The behavior of the exact impulse wave function is investigated at intermediate and high impact energies. Numerical details of the wave function and its perturbative potential are reported. We conclude that the impulse wave function does not tend to the proper Coulomb asymptotic limit. For electron capture, however, it is shown that the impulse wave function produces reliable probabilities even for intermediate velocities and symmetric collision systems.

We present a variation of the isolated-core excitation (ICE) method that measures the linewidths of autoionizing resonances regardless of the limitations imposed by an instrumental linewidth. By exciting an autoionizing state via different ICE satellite transitions, we determine the linewidth of the state from Fano q values of asymmetric spectral profiles. Since the Fano q is insensitive to instrumental broadening, we can measure autoionizing resonance linewidths below the bandwidth of our laser.

The result that Lynch and Mavromatis [Phys. Rev. A 52, 55 (1995)] obtained by Puri's definition of squeezing has no relation to Hong and Mandel"s higher-order squeezing [Phys. Rev. Lett. 54, 323 (1985)]. We also point out that, for an electromagnetic field, the nonclassicality of the squeezed state defined according to Puri's general uncertainty relation is not preserved.

Arguments made recently by Howard [Phys. Rev. A 51, 3934 (1995)] as to (i) the consequences of the nonexistence of an effective potential in the problem of a hydrogen atom in a circularly polarized microwave field, and (ii) the claimed advantages of his stability analysis as compared to methods based on harmonic expansion at an equilibrium point are examined.

The criticisms of Farrelly [preceding paper, Phys. Rev. A 55, 1550 (1997)] are shown to stem from confusion concerning basic physical concepts. Similarities and differences between ``effective potentials'' and ``zero-velocity curves'' are elucidated.

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.

We analyze the difference between classical and quantum nonlinear dynamics by computing the time evolution of the Wigner functions for the simplest polynomial Hamiltonians of fourth degree in coordinate and momentum. This class of Hamiltonians contains examples which are important in wave and quantum optics. The Hamiltonians under study describe the third-order aberrations to the paraxial approximation and the nonlinear Kerr medium. Special attention is given to the quantum analog of the conservation of the volume element in classical phase space.

The electric Aharonov-Bohm effect is usually explained by means of the scalar potential, which is present in a multiply connected region of space time where no electric field acts on the charged particle. An alternative interpretation is given in terms of the particle's polarization field penetrating the region occupied by the electric field but inaccessible to the particle itself. Similarly, the magnetic Aharonov-Bohm effect is usually explained by means of the vector potential, which is present in a multiply connected region of space where no magnetic-induction field acts on the charged particle. An alternative interpretation of this effect is given in terms of the particle's magnetization field penetrating the region occupied by the magnetic-induction field but inaccessible to the particle itself. Our interpretations of the electric and magnetic Aharonov-Bohm effects are both developed by using the multipolar form of the Lagrangian instead of the minimal-coupling form in the Feynman path integral.

Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. We show that the error for entangled states is bounded linearly by the error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component.

We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

Omitted end note.

The microscopic operators have been investigated for radiation and polarization fields within a discrete molecular medium. The medium comprises atoms (or molecules) each containing an arbitrary number of energy levels. Explicit mode expansions have been derived for the quantized microfields in terms of normal Bose operators for polariton creation and annihilation. These microscopic operators have been demonstrated to yield the correct macroscopic and local field operators presented in part I [Phys. Rev. A 53, 3543 (1996)]. On the other hand, the commutation relations between the expanded microfields differ from the exact commutation relationships. This happens because the microfields have been described in terms of a continuous refractive index. Hence the expanded field operators do not extend to modes with extremely high frequencies ranging over the photon umklapp frequencies cG. In spite of that, the proper commutation relations hold between the resultant macroscopic (averaged) fields. This justifies separate quantization of the slowly modulated (macroscopic) part of the radiation field in linear dielectrics: such an approach is utilized in phenomenological quantization schemes. Finally, although the microscopic operators presented are not complete, the mode expansions adequately represent the quantized microfields associated with the optical modes in condensed molecular media.

Caldirola [Nuovo Cimento 18, 393 (1941)] and Kanai's [Prog. Theor. Phys. 3, 440 (1948)] time-dependent approach for dissipative systems can be traced back to the conventional system-plus-reservoir approach; however, it apparently violates the uncertainty principle. This discrepancy can be avoided by considering a consistent transition between the Caldirola-Kanai formalism and a logarithmic nonlinear Schrödinger equation that requires not only a transformation of the operators, but also a nonunitary transformation of the wave function. This procedure also shows the equivalence of three at first sight incompatible approaches to describe dissipative quantum systems.

By using an appropriate dynamic stochastic quantization method, we quantize a Marcoffian process obeying a generalized Pauli exclusion-inclusion principle. The dynamics of the so obtained quantum system is governed by a nonlinear Schrödinger equation. If the exclusion-inclusion principle holds in the momentum space, the ground states of the system are described by statistical distributions interpolating between boson and fermion ones.

An efficient coding circuit is given for the perfect quantum-error correction of a single quantum bit (qubit) against arbitrary one-qubit errors within a five-qubit code. The circuit presented employs a double ``classical'' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. Another circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary one-qubit errors. In addition, the performances of two error-correction schemes, one based on the quantum Zeno effect and the other using standard methods, are compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase diffusion.

We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm effect, regarding how to measure in principle the zigzagness of the trajectory of propagation (aberration from its classical trajectory) of a massive particle in quantum mechanics. Experiment I is conceived to show that contributions from quantum paths aberrating from the classical trajectory are directly observable. Experiment II is conceived to measure average length, scaling behavior, and critical exponent (Hausdorff dimension) of quantum-mechanical paths.

The n=10 ${}_{}{}^{+}{}_{}{}^{}\mathrm{F}_3^{}{}_{}{}^{}$${\mathrm{-}}^{+}$${\mathrm{G}}_4$ energy interval in helium is measured to an accuracy of 200 parts per billion. Rydberg states of helium are created by charge exchange between a helium ion beam of a few keV and a dense thermal beam of neutral cesium atoms. A microwave transition is driven between the two states in a Ramsey-separated-oscillatory-field configuration yielding a linewidth of less than 0.2 MHz. The result of 2017.3254(4) MHz is the most accurate measurement of any Rydberg fine structure and can be compared to a similarly accurate theoretical prediction of this interval. This comparison gives a very high-precision test of physics on the large-distance scale of these Rydberg states, including the nonrelativistic Coulomb potential, relativistic effects, and quantum-electrodynamical effects such as the retardation (or Casimir) interactions. A disagreement between theory and experiment indicates the possibility of additional new physics on this distance scale.

This paper presents theoretical ab initio calculations and experimental measurements of the binding energy of the metastable ${\mathrm{He}}^{\mathrm{-}}$1s2s2p${\mathrm{}}^4$P ion. The calculated 77.518±0.011 meV and the measured 77.516±0.006 meV values for the binding energy are in excellent agreement and they represent a significant improvement in the accuracy compared to previous studies. The experimental technique is based on the determination of the εs-wave Wigner threshold associated with detachment to the 1s3s${\mathrm{}}^3$S state of the neutral He atom. The yield of the 1s3s${\mathrm{}}^3$S He level was monitored by applying resonant ionization spectroscopy.