measurable with current techniques. Our results may provide useful information for the implementation of geometric quantum computation.

The relation between Bell’s inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multipartite quantum key distribution protocols.

We study the entanglement properties of some fractional quantum Hall liquids. We calculate the entanglement of the Laughlin wave function and the wave functions that are generated by the K matrix using the modified entanglement measure of indistinguishable fermions that is first proposed by Paškauskas and You [Phys. Rev. A64, 042310 (2001)].

A critical analysis of the speed-dependent spectral line-shape models is presented. With this aim, a comparison of these models is done with molecular-dynamics results for ${\mathrm{H}}_2-X$ gaseous mixtures. This allows us to get a clear understanding of the consequences of the assumptions underlying these models on the line profile. This proves the requirement to introduce, in the collisional confinement regime, distinct treatments for the velocity-orientation and velocity-modulus memory mechanisms. Such a requirement applies when the goal is to get both a high accuracy with experimental stimulated Raman profiles and a high consistency with molecular dynamics (i.e., with first principles).

We study quantum reflection in a system of two attractive step potentials with a steplike coupling term. The amplitude $R_{11}$ for elastic reflection generally has the near-threshold behavior $|R_{11}|\stackrel{\overrightarrow{k}0}{\sim }1-2bk$ familiar from the single-channel case. Reflectivity in the elastic channel is quenched in the presence of a second adiabatic channel open for transmission, while it is enhanced when the second transmission channel is closed; there is a pronounced minimum in the reflectivity when the potential in the upper adiabatic channel is zero or close to zero. When the upper adiabatic channel is repulsive, the elastic reflectivity can have an exact zero, at which quantum reflection leads to complete transfer into the excited state. Any degree of entanglement of translational and internal motion can be achieved at an appropriate energy between the threshold for inelastic reflection and this zero of the elastic reflectivity. For degenerate reflection channels, the unusual case of incomplete reflection at threshold occurs when the potential in the upper adiabatic channel vanishes.