The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schrödinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.

Phase separation of two-component untrapped and trapped Bose gases at finite temperature is studied. Conditions for the stability of a homogeneous binary Bose gas mixture at finite temperature and the density profile of the trapped binary mixture are obtained. Our extended results include the known results for zero temperature.

We show that noninterferometric techniques can produce quantitative phase measurements of quantum-mechanical wave fields with coherence requirements that are considerably reduced over those for interferometry.

We study the low-energy collective oscillations of a dilute Bose gas at finite temperature in the collisionless regime. By using a time-dependent mean-field scheme we derive for the dynamics of the condensate and noncondensate components a set of coupled equations, which we solve perturbatively to second order in the interaction coupling constant. This approach is equivalent to the finite-temperature extension of the Beliaev approximation and includes corrections to the Gross-Pitaevskii theory due to both quantum and thermal fluctuations. For a homogeneous system we explicitly calculate the temperature dependence of the velocity of propagation and damping rate of zero sound. In the case of harmonically trapped systems in the thermodynamic limit, we calculate, as a function of temperature, the frequency shift of the low-energy compressional and surface modes.

In the absence of incoherent relaxation processes, the emission, absorption, and transport of resonant radiation by an extended medium are all cooperative processes in which the medium participates as a whole. Such radiative processes depend sensitively on the geometry of the source, on its size and density, and on the interplay of electric polarization resonances with the ambient electromagnetic field. By making a succession of simple approximations, we reduce the radiative interaction problem to one of solving a linear integral equation for the time-dependent polarization of the radiating medium. For the example of one-dimensional geometry, we show that the polarization possesses a sequence of exponentially decaying eigenmodes that oscillate at frequencies slightly shifted from that of the fundamental resonance. Only a few of these modes, for any radiating medium, are strongly coupled to the electromagnetic field, and thereby radiate efficiently. All of the other modes, infinitely many of them, are found to radiate quite slowly, or not at all. We consider in detail the radiation emitted by an arbitrary initial polarization distribution when the electromagnetic field is initially empty. Analytical and numerical results are presented for the time-dependent fields that follow from a wide variety of initial excitations. A locally oscillatory exchange of energy is found to take place between the electric and polarization fields, which gives rise to a ringing of the radiated intensity. The spectra of the emitted light are shown accordingly to be complex in structure, and to have a frequency gap which becomes independent of the size of the medium and its initial polarization distribution for media that are sufficiently large. The gap is caused by the interference and interaction of oppositely propagating excitations.

The coherent, radiative excitation modes of a resonant medium lend a resonant character to the amplitudes for reflection and transmission of light. For a plane wave incident upon a slab-shaped medium of two-level atoms, the reflection and transmission coefficients exhibit sharp peaks and dips as a function of the detuning of the wave from the central atomic resonance frequency. The locations and widths of these resonant features for a normally incident plane wave correspond to the imaginary and real parts, respectively, of the radiative decay constants of the coherent excitation modes of the medium discussed in the preceding paper [Phys. Rev. A 61, 063814 (2000)]. For the case of oblique incidence, generalizations of the modes discussed in the preceding paper are required. The richly detailed, resonant frequency dependence of the reflected and transmitted intensities is shown to depend significantly on the angle of incidence and the polarization of the incident light.

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with s-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions—even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC’s) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze “superchemistry” dynamics.

The adiabatic passage scheme for quantum state synthesis, in which atomic Zeeman coherences are mapped to photon states in an optical cavity, is extended to the general case of two degenerate cavity modes with orthogonal polarization. Analytical calculations of the dressed-state structure and Monte Carlo wave-function simulations of the system dynamics show that, for a suitably chosen cavity detuning, it is possible to generate states of photon multiplets that are maximally entangled in polarization. These states display nonclassical correlations of the type described by Greenberger, Horne, and Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using coincidence detection of the photons escaping from the cavity is proposed. The correlations are found to originate in the dynamics of the adiabatic passage and persist even if cavity decay and GHZ state synthesis compete on the same time scale. Beyond entangled field states, it is also possible to generate entanglement between photons and the atom by using a different atomic transition and initial Zeeman state.

We investigate experimentally pattern formation in a passive semiconductor microresonator, one of the simplest nonlinear optical feedback systems, and potentially useful for optical parallel information processing. Dynamics of switching fronts and steady-state structures, as well as requirements for formation of solitons or localized structures are investigated in the spectral range where the nonlinearity of the semiconductor material is dispersive and defocusing. Extended patterns are found as predicted theoretically. Evidence of localization of structures is given.

