We present the quantum theory of a two-photon nonlinear laser when the lasing medium consists of long-lived atoms. There is no population inversion in this laser, but the system exhibits gain arising from the four-wave-mixing process in an active nonlinear medium. The strong phase correlation between the photons generated in four-wave mixing leads to a narrower than usual linewidth of the two-photon laser far above threshold. The laser output is also squeezed. Systems with a higher lifetime have the advantage of requiring a lower pump to reach the threshold of laser oscillation. We give explicit solutions for the noise spectrum of the intensity difference of the two output modes in the steady state and show that it is highly squeezed even for non-Markov systems.

In a recent paper [D. H. Kobe, V. C. Aguilera-Navarro, and R. M. Ricotta, Phys. Rev. A 45, 6192 (1992)], Kobe et al. have calculated the expectation values of position and momentum in the Aharonov-Bohm effect and have found that both are shifted by the Aharonov-Bohm potentials. Although these shifts appear to contradict certain ‘‘no-shift’’ theorems proved by various authors, we show that this apparent contradiction is the result of different assumptions. Specifically, one of the assumptions on which the no-shift theorems are based does not hold for the parameters used by Kobe et al.; that is, with their parameters, there is no reason to expect the no-shift theorems to hold. On the other hand, with the parameters of actual two-slit experiments, all of the conditions of the no-shift theorems do hold and the no-shift theorems do apply.

The assumptions under which the ‘‘no-shift’’ theorem of Semon and Taylor [preceding Comment, Phys. Rev. A 50, 1954 (1994)] is valid are examined. For some choices of possible experimental parameters, the assumptions are not satisfied.

A derivation from first principles is given of the energy-time uncertainty relation in quantum mechanics. A canonical transformation is made in classical mechanics to a new canonical momentum, which is energy E, and a new canonical coordinate T, which is called tempus, conjugate to the energy. Tempus T, the canonical coordinate conjugate to the energy, is conceptually different from the time t in which the system evolves. The Poisson bracket is a canonical invariant, so that energy and tempus satisfy the same Poisson bracket as do p and q. When the system is quantized, we find the energy-time uncertainty relation ΔEΔT≥ħ/2. For a conservative system the average of the tempus operator T^ is the time t plus a constant. For a free particle and a particle acted on by a constant force, the tempus operators are constructed explicitly, and the energy-time uncertainty relation is explicitly verified.

We investigate two models of measuring devices designed to detect a nonrelativistic free particle in a given region of space-time. These models predict different probabilities for a free quantum particle to enter a space-time region R; therefore, this notion is device dependent. The first model is of a von Neumann coupling, which we present as a contrast to the second model. The second model is shown to be related to probabilites defined through partitions of configuration-space paths in a path integral. This study thus provides insight into the physical situations to which such definitions of probabilities are appropriate.

The number-phase uncertainty product for displaced number states of the harmonic oscillator is examined within the framework of three different approaches: (i) the Carruthers-Nieto number-phase uncertainty relation in terms of the Susskind-Glogower sine and cosine phase operators, (ii) a similar relation to this calculated with the Pegg-Barnett unitary phase operator, and (iii) the number-phase uncertainty relation arising from the Pegg-Barnett Hermitian phase operator. The corresponding number-phase uncertainty product is calculated extending from average photon numbers 30 down to m for the first few classes of displaced number states (m=0,1,...,5). It is found that, for a displaced number state with a reasonable average number of excited quanta, all three rival phase formalisms yield similar number-phase uncertainty products, tending, for increasingly large magnitude of the displacement parameter, to the constant value m+1/2. On the other hand, for a small number of excited quanta it is found that, according to the first two formalisms, the number-phase uncertainty product for a given class of displaced number states tends to the maximum value √2m+1 /(√m+1 - √m ), while the third phase formalism predicts an entirely different behavior; with decreasing magnitude of displacement parameter, after passing through a maximum, the number-phase uncertainty product falls off eventually to zero making, in particular, the search for minimum number-phase uncertainty states futile. It is argued in favor of this last result, and the possibility of experimental verification, in the realm of quantum optics, is briefly considered.

