We study the influence of the quantum statistics of the incident atoms in the Raman-Nath regime of atomic diffraction by an optical standing wave. The diffraction pattern of fermions shows a clear signature of the ‘‘exchange force’’ between particles.

We have analyzed the experimental results of ‘‘fast electrons’’ from slow atomic collisions [Baragiola et al., Phys. Rev. A 45, 5286 (1992)]. It is suggested that the observed negatively charged particles are not electrons, but sputtered or reflected ions.

We show reasons why negative ions cannot contribute significantly to our observation of fast electrons in slow atomic collisions [Phys. Rev. 45, 5286 (1992)]. We point out that the opposite suggestion by Yasui [preceding Comment, Phys. Rev. A 48, 1711 (1993)] results from multiple errors in his analysis, including inadequate consideration of energy conservation, the use of nonapplicable data from the literature, neglect of decay in flight of metastable negative ions, nonconsideration of detection efficiency, and the inconsistent fit of experimental data.

The normalization of the phase experiment of the scheme 1 in the paper of Noh, Fougères, and Mandel [Phys. Rev. A 46, 2840 (1992)] is inappropriate. The correct treatment of this measurement tends to the same result as in their scheme 2.

It is pointed out in response to Hradil and Bajer [preceding Comment, Phys. Rev. A 48, 1717 (1993)] that C${\mathrm{^}}_{\mathit{M}}$ and S${\mathrm{^}}_{\mathit{M}}$ cannot both be measured together by scheme 1, whereas they can by scheme 2. There is no phase angle whose cosine and sine both vanish, and putting C+iS equal to zero for certain measurement outcomes breaks the connection with phase.

In this paper, a quantum dynamical model describing the quantum-measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and the macroscopic limit with very large particle number in the measuring instrument, this model generally realizes the wave-packet collapse in quantum measurement as a consequence of the Schrödinger time evolution in either the exactly solvable case or the non-exactly-solvable case. For the latter, the quasiadiabatic case is explicitly analyzed by making use of the high-order adiabatic-approximation method, which manifests the wave-packet collapse as well as in the exactly solvable case. By highlighting these analyses, it is finally found that an essence of the dynamical model of wave-packet collapse is the factorization of the Schrödinger evolution rather than the exact solvability. Therefore many dynamical models including the previous well-known ones, whether they are exactly solvable or not, can be shown to be only the concrete realizations of this factorizability.

The group-theoretical treatment of Berry’s aholonomy developed in a paper of Giller, Kosiński, and Szijmanowski [Int. J. Mod. Phys. A 4, 1453 (1989)] is applied to some specific examples. The general structure of the corresponding Berry matrices is determined. All irreducible representations of SO(n) are found for which the Berry matrices parametrized by the points of ${\mathit{S}}^{\mathit{n}\mathrm{-}1}$≃SO(n)/SO(n-1) are determined by the Riemannian connection on ${\mathit{S}}^{\mathit{n}\mathrm{-}1}$.

The continuous-spontaneous-localization (CSL) description of state-vector reduction allows one to describe reality by the state vector. The mathematical structure of the theory, based upon a c-number white-noise source interacting with the quantum system, is reviewed. Then this description is generalized in two ways. First, a generalization is made to a wide class of c-number stochastic processes: using the square root of the probability density functional of the process, it is shown how to construct an evolution equation for the state vector which results in state-vector reduction. Second, within this wider framework the c-number source is completely eliminated and replaced by quantum operators, dubbed ‘‘index’’ operators, representing new physical variables which interact with the quantum system. In this case the state vector cannot represent reality as in the previous case, but it is shown how to write it unambiguously as a sum of ‘‘preferred basis’’ states, any one of which can represent reality. Therefore this quantum theory is open to the ensemble interpretation, where ‘‘ensemble’’ refers to the collection of possible real states. Three requirements sufficient for a viable ensemble interpretation are specified. It is shown how to satisfy these requirements, obtaining a purely quantum model that is equivalent to CSL and capable of describing reality.

The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution.

The interaction of two excited hydrogen atoms at large separations R is governed by the dipole-dipole term (≃${\mathit{R}}^{\mathrm{-}3}$). The potential-curve asymptotes are obtained by diagonalizing the dipole-dipole-interaction operator in the subspace of the degenerate unperturbed states. The symmetry properties are used for the reduction of the matrix size. In some special cases the eigenvalues are found analytically. For the interaction of highly excited atoms an approximate semiclassical quantization procedure is developed. The problem is reformulated via the three-dimensional three-term recursion relations. The discrete (index) variables are converted into continuous variables and approximate (adiabatic-type) separation of variables is achieved. This makes the problem effectively one dimensional and provides a qualitative interpretation of the spectrum structure. The simplest explicit expression for the spectrum is obtained by using the harmonic approximation in the index space. It applies for the extreme eigenvalues.

A general technique is outlined for investigating supersymmetry properties of a charged spin-1/2 quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schrödinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.

The quantum manifestations of chaos in the hydrogen atom in a generalized van der Waals potential, which includes the celebrated quadratic-Zeeman-effect problem under an appropriate limiting condition, are studied in detail. Using group-theoretical methods, we derive the matrix elements in an algebraic form. As the Hamiltonian is scale invariant, we introduce an appropriate scaling parameter. By considering the unperturbed hydrogen-atom problem, we demonstrate that suitable changes in the scaling parameter stabilize different parts of the spectrum depending upon the parameter’s value. For the present generalized van der Waals potential problem, we utilize this property of the scaling parameter effectively to improve the convergence of eigenvalues while diagonalizing the matrices for various parametric values. Then, we vary one of the system parameters in the range [0,3], study the level statistics, and observe a GOE-Poisson-Brody-Poisson-Brody-Poisson-GOE-type (where GOE means Gaussian orthogonal ensemble) of transition regime hitherto unidentified in any of the perturbed hydrogen-atom problems. Our results are not only in agreement with random-matrix-theory predictions but also justify classical and semiclassical investigations.

