It was recently shown [Phys. Rev. A 45, 1919 (1992)] that the phase shift induced by a control beam on a signal in cross Kerr modulation is limited by the quantum nature of the control. We show that dissipation rapidly restores the classical phase shift.

Interpretational difficulties of a quantum measurement [J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 45, 424 (1992)] are pointed out. The nonunitarity of the respective exponential phase operator reflects an enhanced noise, which can be reduced by discarding ambiguous output data. Consequently, dispersion of such measurements does not represent a meaningful performance measure relevant to the input state. Moreover, the proposed model of quantum phase measurements provides a discrete spectrum of the quantum phase operator, whereas the phase-shift parameter is continuous.

In response to Hradil’s Comment [preceding Comment, Phys. Rev. A 47, 4532 (1993)], we point out that his prescription for putting both the cosine and sine equal to zero when the data yield ${\mathit{n}}_3$=${\mathit{n}}_4$ and ${\mathit{n}}_5$=${\mathit{n}}_6$ can lead to meaningless results. Moreover, Hradil’s Eq. (5) for obtaining ${\mathit{D}}^2$ from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.

We address the problem of identifying an operational prescription for quantum phase measurements. As is known, different experiments can lead to different measured phase operators. However, we show that ambiguities of interpretation can arise even if a single experiment, such as that of Noh, Fougères, and Mandel [Phys. Rev. Lett. 67, 1426 (1991)], is chosen as defining a phase measurement. We show by reference to a simple but fundamental example that it is not possible to deduce a unique phase difference from the measurements.

In response to the Comment by Barnett and Pegg [preceding paper, Phys. Rev. A 47, 4537 (1993)] it is pointed out that their objection is really based on a different measurement scheme. If our measurement procedure is repeated many times with different phase shifters inserted at one input port, the method yields an almost continuous probability density.

A derivation of the coordinate representation of the q-deformed oscillator is given. The Hilbert space associated with it is defined on a finite coordinate space y: (-π/2s,π/2s), where s is related to the deformation q via q=exp(-${\mathit{s}}^2$), with the respective ‘‘coordinate’’ and ‘‘momentum’’ operators given by X${\mathrm{^}}_{\mathit{s}}$=y-${\mathit{A}}_{\mathit{s}}$(y), P${\mathrm{^}}_{\mathit{s}}$=-id/dy-${\mathit{iA}}_{\mathit{s}}$(y), where ${\mathit{A}}_{\mathit{s}}$(y)=1/2d ln${\mathrm{\sigma }}_{\mathit{s}}$(y)/dy, ${\mathrm{\sigma }}_{\mathit{s}}$ being a measure in this space. The commutation rule obeyed by them is X${\mathrm{^}}_{\mathit{s}}$P${\mathrm{^}}_{\mathit{s}}$-P${\mathrm{^}}_{\mathit{s}}$X${\mathrm{^}}_{\mathit{s}}$=i${\mathrm{ħ}}_{\mathit{s}}$(y)=i{1-${\mathit{dA}}_{\mathit{s}}$ /dy}. After constructing a suitable representation in the momentum space, we also set up the Wigner distribution function in this phase space. A brief discussion of these results and their interpretation are given.

Using Feynman path integrals and the stationary-phase method, we develop a semiclassical theory for quantum trace formulas in classically hyperbolic systems. In this way, we obtain corrections to the Gutzwiller-Selberg trace formula as an asymptotic series in powers of the Planck constant. The first coefficient of this series is given explicitly. We illustrate the theory with the calculation of complex-wave-number resonances for the two-disk scatterer and show that effects beyond the Gutzwiller leading approximation are at the origin of a lengthening of the resonance lifetimes at low energy.

Dielectronic recombination was investigated for ${\mathrm{He}}^{+}$, the simplest ion for which this process is possible. This work was done using the light-ion storage ring and electron cooler at the Indiana University Cyclotron Facility. Resonant recombination yields resulting from 1s+${\mathit{e}}^{\mathrm{-}}$→nln’l’ transitions were observed with sufficient resolution (about 1 eV in the center of mass) to isolate and obtain cross sections for the 2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ and 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D terms. The measured cross sections, integrated over the Δn=1 2ln’l’ states, agree in magnitude with theoretical calculations. Additionally, Δn=2 dielectronic recombination events associated with 3ln’l’ intermediate states were observed.

The Faddeev approach in the total-angular-momentum representation is applied to study s-wave p+pμ scattering at very low energies. It is shown that the threshold behavior of phase shifts and cross sections is strongly affected by a virtual state leading to a significant amplification of cross sections near k=0.

The cross section for coincident two-photon emission in the bombardment of thin targets of Al, Cu, Tb, and Au with 70-keV electrons has been measured in the ±90° geometry. The present results for Au are about two orders of magnitude lower than the results of Altman and Quarles [Phys. Rev. A 31, 2744 (1985); Nucl. Instrum. Methods Phys. Res. A 240, 538 (1985)] for 75-keV incident electrons in the same geometry. The present results are generally consistent with the relativistic first Born approximation for double bremsstrahlung. While an explanation for the larger yield observed earlier is still not available, we believe that the increased sensitivity of the present coincidence setup makes the present data more reliable. We have also directly observed a coincident cross-talk effect due to the escape of a Ge K x ray from one detector and its coincident detection by the second detector. This effect leads to a large coincidence yield when an energy window includes the Ge K x ray. The implication of such escape effects in ±90° geometry experiments is discussed.

