The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time scale much longer than the revival time for the two-state inversion. The behavior is essentially that of a nonlinear quantum oscillator with Hamiltonian H=√(A${\mathrm{^}}^{\mathrm{°}}$+α)(A^+α). © 1996 The American Physical Society.

It is demonstrated that the universality of any quantum computing element can be understood and verified via a precise mathematical criterion which tests for the controllability of an associated quantum control system. This relation between quantum computing and quantum control is deeper in that tools of coherent control of quantum dynamics may be used to arrive at specific designs for quantum computing devices. © 1996 The American Physical Society.

An analysis of the binary collision-induced absorption spectrum of helium-xenon mixtures is presented, based on a refined interaction potential and quantum line-shape calculations. This line-shape analysis is more discriminating than a previous analysis in terms of spectral integrals and sum formulas. An improved empirical interaction-induced dipole moment of He-Xe pairs is of the ‘‘exponential plus ${\mathit{D}}_7$/${\mathit{R}}^7$ dispersion’’ form, where both parts are significant for the agreement of measured and calculated spectral profiles. © 1996 The American Physical Society.

The Lippmann-Schwinger equation for positronium-proton elastic scattering lacks a first-order term because the center of mass and center of charge are coincident. A consequence of this is that the high-energy behavior of the phase shift is governed by the second-Born approximation. Asymptotic analysis indicates that the high-energy form of the phase shift is ${\mathrm{\delta }}_{\mathit{L}}$∼O(1/${\mathit{k}}^3$), where k is the incident positronium momentum. The asymptotic analysis has been confirmed by an explicit close-coupling calculation including the Ps(1s), Ps(2s), Ps(2p), H(1s), H(2s), and H(2p) states. © 1996 The American Physical Society.

The convergent close-coupling method is applied to the calculation of electron scattering from cesium atoms at intermediate energies (7, 13.5, and 20 eV). Although we use a nonrelativistic model, good agreement is obtained with experimental data for the elastic differential cross section and the spin-exchange asymmetry. This rather surprising result indicates that relativistic effects are less important for these observables than a proper representation of the target continuum states. © 1996 The American Physical Society.

In this paper we present a simple calculation showing the evolution of the atomic spatial distribution for particles held in an external potential during the occurrence of Bose-Einstein condensation. This work is intended to complement a previous calculation done by us [Phys. Rev. A 35, 4354 (1987)]. The results obtained are compared to experiments performed recently. © 1996 The American Physical Society.

The possibility of maser action using a current-biased mesoscopic Josephson junction in a high-Q microcavity is discussed. A mesoscopic Josephson junction behaves like an artificial atom as far as the interaction with the photon field is concerned. Under a certain bias current, the Josephson ‘‘atom’’ is resonantly excited or pumped by quantum-mechanical fluctuations of the Josephson phase, i.e., macroscopic resonant tunneling. When the pumping overcomes the loss of photons from the cavity, maser action is possible. Quantum statistical properties of photons are also investigated numerically, taking into acount the microcavity effect on the basis of a Jaynes-Cummings model with pumping and cavity damping. We found that a mesoscopic Josephson junction within the high-Q microcavity acts as a thresholdless maser with sub-Poissonian photon statstics. © 1996 The American Physical Society.

In the paper with the above-noted title, D. T. Gillespie [Phys. Rev. A 49, 1607 (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie’s ‘‘measurement probabilities’’ are the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which can be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the ${\mathit{Z}}_2$ event space assumption, if we require its existence for all times t∈${\mathbf{R}}_{+}$. © 1996 The American Physical Society.

In reply to the preceding Comment on an article by D. T. Gillespie [Phys. Rev. A 49, 1607 (1994)], it is emphasized that the most plausible interpretation of the singly conditioned probability function implies that the evolution of the two-state quantum system being considered cannot be characterized as a Markov process on those states over any time interval. And it is pointed out that an alternative interpretation that is offered in the Comment appears to be in conflict with quantum mechanics.

The $R$ matrix with pseudostates and convergent close-coupling methods are applied to the calculation of elastic, excitation, and total as well as single-differential ionization cross sections for the simplified $S$-wave model of electron-hydrogen scattering. Excellent agreement is obtained for the total-cross-section results obtained at electron energies between 0 and 100 eV. The two calculations also agree on the single-differential ionization cross section at 54.4 eV for the triplet spin channel, while discrepancies are evident in the singlet channel, which shows remarkable structure.

