We consider the use of arbitrary phases in quantum amplitude amplification, which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan (\phi /2)=\tan (\phi /2)\left(1\mathrm{}-2a\right),$ where φ and φ are the phases used and where a is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $1/\sqrt{a}$ can be tolerated in amplitude amplification.

The static dipole, quadrupole, and octupole polarizabilities of helium are calculated for the four Rydberg series $1sns{}^{1}S,$ $1sns{}^{3}S,$ $1snp{}^{1}P,$ and $1snp{}^{3}P$ with n up to 10, using variational wave functions in Hylleraas coordinates. The large-$n$ expansions for polarizabilities are presented for these series.

Two autodissociating resonances of F and G symmetries in positronium-hydrogen scattering are found using the method of complex-coordinate rotation. The positions and widths of the lowest F and G waves are determined using fully correlated Hylleraas wave functions.

Atomic spectra of singly ionized praseodymium and neodymium have been measured by means of the collinear laser-ion-beam spectroscopy. Hyperfine structures of 19 atomic transitions in the wavelength range from 560 to 590 nm were resolved and hyperfine structure constants A and B were determined for 28 levels.

Excitation energies for $3l-{4l}^{\prime }$ particle-hole states of Ni-like ions are determined to second order in relativistic many body perturbation theory. The calculations start from a closed-shell Dirac-Fock potential, and include second-order Coulomb and Breit-Coulomb interactions. Retarded electric-dipole matrix elements (in length and velocity forms) are calculated in second order for transitions from excited $3l-{4l}^{\prime }$ states to the closed-shell ground state. Wavelengths for 3-4 and 4-4 transitions are compared with experimental data, and with other high-precision calculations. Trends of oscillator strengths as functions of nuclear charge Z are shown graphically for selected transitions.

In this paper we investigate the existence and study the properties of linear dichroism and of circular dichroism in a linear, achiral molecule through a process in which absorption of a single photon results in the simultaneous ejection of two electrons. The two dichroic effects are found to provide complementary information about molecular double photoionization and possess very different properties. Dependence of such chiralities on nuclear rotation has properly been studied by using parity-adapted states to represent the target molecule and its doubly charged residual photoion. The discussion presented is independent of any dynamical models. Both magnitude and behavior of the linear as well as circular dichroisms have phenomenologically been calculated for double photoionization in a ${\sigma }_g^2$ shell of a $D_{\infty h}$ molecule rotating in its ${}^1{\Sigma }_g^{+}$ electronic state.

The $3p$ photoelectron spectra of Cr, Mn, Fe, and Co atoms have been studied experimentally and theoretically. The $3p$-$3d$ interaction in the final ionic state gives rise to an $\mathrm{LS}$ multiplet structure spanning a binding-energy range of around 20 eV. The prominent high-spin components at low binding energies contrast with the broad and weak low-spin components at high binding energies. Term-dependent lifetime broadening by super-Coster-Kronig decays is the main cause of the almost complete suppression of the latter lines. The corresponding $3p$ photoelectron spectra of the metals display only a single broad asymmetric line. The influence of correlation on the $3p$ photoelectron spectra is shown to be less dramatic than in the case of the better known $3s$ photoelectron spectra. We show that, while the peculiarities in the $3s$ spectrum are caused by configuration interaction, the single-configuration approximation already provides the clue to the interpretation of the $3p$ spectrum.

We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schrödinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In this manner we take into account both collisions between noncondensate-noncondensate and condensate-noncondensate atoms. We solve the linear response of these equations, using a time-dependent Gaussian trial function for the condensate wave function and a truncated power expansion for the deviation function of the thermal cloud. As a result, our calculation turns out to be characterized by two dimensionless parameters proportional to the noncondensate-noncondensate and condensate-noncondensate mean collision times. We find in general quite good agreement with experiment, both for the frequencies and damping of the collective modes.

The influence of the anisotropy of the effective dielectric constant, effective electro-optic effect, drift mobility, and photoexcitation cross section on the photorefractive two-wave mixing gain and speed are analyzed in detail. Theoretical expressions that include all these influences and that are valid for the single-level band model are reported. They can give the necessary guidance for optimizing the interaction geometries and the extrinsic crystal properties for systems based on two- and four-wave mixing or self-pumped phase conjugation. Concrete examples are given for ${\mathrm{KNbO}}_3$ and ${\mathrm{BaTiO}\mathrm{}}_3,$ where all possible two-beams interaction geometries are analyzed in the plane of maximum photorefractive nonlinearity $(bc$ and $\mathrm{ac}$ plane, respectively). It is shown that, besides the dielectric constant and the electro-optic effect, also the anisotropy of the photoexcitation with respect to wave polarization plays a major role and strongly influences the optimum geometry, allowing potentially very large enhancement of the exponential gain. Corrections to the standard expressions for photorefractive two-wave mixing amplification in the depleted pump regime are also given. They apply in the case of asymmetric incidence and/or under the presence of anisotropic photoexcitation.

