We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the nonlinear Schrödinger-Langevin equation, and the Caldirola-Kanai equation (with an additional term), as particular cases.

The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm [Phys. Rev. 122, 1649 (1961)] and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the arrival time of the eigenfunctions is not sharply defined. However, strongly peaked real-space (normalized) wave packets constructed with narrow Gaussian envelopes centered on one of the eigenfunctions provide an arbitrarily sharp arrival time.

We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator.

It has been suggested that a single photon can interfere with itself even if the difference between the two paths in the interferometer is larger than the “length” of the photon [Kessel’ and Moiseev, JETP Lett. 58, 81 (1993)]. The interference is regained by detecting the photons using a photon-echo process, where the absorbing atoms will, effectively, act as narrow-band filters. Such an experiment has several unique features. For example, single photons are used to carry out what is generally regarded as a multiphoton process; the absorption of a single photon can be regarded as separated into two different moments in time; the fact that the single-photon interference is regained using atoms acting as narrow-band filters as the detector means that the control of the detection process is quite different from cases where electronic (or possibly photographic) detection is used to register the interference etc. In general, interference and absorption are combined and intertwined in the experiment, which is discussed in this paper, in a way that has not been done before. In the present paper the possibility to carry out such an experiment in practice is investigated in some detail. The signal strength is explicitly calculated and the results are compared with our experimental data for the case of many interfering photons. We imply that this result can readily be extrapolated to the single-photon situation. We analyze the material parameters that are important for carrying out the experiment and give specific examples of some suitable materials.

In this paper, we discuss the tunneling time of a quantum particle through a rectangular barrier. The reflection and transmission times associated with the wave packets representing the particle are discussed. By using an initial Gaussian momentum distribution, we carry out a comparative analysis of the stationary phases of the incident, reflected, and transmitted wave packets leading to the reflection and transmission times $\Delta t_R$ and $\Delta t_T,$ respectively. In the present treatment of this old and very known problem we take into account the deformations of the reflected and transmitted momentum distributions. These deformations produce a dependence of the reflection and transmission times on the location of the initial wave packet. In a parallel calculation, by numerically monitoring the time evolution of the system, we characterize a reflection and a transmission time. Such times agree with the ones obtained via the stationary phase method.

We consider the teleportation of a field state, which is in a coherent superposition of $2^n$ Fock states, from one cavity to another, and present an experimentally feasible scheme for this purpose.

We present a general solution to the construction of such an entanglement in an N-dimensional Hilbert space that effects state teleportation. For $N>\mathrm{}2\mathrm{}$ the construction is nonunique and can be chosen to transfer the state to a preselected basis. We discuss possible applications to state preparation in various physical systems.

A quantum copying machine producing two (in general nonidentical) copies of an arbitrary input state of a two-dimensional Hilbert space (quantum bit) is studied using a quality measure based on distinguishability of states, rather than fidelity. The problem of producing optimal copies is investigated with the help of a Bloch sphere representation, and shown to have a well-defined solution, including cases in which the two copies have an unequal quality, or the quality depends upon the input state (is “anisotropic” in Bloch sphere language), or both. A simple quantum circuit yields the optimal copying machine. With a suitable choice of parameters it becomes an optimal eavesdropping machine for some versions of quantum cryptography, or reproduces the Bužek and Hillery result for isotropic copies.

We investigate the “teleportation” of a quantum state using three-particle entanglement to either one of two receivers in such a way that, generally, either one of the two, but only one, can fully reconstruct the quantum state conditioned on the measurement outcome of the other. We furthermore delineate the similarities between this process and a quantum nondemolition measurement.

The multiconfiguration Dirac-Fock model is employed to evaluate the effects of relativity and electron correlation on the hyperfine interaction constants of the ${4d5s}^2{}^2{D}_{3/2}$ and ${}^2{D}_{5/2}$ levels of yttrium. The wave-function expansions are obtained with the active space method, where configuration-state functions of a specific parity and $J$ value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. The calculated electric quadrupole hyperfine constants are used to evaluate the nuclear electric quadrupole moment of isotope 90 of yttrium, for which the value $Q=-0.125\left(11\right)\mathrm{}$ b is found.

