We investigate the behavior of the fundamental and second-harmonic fields in phase-matched traveling plane-wave second-harmonic generation, using the full-operator equations of motion. We find that, after a certain interaction length, both the macroscopic and quantum-statistical properties of the harmonic and fundamental fields are qualitatively different from those found in previous analyses. The mean fields do not vary in a monotonic way, but oscillate with the propagation length, leading to an unexpected periodic revival of the fundamental field, triggered by the quantum fluctuations always present in the mode. Accordingly, the amplitude noise of the fundamental, previously predicted to be perfectly squeezed for long interaction lengths, actually reaches a very small minimum for a definite length, then increases again.

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. The algorithm itself is not unitary because it involves a conditional measurement. However, it does yield a constant probability of the conditional measurement which does not depend on the input state of the bosonic system. We consider a physical implementation of unitary transformations acting on one-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.

An alternative representation for the parity-projected Wigner ${\mathbf{d}}^j\left(\beta \right)$ rotation matrix is derived as the product of two triangular matrices composed of Gegenbauer polynomials with negative and positive upper indices, respectively. We relate this representation for ${\mathbf{d}}^j\left(\beta \right)$ to the one presented by Matveenko [Phys. Rev. A 59, 1034 (1999)], which, in contrast with our result, requires for its evaluation a matrix inversion. In addition, identities for bilinear sums of Gegenbauer polynomials are derived. This work is based on our recently introduced invariant representations for finite rotation matrices [Phys. Rev. A 57, 3233 (1998)].

Experimental investigations of the photodetachment cross section for the negative hydrogen ion in the region near the $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold are discussed. Doppler-tuned spectroscopy in a collinear geometry is used to obtain a comparatively high resolution in this photon-energy range. The ions are accelerated in the ASTRID storage ring, which allows an accurate velocity measurement and further enables the application of momentum-spread reduction techniques. The fixed-frequency vacuum-ultraviolet laser beam (118 nm) is generated by sum-frequency mixing in a xenon gas cell. The photodetachment cross section exhibits pronounced resonances that correspond to the rich spectrum of doubly excited ${}^{1}P$ states near the $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold. The position of the resonances is determined with an accuracy that challenges the current theoretical developments. The experimental observations are used to predict the behavior of a dipole series below $\mathrm{H}\mathrm{}(n=2\mathrm{}).$ The measurement on both hydrogen and deuterium facilitates a study of isotope effects. By means of momentum-spread-reduction techniques it should be possible to resolve the natural linewidth of the narrow dipole resonances. Preliminary studies show that improvements in electron cooling of the ${\mathrm{H}}^{-}$ beam promise to reach this limit. Finally, the feasibility of extending the high-resolution work to higher-lying $\mathrm{}(n=3\mathrm{})\mathrm{}$ resonances is briefly discussed.

We have performed a kinematically complete experiment for triple ionization in atomic collisions. Data were obtained for 3.6-MeV/amu ${\mathrm{Au}}^{53+}$ impact on Ne. A specific Dalitz representation was developed allowing one to plot in a single spectrum the energy of all three ionized electrons and, simultaneously, obtain information on their emission angles with respect to the projectile direction. The data show distinct fragmentation patterns favoring very asymmetric energy partitionings with one fast and two slow electrons. They are compared to various Classical Trajectory Monte Carlo (CTMC) models. The experimental results are well described only if the electron-electron interaction is included throughout the collision and surprisingly, if the classically modeled electrons are fully correlated in the initial state.

A self-interacting two-level system depending on an external parameter is investigated. The most striking feature exhibited in this system is the presence of a nonzero tunneling probability in the adiabatic limit for large enough interaction strength. Possible experimental observation of this breakdown of adiabaticity using a Bose-Einstein condensate in an optical potential is suggested.

We present a quantization scheme for the electromagnetic field in dispersive and lossy dielectrics with planar interfaces, incorporating propagation in all the spatial directions, and including both TE and TM polarized fields. Field quantization is carried out starting from a microscopic model for the polarization quanta interacting with the electromagnetic field. Dissipation is described by considering the coupling of the polarization quanta of the system with the reservoir oscillators in the usual Langevin approach. The method is applied to a semi-infinite medium and expressions for the electromagnetic field operators are obtained in the two different spatial regions, i.e., in the vacuum and in the dielectric. As a check of our quantization scheme, we have verified that the obtained vector potential operator and its conjugate momentum satisfy equal-time canonical commutation rules, giving rise to the prescribed transverse Dirac $\delta$ function.

Total cross sections for electron scattering on ${\mathrm{WF}}_6$ molecules have been measured in the 75–3500-eV energy range by an absolute transmission method. The data are compared to other heavy gases, ${\mathrm{SF}}_6,$ Xe, and ${\mathrm{GeH}}_4.$ Apparently different energy dependencies for these gases can be described by the same, simple four-parameter formula. A study of atomic total-cross-section parameters in the keV energy range for 15 atoms from H to W is presented.

We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both approaches, we show that the output state of the algorithm, after long enough time, is the desired equilibrium. We present a numerical analysis of one of these approaches for small systems. We show how equilibrium (time-)correlation functions can be efficiently estimated on a quantum computer, given a preparation of the equilibrium state. The quantum algorithms that we present are hard to simulate on a classical computer. This indicates that they could provide an exponential speedup over what can be achieved with a classical device.