Coincidence experiments for electron-impact ionization of helium in a symmetric coplanar energy-sharing geometry at incident energies from 45 to 500 eV and an angle of 45° are described. Results are put on an absolute scale by normalization to elastic-scattering data and are compared to theoretical calculations in distorted-wave Born and impulse-type approximations. We suggest that an old debate concerning the proper way to evaluate the half-off-shell Coulomb T matrix should be reopened.

We have calculated the energy and angular distributions for double ionization of He by one photon, over a range of photon energies up to 8 keV. We identify, from structures in the angular distributions, three different mechanisms for double ionization at high photon energies, and we compare the ratio of cross sections for double to single ionization with experimental data.

We present experimental results of field ionization of high Rydberg states of an impurity doped into a dense medium. The experiments allowed us to determine the change of the vertical ionization potential of ${\mathrm{CH}}_3$I in fluid argon up to the critical density. The lowering of the vertical ionization potential as a function of the argon number density (ρ) is explained quantitatively on the basis of the energy of the lowest extended state of an excess electron (${\mathit{V}}_0$) in argon and on the sudden polarization energy resulting from the interaction between the dopant ion and the medium. Our results for ${\mathit{V}}_0$(ρ) are compared with several recent theoretical calculations.

We present measurements of excited-state trap-loss collisions of optically trapped ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ atoms as a function of the frequency of the light used to excite the colliding atom pairs. For detunings outside the excited-state hyperfine structure, the trap-loss rates are found to be the same for the two isotopes. For detunings inside the excited-state hyperfine structure, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ collisions occur at a substantially lower rate than those of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$. The spectra make it clear that the long-range dynamics of the collisions are strongly modified by the excited-state hyperfine structure, and that the dynamics are different for the two isotopes.

A charge-transfer experiment has been done in which 63-keV ${\mathrm{Ar}}^{7+}$ was incident on sodium in the ground and first excited states. The electron-capture ratio σ(Na(3p))/σ(Na(3s)) was experimentally determined for this system. The charge-capture cross section was observed to increase by a factor of 1.5 for the excited target.

It is predicted that the stimulated Raman scattering in nonlinear fibers may support propagation of the so-called optical double layers, nonlinear waves with nonequal asymptotic values of the envelope. These waves appear for the normal dispersion regime, and they have monotonic or oscillatory profiles. In the latter case the double layer may be treated as a train of dark solitons with varying amplitudes.

Quantum-mechanical evolution in a slowly varying double-well potential is analyzed in the semiclassical limit to determine the transition probability due to loss of adiabatic invariance of states having energy close to that of a separatrix in the equivalent classical system. Transformation to the rotating-axis basis reduces the problem to the integration of a set of coupled differential equations. In the adiabatic limit the integration is carried out by the method of successive approximations. For adiabatic parameter ε of the order of the inverse, 1/N, of the number of quantum states with energy below the separatrix, the spread of the quantum adiabatic invariant is exponentially small in the inverse of the adiabaticity parameter. Surprisingly, the transition to this quantum adiabatic behavior occurs far below the minimum transition frequency of the system.

We describe the measurement process for a model system whose Schrödinger equation yields to explicit solution. Any device for an effectively irreversible measurement must not just be a ‘‘meter’’ with a single degree of freedom; it must also contain a ‘‘heat bath’’ with many degrees of freedom. Such a bath may cause an effectively instantaneous decay of quantum coherences between macroscopically distinct meter readings, i.e., impart practically classical behavior to the meter. In turn, such a meter can be read without thereby suffering back reactions. We establish the limits in which a meter reading is uniquely related, with reasonable certainty, to a definite eigenvalue of the measured observable.

We present a concept for measuring a Berry phase using an atom interferometer in an optical Ramsey arrangement. The adiabatic cyclic process needed for the appearance of a Berry phase consists of the adiabatic change of population in one of the interferometer arms. A closed circuit in parameter space is realized by the time-dependent Doppler detuning of two additional strongly focused Gaussian beams, which couple selectively to one of the interferometer arms. It is shown that the resulting additional atomic phase consists of a Berry phase corresponding to the phase difference of the two Gaussian beams and a dynamical phase caused by the dynamical Stark effect. By recombining the two interferometer arms this total phase gives rise to a shift of the interference pattern. In case of a Ramsey arrangement with magnesium atoms the parameters of an experimental realization have been calculated. Further improvements using laser-cooled and trapped atoms are discussed.

In this paper, we consider a system with both translational degrees of freedom and a structure of discrete internal states. Applying a multiple-time-scale approach we can separate the dynamical processes describing internal quantum transitions between the states and semiclassical propagation in phase space. The freedom provided by the multiple-time-scale method seems to offer the possibility of carrying out such a separation without internal contradictions. The case with no internal states is extracted and compared with other semiclassical results in the literature; it is found that our approach can be related to these, but it is not identical with any previously reported results. When a unique particle trajectory can be defined, the procedure is shown to lead to the customary classical-path approximation often employed in scattering theory and quantum optics. This approach is generalized into a self-consistent method, but it is not expected to be applicable in the coherence-destroying case with widely separated trajectories for the internal states. The validity of the approach and its limitations are discussed.