Two experiments have been performed at the CERN Low Energy Antiproton Ring (LEAR) facility to study the lifetime shortening of metastable antiprotonic helium atoms by the presence of ppm admixtures of oxygen. The change in shape and lifetime of the delayed annihilation time spectra can be reproduced fairly well by fitting a simple four-level model to the data and assuming equal quenching cross sections for all metastable levels. From this we deduce a quenching cross section of $(1.35\mathrm{}\pm 0.03)\times {10}^{-15}\hspace{0.5em}{\mathrm{cm}}^2$ at a temperature of 100 K. An analysis of data from a previous experiment gives a value for the quenching cross section at room temperature of $(1.34\mathrm{}\pm 0.07)\times {10}^{-15}\hspace{0.5em}{\mathrm{cm}}^2.$ Resonant laser deexcitation of the levels $\mathrm{}(n,l)=(37,34)\mathrm{}$ and $\mathrm{}(39,35)\mathrm{}$ (the lowest metastable levels of the cascades $\upsilon =n-l-1=2$ and $3,$ respectively) was used to examine the time development of the population of these levels. Quenching cross sections of $(1.32\mathrm{}\pm 0.10)\times {10}^{-15}\hspace{0.5em}{\mathrm{cm}}^2$ and $(1.90\mathrm{}\pm 0.10)\times {10}^{-15}\hspace{0.5em}{\mathrm{cm}}^2$ were deduced for the $\upsilon =2\mathrm{}$ and $\upsilon =3\mathrm{}$ cascades from these studies at 100 K.

The time-resolved spectrum of a laser-produced plasma in ${\mathrm{H}}_2$ exhibits a continuum that we attribute to radiative collisions of H atoms in a $2p$ state with ground-state neutral atoms and protons. This binary collision Lyman-α line wing observed from 1150 Å to 1700 Å is emitted by the shock dissociated gas that surrounds the focal region. The observed temperature, electron density, and shock front speed confirm models of the shock that predict that Lyman α arises from a shell of atomic hydrogen in which the neutral atom and ion densities are sufficient to create the observed line broadening. The experimental far wing spectrum agrees with unified theory calculations of the Lyman-α line, which allow for the dependence of the radiative dipole moment on internuclear separation during a radiative collision. Broad neutral atom effects become evident at 1180 Å, 1260 Å, and 1600 Å when the density of neutral perturbers is of the order of ${10}^{20}{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{m}}^3,$ while features at 1230 Å, 1240 Å, and 1400 Å appear when the plasma is highly ionized. These satellites result from free-free transitions of a H atom during collisions with other neutral atoms and protons and are correlated with potential curves and radiative dipole moments of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}.$

The processes of Coulomb deexcitation and quasiresonant charge exchange have been considered in the framework of the asymptotic theory of the nonadiabatic transitions. The approach used is scrutinized and improved in the light of recent critical statements. The unambiguous agreement between different calculations for energies $\epsilon >0.5\mathrm{}\mathrm{eV}$ proves the approximation used to be valid.

In previous papers [Phys. Rev. A 50, 4743 (1994); 54, 4815 (1996)] a theoretical description of the signals associated with the muon spin relaxation of simple muonated gaseous radicals has been presented. These gaseous radicals were assumed to have been formed during the slowing down process of the muons in the gaseous target and assumed to be stable chemical species at the initial observation time. The observed signals were attributed to these stable radicals. In this paper the theoretical description is extended to include situations where the radicals are formed in slow processes as opposed to fast processes with the assumption that the muon exists as muonium at the initial observation time. This muonium then reacts for the time duration of the experiment, which is limited by the muon’s lifetime. The theoretical treatment is based on an operator expansion of the spin density operators for muonium and for the molecular radicals whose time dependences are described by a set of coupled linearized quantum kinetic equations. Relaxation of the signals is due to two effects, namely, the chemical reactions themselves and the collisions that reorient the molecular radical’s rotational angular momentum. This affects the muon’s spin via intramolecular couplings between the muon’s spin, the radical’s free-electron spin, and the radical’s rotational angular momentum. The coefficients of the radical’s spin Hamiltonian, the collisional reorientation lifetimes (cross sections), and the chemical reaction rates may be used as fitting parameters to describe the experimental signals. These could also be calculated from first principles.