It is shown that encoding the state of a quantum computer (or other quantum information-processing device) for error correction has the effect of making its operating states macroscopically indistinguishable; all the more, the more “stable” the code is, that is, the more errors it can correct in each pass. It is also shown that for nondegenerate codes the expectation values of macroscopic observables in such encoded states are identical to those that would be obtained for a totally mixed state of maximum entropy, where again the degree of indistinguishability increases with the number of errors corrected by the code. The results can be used to estimate the decoherence rates for systems of qubits under certain forms of interaction with the environment: it is found that when the qubits are encoded all coherent superpositions decay, to lowest order, at the same rate, which scales more slowly with the number of physical qubits than the decoherence rate for macroscopic coherent superpositions (“Schrödinger cats”) of the bare qubits.

An invariant graph-theoretical approach is proposed which allows to be determined the nodal structure of degenerate-state wave functions up to some equivalence. Nodal structures of p- and d-state wave functions for one-electron systems in a spherically symmetrical field are analyzed.

Electron-impact excitation of argon from the ${3p}^{5}4s$ $\mathrm{}(J=0,2\mathrm{})\mathrm{}$ metastable states to the ${3p}^{5}4p$ $\mathrm{}(J=0,1,2,3\mathrm{})\mathrm{}$ manifold has been investigated in the semirelativistic first-order distorted-wave and plane-wave Born approximations. The results are compared with recent experimental data of Boffard et al. [Phys. Rev. A 59, 2749 (1999)] and R-matrix predictions by Bartschat and Zeman [Phys. Rev. A 59, R2552 (1999)]. In cases for which perturbative approaches are expected to be valid, the plane-wave Born approximation is found to be sufficiently accurate and thus allows for an efficient calculation of results over a wide range of collision energies.

We report the observation of the electromagnetically induced inhibition of two-photon absorption with atomic sodium vapor as a test medium. A 60% reduction of two-photon resonant absorption was recorded at the $3S-4D$ transition when a cw coupling laser was applied at the $3P-5S$ transition.

Conditional interference fringes are found when parametric down-converted photon pairs are sent to two Young’s double slits. The transmitted photon pairs are detected in coincidence as a function of the transverse spatial coordinates. Conditional interference is found in the fourth-order interference pattern with and without second-order interference. A quantum multimode calculation shows that the fourth-order Young interference pattern is strongly dependent on the transverse profile of the pump laser that generates the twin photon pairs. Conditionality is observed by tailoring this profile. A control of the conditionality is obtained via the pump laser beam transverse profile.

The effect of the exciton-exciton interaction on the resonance fluorescence of quantum-well excitons is studied. At relative low exciton density, the resonance fluorescence exists only when the exciton-exciton interaction is not negligible. The fluorescence spectrum changes from one peak to two peaks when the pump light intensity is increased beyond a critical value. The fluorescence light is antibunching when the mean exciton number in the quantum well is more than 0.5. The difference between exciton resonance fluorescence and two-level atom resonance fluorescence is presented.

For a time-dependent $\tau$-periodic harmonic oscillator of two linearly independent homogeneous solutions of the classical equation of motion that are both bounded over time (stable), it is shown that there is a representation of states that are cyclic up to multiplicative constants under $\tau$ evolution or $2\tau$ evolution depending on the model. The set of the wave functions is complete. Berry’s phase, which could depend on the choice of representation, can be defined under the $\tau$ or $2\tau$ evolution in this representation. If a homogeneous solution diverges as time goes to infinity, it is shown that such a Berry phase cannot be defined in any representation considered. Berry’s phase for the driven harmonic oscillator is also considered. For the cases where Berry’s phase can be defined, the phase is given in terms of solutions of the classical equation of motion.

We propose a scheme to generate number states, and specific superpositions of them, of the vibrational motion of a trapped ion via laser excitation of two vibronic transitions. Without detrimental effects on the internal state preparation, the ion can be initially in thermal motion and undergo spontaneous emission. In particular, qubits that are robust against noise $(\alpha |0〉+\beta |1〉$ states) can be generated with arbitrary amplitudes.

In a recent paper [Phys. Rev. A 55, 1647 (1997)], Pardy has proposed an experiment to measure the Lorentz contraction starting from the zeros of the power spectral density of the Čerenkov radiation emitted by two bunches of electrons. It is shown that this is not the case since all the calculations and results are relative to the laboratory system S. The Lorentz contraction would be measured only if the rest length $l_0=\gamma l$ in the system $S^{\prime }$ comoving with the two bunches of electrons could be performed.

We have investigated the effect of free electrons on the spectral properties of high-order harmonics generated by 30-fs Ti:sapphire laser pulses in a neon gas jet. Our observations clearly indicate the possibility of continuously tuning the harmonic wavelength in the region below 20 nm, by taking advantage of the blue shift of the harmonic wavelength induced by the presence of free electrons in the gas. We have experimentally demonstrated that this allows one to cover the entire spectral region between two consecutive harmonics of the unshifted spectrum. Different amounts of blue shift are imparted by simply changing the gas jet position relative to the laser beam waist, namely, by varying the effective laser intensity experienced by the gas jet when it is moved across the focal region. We have also interpreted the experimental results in terms of a simple model of the generation process based on the tunnel ionization of an atom exposed to an ultraintense laser field.

Neutral fermions of spin $\frac{1}{2}$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac-Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be reduced to two simultaneous ordinary differential equations by separation of variables in spherical coordinates. For a wide variety of central electric fields, bound-state solutions of critical energy values can be found analytically. The degeneracy of these energy levels turns out to be numerably infinite. This reveals the possibility of condensing infinitely many fermions into a single energy level. For radially constant and radially linear electric fields, the system of ordinary differential equations can be completely solved, and all bound-state solutions are obtained in closed forms. The radially constant field supports scattering solutions as well. For radially linear fields, more energy levels (in addition to the critical one) are infinitely degenerate. The simultaneous presence of central magnetic and electric fields is discussed.