Within the framework of a unified approach, we derive several identical representations of the realistic (and ideal) pattern functions $f_{k,l}$ necessary to reconstruct the density-matrix element ${\varrho }_{\mathrm{kl}}$ in the Fock basis from realistic quadrature distributions measured with a nonideal balanced homodyne detector of overall efficiency $\eta .$ To this end we first establish a biorthogonality relation for the pattern functions from which the form of the Fourier-transformed pattern functions can be easily read off. Then a different handling of the inverse Fourier transform yields several identical representations for the desired pattern functions provided that $\eta >1/2.\mathrm{}$ In particular, we derive a representation of the realistic pattern functions in terms of a finite weighted sum over scaled ideal ones. Compared to a previously given form, this expression has a nice analytical structure, reveals some general features of the realistic pattern functions, and is particularly well suited for their numerical computation. From this representation sum relations for the pattern functions follow. With their help we show that both a smoothed Wigner function and a generalized moment generating function can be directly sampled from realistic quadrature distributions. The corresponding sampling functions are basically shifted and/or scaled versions of the ideal pattern functions $f_{0,0}$ and $f_{0,k},$ respectively. As a by-product we derive the sampling functions needed to reconstruct the density matrix from the Fourier-transformed realistic quadrature distribution, i.e., from the s-ordered characteristic function with $s=-\left(1\mathrm{}-\eta \right)/\eta .$

In this paper, we describe how to realize conditional frequency entanglement swapping and to produce probabilistically a three-photon frequency entangled state from two pairs of frequency entangled states by using an acoustic-optical modulator. Both schemes are very simple and may be implementable in practice.

The $P\left(5\right)\mathrm{}$ 2-0 overtone transition of the ground electronic state of an HD molecule was studied by a modified-difference spectroscopic method, and its line center was determined with the help of precisely measured ${\mathrm{C}}_2{\mathrm{H}}_2$ transition frequencies. The center was measured to be 6576.896 ${\mathrm{cm}}^{\mathrm{-}1}$ with an accuracy better than 0.01 ${\mathrm{cm}}^{\mathrm{-}1}$, which is consistent with the theoretical calculation.

It is known that variational methods are the most powerful tool for studying the Coulomb three-body bound-state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be cured by applying the multiprecision package designed by D. H. Bailey. We consider variational basis functions of the type $\exp \left(-{\alpha }_n{r}_1-{\beta }_n{r}_2-{\gamma }_n{r}_{12}\right)$ with complex exponents. The method yields the best available energies for the ground states of the helium atom and the positive hydrogen molecular ion as well as many other known atomic and molecular systems.

The intensity of UV resonance transitions excited by electron impact is determined by both direct excitation and cascade processes. The lifetime for decay by spontaneous emission from a resonant state is short (typically < 10 ns). Using a pulsed electron gun technique established to separate these two effects we report a laboratory study of the UV spectrum of ${\mathrm{H}}_2$ attributed to cascade. We utilize the longer lifetimes (> 30 ns) for cascade channels to measure the intense spectrum of the Lyman band system $(B{}^1{\Sigma }_u^{+}–X{}^1{\Sigma }_g^{+})$ of ${\mathrm{H}}_2$ populated by cascade from higher lying $\left({\mathrm{E}\mathrm{F},\mathrm{G}\mathrm{K},\mathrm{H}}^1{\Sigma }_g^{+}\right)$ states.

We detect an omission in the paper “Conditionally exactly soluble class of quantum potentials” by A. de Souza Dutra [Phys. Rev. A 47, R2435 (1993)]. There, two strongly singular s-wave bound-state problems have been claimed completely solvable in closed form. Unfortunately, all the displayed wave functions are merely asymptotically correct solutions which do not satisfy the appropriate threshold boundary condition. We show that the incorporation of the threshold boundary conditions only leads to a very partial exact solvability at a single energy and for special couplings.

We show that the problems raised by Znojil [Phys. Rev. A ▪, ▪ (2000)] preceding paper, can be resolved and that, in fact, there exist the proposed singular conditionally, exactly solvable potentials [Phys. Rev. A 47, R2435 (1993)].

Calculated total cross sections for electron-impact ionization of ${\mathrm{C}}^{3+}$ using a unified theoretical approach are compared with high-resolution high-precision measurements clearly demonstrating interference of resonant multielectron reaction channels with direct ionization and inner-shell excitation. In particular, the so-called READI process, i.e., K-shell excitation with simultaneous capture of the incident electron (resonant-excitation) and a subsequent three-electron interaction resulting in simultaneous ejection of two electrons (auto-double-ionization) has been studied in unprecedented detail. The calculation is in very good agreement with the experimental cross section.

Using an alternative technique to trap keV ion beams, the kinetic-energy release after dissociative charge transfer of vibrationally cold ${\mathrm{HeH}}^{+}$ was measured. The results indicate that rapid radiative vibrational cooling takes place during the trapping, thus allowing a direct observation of the $a{}^3{\Sigma }^{+}$ metastable state of ${\mathrm{HeH}}^{+},$ which has been a subject of controversy in previous dissociative recombination experiments.

In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $\overrightarrow{t}\pm \infty ,$ the transition probabilities between adiabatic states are exponentially small. They are characterized by an exponent that depends on a phase integral along a path around a set of branch points connecting the energy-level surfaces in complex time. Only certain sequences of branch points contribute. We propose that these sequences are determined by a topological rule involving the Stokes lines attached to the branch points. Our hypothesis is supported by theoretical arguments and results of numerical experiments.