Calculated values of the dipole polarizabilities of the ground states of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ are in good agreement with the experimental values of Jacobson et al. [Phys. Rev. A 56, R4361 (1997); 57, 4065(E) (1998)]. Two different approaches are used involving a variational method and a scattering method, the latter providing the prospect of calculating accurate nonadiabatic molecular properties for many of the vibration-rotation levels of the hydrogen molecular cation.

The slow electric-dipole intercombination decay of the ${2s2p}^3{}^5{S}_2^o$ level in the C-like ion ${\mathrm{N}}^{+},$ which appears in the auroral airglow spectrum, has been optically observed from ions circulating in a storage ring. A result of $5.88\pm 0.03\hspace{0.5em}\mathrm{ms}$ was obtained for the natural lifetime of this level. This represents an improvement in precision by a factor of 10 compared to previous radio-frequency and electrostatic ion trap work and is in slight disagreement with the latest theoretical values.

We derive the leading term in an $\alpha Z$ expansion for the negative-energy (virtual electron-positron pair) contributions to the transition amplitudes of heliumlike ions. The resulting expressions allow us to perform a general analysis of the negative-energy contributions to electric- and magnetic-multipole transition amplitudes. We observe a strong dependence on the choice of the zeroth-order Hamiltonian, which defines the negative-energy spectrum. We show that for transitions between states with different values of total spin, the negative-energy contributions calculated in a Coulomb basis vanish in the leading order while they remain finite in a Hartree basis. The ratio of negative-energy contributions to the total transition amplitudes for some of nonrelativistically forbidden transitions is shown to be of order $1/Z.$ In the particular case of the magnetic-dipole transition $3{}^3{S}_1\to 2{}^3{S}_1,$ we demonstrate that the neglect of negative-energy contributions, in an otherwise exact no-pair calculation, would lead one to underestimate the decay rate in helium by a factor of 1.5 in calculations using a Hartree basis and by a factor of 2.9 using a Coulomb basis. Finally, we tabulate revised values of the line strength S for the magnetic-quadrupole ${(M}_2)$ transition $2{}^3{P}_2\to 1{}^1{S}_0.$ These values include negative-energy contributions from higher partial waves, which were neglected in our previous calculations.

A method for calculating dipole transition moments in effective one-electron systems when some channels are closed is investigated within the framework of multichannel quantum-defect theory (MQDT). A treatment of the energy dependence is also given. This method is useful when electronic channel interactions occur and MQDT is combined with frame transformations. Our calculations are made in the Coulomb approximation and include provisions for core transitions. They are tested by comparing transitions between bound states of molecular hydrogen with ab initio computations.

We have obtained very accurately calculated nonrelativistic values of the index of refraction and the Verdet constant of helium gas. We have used the Breit-Pauli operator to obtain corrections of order ${\alpha }^2$ to the same optical quantities. This required us to analyze the scattering of light by helium atoms correct up to third order: second order in the electromagnetic field and first order in the Breit-Pauli operator. We compare these results with experimental values and find some significant discrepancies.

We have experimentally investigated the selective reflection of the $P-D$ transition in a high-density rubidium vapor and shown it to be sensitive to the exact spatial distribution of $P$-state atoms near the dielectric-vapor interface. This distribution results from the radiative and nonradiative transport of excitation and from wall-quenching collisions of excited-state atoms and is highly inhomogeneous. Selective reflection thus acts as a probe of the spatial dispersion in the vapor. The resulting spectra have been analyzed to show that the broadening due to $S-D$ collisions contributes considerably to the self-broadened linewidth of the $P-D$ transition.