Birkhoff and von Neumann [Ann. Math. 37, 823 (1936)] proposed a nonstandard logic to describe quantum mechanics, in which the distributive laws of Boolean logic do not hold. In this paper we develop two algebras of propositions for classical mechanics that, like the quantum logical algebra, are based on a measurement theory. We adopt a simple classical measurement theory that allows the determination of any continuous phase-space function to any finite precision. Surprisingly, the resulting ‘‘classical logics’’ are non-Boolean, though the distributive laws hold. It appears that any physical theory with a mathematical space of physical states and an adequate description of measurement naturally yields a logiclike structure of experimental propositions, and that this ‘‘derived logic’’ can be non-Boolean even for theories much less radical than quantum theory.

Harmonic oscillators with time-dependent frequencies describe physics of the Paul trap of ions, radiation fields in media of time-varying dielectric constants, and so on. Their ground states are generically squeezed states. Here the effects of small anharmonicity on such nonclassical states are discussed. A perturbative calculation is performed, in which the unperturbed states are prepared in terms of the Hermitian invariant of the time-dependent harmonic oscillator. A quartic potential perturbation is investigated in detail. It is found that the correction term as well as the unperturbed term in the ground-state persistence probability can be expressed by the moments of a number operator alone. The oscillatory behavior is found in that correction term, which shows a competition of excitation and deexcitation due to the time dependence of the frequency and the nonlinear interaction. This may be observed experimentally as the temporal fluctuation of the quasienergy levels. Some formulas are also presented for the variances and correlations of the quadratures in the perturbed states.

As a prelude to a discussion of tunneling in the presence of dissipation, we discuss the damped harmonic oscillator. We show that for a harmonic-oscillator potential, the Caldeira-Leggett Hamiltonian can be reduced to a sum of independent harmonic-oscillator Hamiltonians by a normal-mode transformation. We then discuss tunneling through a parabolic barrier and explain the apparently contradictory results in the literature. The decay of a metastable state is then discussed. We argue that much of the published work on tunneling in dissipative systems has assumed unphysical initial conditions. We calculate the tunneling out of a metastable state, on the assumption that the environment is initially at zero temperature, and find that quantum tunneling is enhanced by dissipation.

Using monochromatized synchrotron radiation combined with angle-resolved photoelectron spectroscopy, we have measured the relative partial photoionization cross sections σ and photoelectron asymmetry parameters β for populating the ${\mathrm{Ca}}^{+}$ 4s, 3d, and 4p levels in the vicinity of the 3p-3d giant resonance of Ca.

Using correlated photon pairs produced via spontaneous parametric down-conversion, we have measured the absolute single-photon detection efficiencies and time responses of four detectors: two solid-state photomultipliers (SSPM’s) manufactured by Rockwell International Corp., and two custom-modified single-photon counting modules (SSPM’s) manufactured by EG&G, Canada. The highest observed efficiencies were 70.9±1.9% (with an SSPM, at a wavelength of 632 nm) and 76.4±2.3% (with an SPCM, at 702 nm). We believe these to be the highest reported single-photon detection efficiencies in the visible spectrum; they are important for quantum cryptography and loophole-free tests of Bell’s inequalities, as well as more prosaic applications such as photon correlation spectroscopy and velocimetry. We found that the time profile for coincidences between the SSPM and the SPCM consisted of a main peak with a 3.5-ns full width at half maximum (FWHM) preceded by a smaller peak by 11 ns. A similar time profile between two SPCM’s displayed only one peak, with a 300-ps FWHM. Afterpulses were detected in the SPCM’s at a level of less than ${10}^{\mathrm{-}4}$ of the counting rate, with an exponential decay time constant of 4.5 μs.

The angular distribution of electrons near the threshold of double ionization is considered in the framework of the Wannier mechanism [Phys. Rev. 90, 817 (1953)]. The wave propagation from the reaction to the free zone along the Wannier saddle is calculated in a general form for an arbitrary initial condition. The mapping of the initial boundary condition onto the final angular distribution has some special features. It is demonstrated that the Wannier mechanism does not necessarily imply a Gaussian distribution over the correlation angle.

We have calculated the energy and angular distributions for double ionization of He by one photon, over the range of photon energies 89–140 eV. Our results compare favorably with experimental data.

We have magneto-optically trapped the nine stable isotopes of xenon. Using the Zeeman slowing method to decelerate a beam of xenon atoms in the metastable 6s 3/2 [3/2${]}_2$ state (notation representing nl ${\mathit{J}}_{\mathrm{core}}$ [K=${\mathit{J}}_{\mathrm{core}}$+l${]}_{\mathit{J}}$), we load our trap to a collisionally limited density of more than ${10}^{10}$ atoms/${\mathrm{cm}}^3$. The two odd isotopes are trapped without a repumping frequency, even though they have hyperfine structure. The sensitivity of the trapping process to the laser frequency is exploited to make accurate measurements of the isotope shifts for the 6s 3/2 [3/2${]}_2$→6p 3/2 [5/2${]}_3$ laser-cooling transition and of the hyperfine constants for ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$.