We derive a regularized semiclassical radial propagator for the Coulomb potential, a case for which standard approaches run into well-known difficulties associated with a non-Cartesian radial coordinate and a potential singularity. Following Kleinert [Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1990)], we first perform a quantum-mechanical regularization of the propagator. The semiclassical limit is then obtained by stationary phase approximation of the resulting integrals. The semiclassical propagator so derived has the standard Van Vleck–Gutzwiller form for the radial Coulomb problem with a potential correction (Langer modification) term included. The regularized semiclassical propagator is applied to compute the autocorrelation function for a Gaussian Rydberg wave packet.

We study the effect that the state-vector reduction of Ghirardi, Rimini, and Weber (GRW) [Phys. Rev. D 34, 470 (1986)] has on the quantum fluctuation-dissipation process. A conventional fluctuation-dissipation process stems from the interaction between a system of interest and a macroscopic number of microscopic variables, thereby suggesting the possible occurrence of an enhancement of the GRW wave-function collapse. We carry out an exact treatment of the joint action of conventional quantum dissipation and GRW wave-function collapse in the special case where the system of interest is a harmonic oscillator. We prove that the GRW dynamics does not lead to any significant departure from the predictions of ordinary quantum mechanics, if the region of astronomically large times is disregarded, where the energy of the system diverges as an effect of a slow but steady increase caused by the GRW collapses.

A method for measuring the Earth’s gravitational acceleration g on antiprotons is proposed. The value of g is obtained by measuring the gravity-induced shift of the center of the radial orbits of antiprotons that are stored in a Penning trap. Such a shift is a measurable effect for particles of very low energy (≃1 μeV) if the point of injection lies near the axis of a big Penning trap in which the magnetic field is perpendicular to the direction of g. A possible experimental setup is described and several sources of error are analyzed. A comparison with a time-of-flight method, originally proposed to measure g on antiprotons (and now under experimental investigation by an international collaboration), indicates the advantages of the present proposal. The experimental feasibility of the method of measurement that we propose relies on the practical limit that can be achieved in minimizing the antiprotons’ energy and on controlling the radial coordinates of the particles before injection into the g-sensitive trap.

The eigenvalue moment method (EMM) is a general theory for generating converging lower and upper bounds to the discrete, low-lying spectrum of Schrödinger Hamiltonians. Recently, Handy, Giraud, and Bessis [Phys. Rev. A 44, 1505 (1991)] developed a dynamical systems EMM formulation through the discovery of a fundamental convex function, ${\mathit{F}}_{\mathit{E}}$[u]=${\mathrm{Min}}_{\mathrm{\sigma }=0,1\mathrm{}}$〈${\mathit{V}}^{(\mathrm{\sigma },\mathit{E})}$ [u]‖${\mathit{M}}^{(\mathrm{\sigma },\mathit{E})}$[u]‖${\mathit{V}}^{(\mathrm{\sigma },\mathit{E})}$[u]〉. By incorporating this within the c-shift EMM theory of Handy and Lee [J. Phys. A 24, 1565 (1991)], there results an alternative quantization procedure involving the function V(E)=${\mathrm{Max}}_{\mathit{u}}$${\mathrm{Min}}_{\mathrm{\sigma }=0,1\mathrm{}}$〈${\mathit{V}}^{\mathrm{\sigma },\mathit{E},\mathit{S})}$[u] ‖${\mathit{S}}_{\mathrm{\sigma }}^{\mathrm{-}1}$${\mathit{M}}^{(\mathrm{\sigma },\mathit{E})}$[u]${\mathit{S}}_{\mathrm{\sigma }}^{\mathrm{-}1}$‖ ${\mathit{V}}^{(\mathrm{\sigma },\mathit{E},\mathit{S})}$〉, whose local maxima converge to the discrete energy states of the system. We discuss the relevant theory and present several examples.

