In this paper we report on a method for quantitative measurement and characterization of the Goos-Hanchen effect based upon the real world performance of optical sources. A numerical model of a nonideal plane wave is developed in terms of uniform divergence properties. This model is applied to the Goos-Hanchen shift equations to determine beam shift displacement characteristics, which provides quantitative estimates of finite shifts near critical angle. As a potential technique for carrying out a meaningful comparison with experiments, a classical method of edge detection is discussed. To this end a line spread Green’s function is defined which can be used to determine the effective transfer function of the near critical angle behavior of divergent plane waves. The process yields a distributed (blurred) output with a line spread function characteristic of the inverse square root nature of the Goos-Hanchen shift equation. A parameter of interest for measurement is given by the edge shift function. Modern imaging and image processing methods provide suitable techniques for exploiting the edge shift phenomena to attain refractive index sensitivities of the order of ${10}^{-6}$, comparable with the recent results reported in the literature.

We show that strongly correlated and anticorrelated photons can be produced from two fluorescent fields emitted by a driven cascade atom with split metastable states. Depending on the choice of parameters, we have strong correlations for both fluorescent fields, anticorrelations for both, and strong correlation for one and anticorrelation for the other. In the presence of level splitting, we have two interfering cascade-dressed transitions from the top state to the antisymmetric superposition of the metastable states. The interference between the two cascade-dressed transitions is responsible for the strong correlations and anticorrelations.

We have calculated polarizabilities (${\alpha }_1$, ${\beta }_1$, ${\gamma }_1$, ${\alpha }_2$, ${\beta }_2$, and ${\gamma }_2$) of ${\mathrm{Ps}}^{-}$ by the pseudostate method. These parameters can be used to calculate Rydberg states of ${\mathrm{Ps}}^{-}$ in the presence of an external electron with high quantum numbers $N$ and $L$. They are also of importance in a system containing ${\mathrm{Ps}}^{-}$ bound to a proton [PsH] and also Rydberg states of ${\mathrm{Ps}}_2$.

We formulate a relativistic algebraic method of scattering for systems with spatially dependent mass based on the $J$-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is position-dependent with a constant asymptotic limit. Additionally, this effective mass distribution is locally represented in a finite dimensional function subspace. The spinor couples to spherically symmetric vector and pseudo scalar potentials that are short-range such that they are accurately represented by their matrix elements in the same finite dimensional subspace. We calculate the relativistic phase shift as a function of energy for a given configuration and study the effect of spatial variation of the mass on the energy resonance structure.

High-order above-threshold ionization (ATI) is investigated in the frequency domain, based on a nonperturbative quantum electrodynamics theoretical approach. The transition matrix element of high-order ATI is expressed as a superposition of products of generalized Bessel functions, which represent probability amplitudes of finding electrons with given energies. From the frequency-domain viewpoint the high-order ATI can be described simply as an ATI followed by laser-assisted collision (LAC), and the features of high-order ATI reflect mainly the characteristics of LAC. We investigate thoroughly the LAC, finding that the plateau can be simulated by a simple classical model. We also discuss the correspondence between the time- and frequency-domain pictures of rescattering ATI.

A method for determining the laser-induced dissociation pathways of multielectron diatomic molecules is developed. Despite the abundance of possible dissociation pathways inherent to such molecules, this technique allows one to resolve the dissociation pathways that contribute to the measured intensity-dependent three-dimensional momentum distribution. To illustrate this method, the unique dissociation mechanisms and pathways producing a few predominant features in the laser-induced dissociation momentum distribution of ${\mathrm{O}}_2^{+}$ are determined.

We establish that the ability of a localized trapping potential to bind weakly interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound state of the trap. Specifically, for repulsive particles and a superthreshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a subthreshold trap, a collective bound state always forms for a sufficiently large number of bosons, despite the inability of interparticle attraction alone to form a two-body bound state.

We study an atomic Bose-Fermi mixture with unpolarized fermions in an optical lattice. We obtain the Mott ground states of such a system in the limit of the deep optical lattice and discuss the effect of quantum fluctuations on these states. We also study the superfluid-insulator transitions of bosons and metal-insulator transition of fermions in such a mixture within a slave-rotor mean-field approximation, and obtain the corresponding phase diagram. We discuss experimental implications of our results.

The Hamiltonian of an $N$-boson system confined on a ring with zero spin and repulsive interaction is diagonalized. The excitation of a pair of $p$-wave particles rotating reversely appears to be a basic mode. The fluctuation of many of these excited pairs provides a mechanism of oscillation; the states can be thereby classified as oscillation bands. The particle correlation is studied intuitively via the two-body densities. Bose clustering originating from the symmetrization of wave functions is found, which leads to the appearance of one-, two-, and three-cluster structures. The motion is divided into being collective and relative; this leads to the establishment of a relation between the very high vortex states and the low-lying states.