We report a direct measurement of the ${\mathrm{Na}}_2$ $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ ground-state dissociation energy. Three spectroscopic measurements are combined to directly yield the energy of the lowest ($v=0\mathrm{}$) vibrational level relative to the free-atom limit. The $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}(v=0\mathrm{}\to 31)$ splitting is measured by double-resonance spectroscopy; $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\mathrm{}(v=31\mathrm{})\mathrm{}\to A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}(v^{\prime }=165)$ by laser-induced fluorescence; and free $\mathrm{atoms}\to A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}(v^{\prime }=165)$ by photoassociation of ultracold atoms. The result is $D_0=5942.6880\mathrm{}\left(49\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The uncertainty is a factor of 6 improvement over a previous (indirect) determination.

We report the results of electron-spin-resonance studies of Cs atoms trapped in the body-centered-cubic phase of a solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ matrix. Free-induction-decay times longer than 100 ms have been measured in spin-transient experiments. In optical-rf double-resonance experiments we have obtained linewidths of less than 20 Hz (full width at half maximum). The magnetometric sensitivity of our sample is 26 nG/ √Hz. We have also demonstrated that magnetic resonance in such samples can be detected with high sensitivity using forward-scattered optical radiation.

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the $X-Y$ plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly correlated pair coherent state.

Methods of trapping neutral spin-polarized particles are proposed using highly nonuniform magnetic fields rotating at low frequencies, down to the resonance of the particle's orbiting motion. Such fields beget new trapping mechanisms of vast possibilities. The new resonance methods and the new traps of zero-size equilibrium orbit should give much tighter and more stable confinement than previously known. They also give the possibility of a high, resonance selectivity in magnetic separation and evaporative cooling. A general analysis of trapping with rotating fields is given.

Field emission from a monatomic tip in scanning tunneling microscopy (STM) is modeled by a zero-range potential in the presence of a static constant electric field, a problem that has an exact analytic solution. The model yields an electron current that compares favorably to experimental results as well as more sophisticated theoretical models used to describe STM. The width of the current density at the end of the classically forbidden region is identified. A Gaussian wave packet starting from the end of the tunnel with this width provides an excellent description of the ensuing electron motion. Next, changing the subject, exact zero-range potential calculations of high-harmonic generation in an elliptically polarized laser field are presented. These calculations are then modeled in terms of Gaussian wave packets whose centers follow classical electronic orbits that originate from and return to the ionic core. For the initial widths of these wave packets the width derived above in the context of STM is used. Good agreement with the exact harmonic rates is obtained from the tunneling regime well into the multiphoton regime.

We solve the one-dimensional wave equation for high-order mixing of the type ${\omega }_h=q{\omega }_0-l{\omega }_c(q\gg l>=1)$ using a Keldysh-type model to describe the high-field atomic nonlinear susceptibility. When ${\omega }_c$ is selected to give static phase matching, we show that the conversion efficiency of the mixed field can be increased by about an order of magnitude compared to non-phase-matched high-order harmonic generation but that fundamental limitations are introduced by axial electron-density gradients.

We measure the depth of an optical atom trap using repulsive trap-loss collisions. These collisions involve excitation by a laser tuned to a frequency above the atomic resonance. Simple conservation of energy considerations give direct quantitative measurements of the trap depth. Further analysis allows measurement of the escape probability as a function of energy. We apply the methods to Rb traps, and use the results to form conclusions about ground-state hyperfine-changing collisions.

Using operators of the invariance group of their time-dependent Schrödinger equations it is shown that the bound states of Morse oscillators are bases for discrete nonunitary irreducible representations (non-UIRs) of the groups $\mathrm{Sp}(2, R)$, SU(1,1), and SO(2,1). Hermiticity requirements and the dependence of the group generators on the dynamical variables determine the operator of an isometry which connects these non-UIRs of the noncompact invariance groups to UIRs of the compact groups SU(2) and SO(3) that have been used as spectrum-generating groups for Morse systems.

Total-ion-yield measurements and Hartree-Fock calculations are presented for the $1s\to \mathrm{np}$, $n=2\mathrm{} \mathrm{to} 5$ photoexcitations in atomic oxygen. Energies and relative intensities of the $\mathrm{}\left[1s\right]2s^{2}2p^4\left({}_{}{}^4{}_{}{}^{}P\right)np$ and $\mathrm{}\left[1s\right]2s^{2}2p^4\left({}_{}{}^2{}_{}{}^{}P\right)np$ series members are determined, and the apparent linewidths are measured. It is shown that natural widths in an open-shell atom can be deduced from an absorption spectrum only with the aid of theoretical input. The linewidth for the six individual components contained in the $1s\to 2p$ transition is determined to be 140(9) meV.