Initial-value phase-space integral representations for a time-dependent propagator are obtained in the coordinate and momentum representations. To do so we first derive nonuniform semiclassical propagators for the various representations, obtaining the global-time semiclassical phase indices (Maslov indices) due to caustics. Results include readily implementable general phase index formulas for any type of caustic, including cases where the Morse index theorem is inapplicable. The method of obtaining the indices is general and based simply on concatenating uniform short-time propagators which also gives rise to alternative path-integral forms. Initial-value integral representations are then derived by introducing a method of extending short-time initial-value propagator formulas to global times via a simple stationary-phase asympotoic-equivalence approach. The integrals reduce to the nonuniform semiclassical propagators within the stationary-phase approximation, are uniform about caustics, and have integrand phases which properly account for the global-time phases in terms of appropriate Maslov indices. The initial-value integrals are also consistently derived via a canonical mapping procedure on the coordinate-space path integral. Initial-value integrals for time-dependent wave-function propgation are also given. Evaluation of the initial-value integral expressions do not require trajectory root searches for propagation.

Implementing the ideas of Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], we present an experimentally feasible scheme for the teleportation of an unknown atomic state between two high-Q cavities containing a nonlocal quantum superposition of microwave field states. This experiment provides alternative tests of quantum nonlocality involving high-order atomic correlations.

Autodetachment via the collisionally populated (1s2p2p’${)}^4$${\mathit{P}}^{\mathit{e}}$ shape resonance of ${\mathrm{He}}^{\mathrm{-}}$ has been observed by means of 0° electron spectroscopy in a measurement of the double-differential cross section for single and double electron loss to the continuum in ${\mathrm{He}}^{\mathrm{-}}$ on Ar collisions at 75-keV/u projectile energy. An alternative parametrization has been developed for the autodetachment lines emitted with low energy in the projectile reference frame. The determined position and width of the shape resonance are in agreement with the results of theoretical calculations and photodetachment measurements.

Proceeding from the model of a field ‘‘in the box’’ we obtained expressions for electric- and magnetic-field strengths that take into account switching-on and turning-off regimes of the strong electromagnetic field. It is shown that the free electron dressed by our field does not receive any kick connected with the envelope of the field. Our expressions can be used for the superstrong field instead of well-known expressions that are usually applied in perturbation theory.

Measurements of collisional loss of optically trapped Rb atoms are presented for excitation of the colliding atoms by light tuned near the 5${\mathit{S}}_{1/2}$→5${\mathit{P}}_{1/2}$ transitions of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$. Using the ${\mathit{P}}_{1/2}$ state allows the effects of spontaneous emission on excited-state collisions to be studied with minimal complications arising from hyperfine structure. The shapes of the collision spectra are nearly identical for the two isotopes and are consistent with a simple model for the role of spontaneous emission during the collision.

A simple analytical approximation is found for the wave function of an electron simultaneously exposed to a strong, circularly polarized plane-wave field and an atomic Coulomb potential. The approximation is valid when ${\mathrm{\alpha }}_0$≫1, where ${\mathrm{\alpha }}_0$ is the classical radius of motion of a free electron in the plane-wave field. This constraint is sufficiently mild at low frequencies that it makes possible a major extension of the lower bound of laser intensities for which Volkov-solution-based approximations are useful.

We show that complete population transfer is not in general possible through continuum intermediate states. We present a formal theoretical argument and supporting numerical results. In addition, the behavior of the system is compared with the well-known Λ system.

An almost linearly polarized laser beam focused into a sodium vapor cell may split into different patterns ranging from two spots to a spot and a ring of opposite circular polarization. The patterns are controlled by static magnetic fields of the order of the earth’s field. The behavior is explained, allowing for a longitudinal component of the dielectric polarization in the paraxial wave equation. Numerical results reveal the delicate balance between light shift, influence of the magnetic field, and the creation of ground-state orientation by the competing polarization components.

Determination of the wave function from probability distributions for the position and momentum, the so-called phase problem, is studied. An algorithm leading to the local phase reconstruction is given. Illustrative examples are presented and possible generalizations are indicated.

It is shown that the autocorrelation function of the current produced through the ionization of ground-state atoms emerging from a micromaser cavity can be expressed, apart from a shot-noise contribution, in terms of a two-time correlation function of cavity-field variables. Numerical comparisons between this latter correlation function and the intensity correlation function of the cavity field show that the two are closely related and, in fact, in the limit of a zero-temperature cavity-field reservoir, become identical. A proof of this last result is presented.