A generalization of the stochastic wave-function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unraveling is based on a description of the reduced system in a doubled Hilbert space and it is shown that this method is capable of simulating quantum master equations with negative transition rates. Non-Markovian effects in the reduced systems dynamics can be treated within this approach by employing the time-convolutionless projection operator technique. This ansatz yields a systematic perturbative expansion of the reduced systems dynamics in the coupling strength. Several examples such as the damped Jaynes-Cummings model and the spontaneous decay of a two-level system into a photonic band gap are discussed. The power as well as the limitations of the method are demonstrated.

The usual three-wave description of stimulated Brillouin scattering (SBS) in birefringent fibers is revised by considering that the pump beam is not necessarily linearly polarized parallel to one of the main axes. The equations obtained govern the dynamics of SBS in a polarization maintaining fiber whatever the state of polarization of the light. A model describing the polarization dynamics of a Brillouin fiber ring laser is then obtained by completing these equations by appropriate boundary conditions. For various orientations of the fiber axes and various polarizations of the incident pump beam, the behaviors of a short-length Brillouin laser are finally studied by numerical simulations that are systematically compared to experimental results.

We perform a time-resolved quantum interference experiment based on the effect of induced coherence without induced emission using two pulsed parametric down-conversion sources. We periodically vary the transmission of the first source’s idler beam and measure the time-dependent visibility of fringes in the interference between the two signal beams. The visibility is found to be correlated with the transmissivity with a time delay corresponding to a combined path of the first idler and the second signal beam. The experiment is discussed in the context of the delayed choice experiments.

We show that any single-mode quantum state can be generated from the vacuum by alternate application of the coherent displacement operator and the creation operator. We propose an experimental implementation of the scheme for traveling optical fields, which is based on field mixings and conditional measurements in a beam-splitter array, and calculate the probability of state generation.

We present exact analytic solutions to describe the quantum dynamics of the radiation modes in a one-dimensional cavity vibrating at any one of its resonance frequencies. For a cavity vibrating at its $m\mathrm{th}\hspace{0.5em}(m>~2)$ eigenfrequency, m traveling wave packets emerge in the finite part of the field energy density and their amplitudes grow while their widths shrink in time, representing a large concentration of energy. There also exists a “sub-Casimir” region where the energy density equals $m^2$ times the static Casimir energy density.

We develop a quantum theory of a single-mode thresholdless laser. We start from basic Heisenberg–Langevin equations of motion for the field and atomic operators, and obtain an approximate analytical solution to these operator equations. We compare the predictions of this model for the intensity and power spectrum of the field to the results of a Monte Carlo numerical simulation of the original Heisenberg-Langevin equations, and find them in excellent agreement. We also compare these predictions to those of a rate-equation model, which takes into account spontaneous emission. We show that our model gives more reliable results in the bad cavity limit at high intensities. Based upon these results, we propose a simple characterization of the thresholdless behavior. Finally, we apply our model to microsphere Nd-doped lasers at low temperatures, which are promising devices for a well-controlled thresholdless operation.

For a weakly attractive inverse-square potential, $V\left(x\right)=-g{ħ}^2{/(2\mathrm{mx}}^2)$ with $0<g<~1/4,$ the standard WKB wave function shows unphysical divergence near the origin. Introducing an appropriate nonvanishing reference point and a related phase yields WKB wave functions whose deviation from the regular solution of the Schrödinger equation decreases asymptotically as ${1/\left(\mathrm{kx}\right)\mathrm{}}^3.$ This is two orders better than the alternative technique involving the Langer modification of the potential. The performance of the correspondingly modified quantization conditions is demonstrated for the bound states of vanishing angular momentum in the two-dimensional circle billiard and in a two-dimensional Woods-Saxon well.

Koopmans’s theorem is generalized for excited-state ensemble density-functional theory. Formal expressions are derived that relate orbital energy differences to exchange-only excitation energies. These expressions provide stringent requirements for approximating the universal exchange component of the exact exchange-correlation functional for excited-state ensembles, and the expressions lead to a relation, containing a correlation potential, that gives exact excited-state ionization energies.