Following a proposal by two of us [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)], we have measured the Wigner function at the origin of phase space for a single photon field. Its value is negative, exhibiting the nonclassical nature of this state. The experiment is based on the absorption-free detection of the microwave field stored in a superconducting cavity [G. Nogues et al., Nature (London) 400, 239 (1999)]. Extension to a measurement of the Wigner function over the complete phase space is discussed.

We demonstrate the possibility of practical tomographic determination of arbitrary input-output transformations. It is shown that the Liouville-space formalism provides a generalization of standard tomography encompassing the reconstruction of processes as well as of quantum states.

We have studied the excitation and charge transfer (including resonant charge transfer) processes of H and ${\mathrm{H}}^{+}$ collisions in a wide range of collision energies by solving the time-dependent Schrödinger equation with the classical trajectory approximation for the projectile. The time-dependent Schrödinger equation is solved by the split-operator method with a generalized pseudospectral (nonuniform grid) method. The calculated impact excitation and charge transfer cross sections are in reasonable agreement with the available experimental measurements. Such a time-dependent Schrödinger equation method can be used to study atom-ion collisions in a wide range of collision energies. Moreover, the time-dependent Schrödinger equation method can provide more dynamic information and physical insights. Combined with time-dependent density functional theory, our time propagator holds significant promise for many-electron processes in the interactions of highly charged ions with atoms, molecules, and solids.

A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a “soft-pair” approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.

We demonstrate the magnitude dependence of electromagnetically induced transparency, in a three-level cascade scheme in rubidium, on the probe and coupling field polarizations. We show that this dependence is due to the presence of the degenerate magnetic sublevels and the strengths of their relative dipole matrix elements. It is shown that this can lead to modified absorption profiles when electromagnetically induced transparency is used for spectroscopic purposes. We present theory that is in good agreement with our experiments.

It is known that entanglement swapping can be used to realize entanglement purification. In this way, two particles belonging to different nonmaximally entangled pairs can be projected probabilistically to a maximally entangled state or to a less entangled state. In this paper, we show, when the less entangled state is obtained, then a maximally entangled state can be obtained probabilistically from this less entangled state if a unitary transformation is introduced locally. The probability of success of our scheme is equal to the entanglement of a single pair purification (if two original pairs are in the same nonmaximally entangled states) or to the smaller entanglement of a single pair purification of these two pairs (if two original pairs are not in the same nonmaximally entangled states). The advantage of our scheme is that no continuous indefinite iterative procedure is needed to achieve optimal purification.

The properties of a one-dimensional system of bosons interacting via a repulsive delta-function potential are studied here using a modified Bogolyubov method. The motivation for the modification is twofold: First, to cure an internal inconsistency that predicts a single-particle ground-state occupancy of minus infinity when the Bogolyubov scheme is applied to this model. Second, to abandon the initial assumption—at odds with the exact result—of a macroscopically occupied single-particle ground-state. Whereas the Bogolyubov scheme uses the lowest-energy-single-particle state as a reservoir for the other states, our method uses, for each single-particle state, all single-particle states of lower energy collectively as a reservoir. This not only removes the inconsistency but also allows us to estimate the ground-state energy in much better agreement with the exact result.

Each Bell state has the property that by performing just local operations on one qubit, the complete Bell basis can be generated. That is, states generated by local operations are totally distinguishable. This remarkable property is due to maximal quantum entanglement between the two particles. We present a set of local unitary transformations that generate out of partially entangled two-qubit state a set of four maximally distinguishable states that are mutually equally distant. We discuss quantum dense coding based on these alphabet states.

Energy shifts arising from two-photon-exchange graphs are calculated for $n=2\mathrm{}$ triplet states of heliumlike ions and tabulated for the range of nuclear charges $Z=30\mathrm{}–92.$ The results are compared with second-order many-body perturbation theory (MBPT), and the differences are identified as QED effects associated with retardation and negative energy states not included in MBPT.

We study the interaction effects on the condensates by considering a model of one-dimensional bosons. The harmonic external potential allows for the formation of a condensate in these systems. Using a density-functional theory-type formalism we obtain an equation describing the condensate wave function in the limit of very strong interactions between the bosons. We then consider a model of strongly interacting two-component system of bosons and study its stability conditions. Similar to the weakly interacting case, the two-component system exhibits coexisting and segregated phases depending on system parameters.