We have theoretically studied the conversion of radially polarized waveguide modes of a tapered optical fiber into surface plasmon polaritons (SPPs) propagating at the outer surface of an apertureless silver-coated optical tip. Optimization of this process is important in exploiting SPP superfocusing in scanning near-field optical microscopy without the need for external illumination. Our approach is based on analyzing the evolution of the local modal index as a function of the fiber radius. The influence of mode projection, intermodal coupling, and metal dissipation are treated analytically, while a numerical finite integration technique is used to model radiation coupling. The results identify and quantify the mode conversion processes that need to be taken into account. We estimate that at least 10% of the modal energy in an uncoated fiber taper can be fed into the superfocusing mode at a silver-coated tip.

Based on a master equation for the reduced density matrix of an open quantum collective system, the influence of coordinate-dependent microscopical diffusion coefficients on the decay rate from a metastable state is treated. For various frictions and temperatures larger than a crossover temperature, the quasistationary decay rates obtained with the coordinate-dependent microscopical set of diffusion coefficients are compared with those obtained with the coordinate-independent microscopical set of diffusion coefficients and coordinate-independent and -dependent phenomenological sets of diffusion coefficients. Neglecting the coordinate dependence of diffusion coefficients, one can strongly overestimate or underestimate the decay rate at low temperature. The coordinate-dependent phenomenological diffusion coefficient in momentum are shown to be suitable for applications.

In a system of atoms with large positive scattering length, weakly bound diatomic molecules (dimers) are generated dynamically by the strong interactions between the atoms. If the atoms are modeled by a quantum field theory with an atom field only, condensates of dimers cannot be described by the mean-field approximation because there is no field associated with the dimers. We develop a method for describing dimer condensates in such a model based on the one-particle-irreducible (1PI) effective action. We construct an equivalent 1PI effective action that depends not only on the classical atom field but also on a classical dimer field. The method is illustrated by applying it to the many-body behavior of bosonic atoms with large scattering length at zero temperature using an approximation in which the two-atom amplitude is treated exactly, but irreducible $N$-atom amplitudes for $N⩾3$ are neglected. The two 1PI effective actions give identical results for the atom superfluid phase, but the one with a classical dimer field is much more convenient for describing the dimer superfluid phase. The results are also compared with previous work on the Bose gas near a Feshbach resonance.

The output energy dependence of high repetition rate grazing incidence pumped Ni-like Mo, Ni-like Ag, and Ne-like Ti transient collisional soft x-ray lasers on the duration of the pump pulse was studied combining experiments and model simulations. Lasing is observed to occur for a wide range of pump pulse widths (e.g., $2\text{to}18\mathrm{ps}$ for Ni-like Ag), with maximum output occurring for pump pulses of $4–6\mathrm{ps}$ FWHM, corresponding to pump intensities of $1.4–2.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. Moderately short pump pulses are observed to be optimum for lasers that make use of preplasmas in which the mean degree of ionization approaches the charge of the lasing ion, while long pump pulses produce over-ionization and weaker lasing. However, long pump pulses are capable of producing gain and lasing in low $Z$ ions even when the preplasma has a very low degree of ionization after expanding for $5\mathrm{ns}$. As the duration of the pump pulse shortens the optimum delay respect to the prepulse is observed to decrease. The physics that determines these and other measured trends is discussed.

In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase-space of the two-dimensional isotropic harmonic oscillator. Using Dirac’s quantization condition, the authors investigate how these alternative symplectic forms affect this system’s quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent.

We refute the remarks made by Latimer, Comment on “Symplectic quantization, inequivalent quantum theories, and Heisenberg’s principle of uncertainty” [Phys. Rev. A 75, 066101 (2007)].

We discuss the solution of the basic equations of the $N$-level Friedrichs model by using the Feshbach projection operator (FPO) technique and consider the relation between bound states in the continuum (BICs) and form factors. In the FPO formalism, the BICs are eigenstates of a non-Hermitian Hamilton operator with vanishing decay width. The wave function of a BIC is localized inside the system. On the basis of the FPO solutions we discuss the mechanism to yield a BIC at every coupling strength between system and environment. We relate our results to those given by Miyamoto [Phys. Rev. A 72, 063405 (2005)].

We analyze the formation of ${\mathrm{Rb}}_2$ molecules with short photoassociation pulses applied to a cold ${}^{85}\mathrm{Rb}$ sample. A pump laser pulse couples a continuum level of the ground electronic state $X{}^1\Sigma _g^{+}$ with bound levels in the $0_u^{+}(5S+5P_{1∕2})$ and $0_u^{+}(5S+5P_{3∕2})$ vibrational series. The nonadiabatic coupling between the two excited channels induces time-dependent beatings in the populations. We propose to take advantage of these oscillations to design further laser pulses that probe the photoassociation process via photoionization or that optimize the stabilization in deep levels of the ground state.

Upper and lower bounds are established for the survival probability $\mid ⟨\psi \left(0\right)\mid \psi \left(t\right)⟩{\mid }^2$ of a quantum state, in terms of the energy moments $⟨\psi \left(0\right)\mid H^n\mid \psi \left(0\right)⟩$. Introducing a cutoff in the energy generally enables considerable improvement in these bounds and allows the method to be used where the exact energy moments do not exist.