The energy spectrum of the argon ${3p}^{4}4s4p$ and ${3p}^{4}3d4p$ configurations with a total $J=1\mathrm{}$ was calculated within the single-configuration relaxed-core Hartree-Fock approximation. The spin-orbit interaction was included in the calculation. The results indicate strong mixing of the ${}^{1}P$ terms which are the ones allowed to couple to the ground state via electric-dipole excitation. Most experimental lines could be identified using this calculation. The calculated spin-orbit splittings within groups of levels are in very good agreement with experiment. However, differences of the order of 1 eV between experiment and theory were found for the absolute positions of groups of levels.

The Fuller nearside-farside (NF) theory of elastic angular scattering is widely used to understand structure in the differential cross sections of nucleus-nucleus collisions and (more recently) atom-atom and atom-molecule collisions. A long-standing difficulty with the Fuller NF theory has been its failure (by many orders of magnitude) to provide an explanation of structure in the elastic scattering of strongly absorptive systems. We have overcome this failure in a simple and straightforward way, with the help of a resummation of the partial-wave series for the scattering amplitude.

In the first Born approximation, antihydrogen formation in the laser-assisted collision between an antiproton and a positronium is studied. It is found that the antihydrogen formation cross section is notably enhanced at lower impact energy due to the laser modification. For a geometry of laser polarization parallel to the incident direction, the result is modified to the maximum.

The resonance states of a periodically driven barrier potential are investigated. We show that narrow shape-type resonances evolve from overlapping resonances of a static barrier as a result of an increase of the field amplitude. These shape-type resonances are associated with the field-induced barrier transparency phenomenon. It is suggested that cross-section experiments in strong laser fields may be used to uncover overlapping resonances.

We present theoretical results for the photoabsorption spectrum of an atom in parallel electric and magnetic fields, using the R-matrix method combined with quantum-defect theory. We introduce a radial basis set which is complete and orthonormal over a semi-infinite interval $[r_0,\infty ),$ to allow calculations to be performed for high Rydberg states in nonhydrogenic atoms without encountering problems due to linear dependence of the basis set. The nonhydrogenic character of the spectra is analyzed for Li and Rb, and a comparison is made with previous high-precision experiments which shows that the theoretical results agree very well with experiment.

The dynamics of Rydberg states of atomic hydrogen driven by elliptically polarized microwaves of frequency fulfilling the 2:1 classical resonance condition is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical results for quasienergies of the system are shown to be in good agreement with exact quantum data. The structures of the quantum states are found to reflect the underlying classical dynamics; especially we show the existence of nonspreading wave packets propagating on elliptical trajectories.

Possible fragmentation of a Bose-Einstein condensate with negative scattering length is investigated using a simple two-level model. Our results indicate that fragmentation does not take place for values of the coupling for which the system is metastable. We also comment on the possibility of realizing a fragmented condensate in trapping potentials other than an harmonic one.

Two interferometrically split and recombined subbeams which are in the same quantum state are treated as mutually orthogonal states by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)]. This conceptual error has created the illusion of a geometric phase in U(1) evolutions.

A photon position operator with commuting components is constructed, and it is proved that it equals the Pryce operator plus a term that compensates for the adiabatic phase. Its eigenkets are transverse and longitudinal vectors, and thus states can be selected that have definite polarization or helicity. For angular momentum and boost operators defined in the usual way, all of the commutation relations of the Poincaré group are satisfied. This new position operator is unitarily equivalent to the Newton-Wigner-Pryce position operator for massive particles.

The present paper deals with the quantum coordinates of an event in space-time, specified by a quantum object. It is known that these observables cannot be described by self-adjoint operators or by the corresponding spectral projection-valued measure. We describe them by means of a positive-operator-valued (POV) measure in the Minkowski space-time, satisfying a suitable covariance condition with respect to the Poincaré group. This POV measure determines the probability that a measurement of the coordinates of the event gives results belonging to a given set in space-time. We show that this measure must vanish on the vacuum and the one-particle states, which cannot define any event. We give a general expression for the Poincaré covariant POV measures. We define the baricentric events, which lie on the world line of the center of mass, and we find a simple expression for the average values of their coordinates. Finally, we discuss the conditions which permit the determination of the coordinates with an arbitrary accuracy.