Pattern formation near threshold in single longitudinal mode and large aspect ratio optical parametric oscillators (OPOs) operating near resonance are shown to be described by a complex Swift-Hohenberg equation. Such an equation is capable of capturing the main wave-vector selection rules for both degenerate and nondegenerate OPOs. © 1996 The American Physical Society.

Intense 3p-3s, J=0–1 soft-x-ray lasing at 28.5 nm in neonlike chromium has been observed experimentally using a compact Nd:glass laser as the driver. 2.4-cm-long polished chromium slab targets were irradiated with up to 100-J/500-ps pulses at the fundamental wavelength of 1.054 μm. The prepulse technique was applied using a defined prepulse 5 ns before the main pulse and with a prepulse-to-main pulse energy ratio of 0.7%. It is demonstrated that a pump energy of ∼80 J, corresponding to a pump irradiance of approximately 9 TW/${\mathrm{cm}}^2$ is sufficient to observe soft-x-ray lasing at 28.5 nm. At a drive laser energy of ∼90 J a gain coefficient of (2.2±0.5) ${\mathrm{cm}}^{\mathrm{-}1}$ was measured. The one-dimensional space-resolved measurements show that the 28.5-nm laser line is emitted from a 60-μm-wide (full width at half maximum) plasma region. © 1996 The American Physical Society.

In a recent paper, C. T. Lee [ Phys. Rev. A 52, 3374 (1995) ] showed that if ρ^=${\sum }_{\mathit{n},\mathit{m}}$ρ(n,m)|n〉〈m| is the density operator describing an arbitrary state, with ρ(0,0)=〈0|ρ^|0〉=0, the state is as nonclassical as possible. Here we exhibit an example in apparent contradiction with the above theorem. © 1996 The American Physical Society.

Metastable states of antiprotonic helium $\overline{p}{\mathrm{He}}^{+}$ whose energies lie in the range of the $2S$ and $2P$ excited states of He are discussed and their energies are calculated using the hyperspherical method within the "symmetric top" approximation. These states can be populated via collisions of antiprotons with excited He atoms. They represent another group of the potentially observable metastable states of $\overline{p}{\mathrm{He}}^{+}$, which are characterized by the total angular momentum $L\sim 70$, in contrast to the recently discovered metastable states having $L\sim 35$.

We report the experimental results of the total electron-impact ionization cross sections of laser-excited $3P$ sodium in the energy range from threshold to 30 eV. These cross sections were measured simultaneously for both ground-state and $3P$ excited-state atoms as a function of electron-impact energy. Excited-state data were calibrated with respect to the ground-state data that were normalized to the recent Johnston and Burrow measurements [Phys. Rev. A 51, R1735 (1995)]. We find good general agreement with theory. However, the position of the maximum is almost the same as that predicted by the calculations employing generalized oscillator strengths based on the Born approximation, and is at a higher energy than that which the convergent close-coupling predicts.

We use continuous measurement theory to describe the evolution of two Bose condensates in an interference experiment. It is shown how in a single run the system evolves into a state with a fixed relative phase, without violating particle number conservation.

We extend the work of Javanainen and Yoo [Phys. Rev. Lett. 76, 161 (1996)] on the interference between two Bose-Einstein condensates to include the effects of collisions. The competing effects of the atomic detections that establish phase coherence and the decohering effects of the collisions are computed using the Monte Carlo wave-function method. Limits to the tolerance of the condensate phase to atomic collisions are established.

We formulate Bogoliubov theory for a weakly interacting Bose-Einstein condensate confined to a spherically symmetric harmonic-oscillator potential. The theory is solved numerically by diagonalizing a Hamiltonian that is second order in boson creation and annihilation operators with the aid of a symplectic transformation. At zero temperature, the number of noncondensate atoms is well approximated by a heuristic expression based on Bogoliubov theory for free atoms.

We have determined properties of cold ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ singlet and triplet bound states. We predict positive scattering lengths for the ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ singlet potentials, as well as for the ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ triplet potential, and a negative value for ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ triplet scattering. From a study of the magnetic field dependence we conclude that ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the $f=1\mathrm{}$, $m_f=-1\mathrm{}$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.

We have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of ∼3 have been observed. This indicates that the atomic pair-distribution function can be significantly distorted in a typical laser trap environment.

We show how control lasers lead to subnatural linewidths in spontaneous emission as well as to the quenching of the quantum noise. We trace this quenching to the dispersive contributions to the line shape. We obtain analytical expressions for linewidths that for $\wedge$ systems are half the natural linewidths with the possibility of much more reduction for detuned control laser. We further present a simple physical analysis in terms of a two-photon Fermi golden rule to understand cancellation of spontaneous emission. Finally, we relate our results to recent experiments.

Eight-port homodyne detection may be used to perform a joint measurement on a single-mode input to a beam splitter; the $x$ quadrature is measured at one output port, and the $p$ quadrature is measured at the other. This is possible even when the input mode contains only one photon. We show to what extent this "joint measurement of a single photon" may be reconciled with the semiclassical notion that the photon may only exit from one of the beam splitter output ports.

Second-harmonic generation has been obtained by the use of Laguerre-Gaussian beams in a variety of mode orders. Each mode becomes doubled in frequency and transformed to a higher order. We show this to be a consequence of the phase-matching conditions. The experiment is consistent with the interpretation that the orbital angular momentum of the Laguerre-Gaussian mode is directly proportional to the azimuthal mode index $l$.

We have experimentally observed the evolution of the vacuum Rabi doublet into a singlet in the transmission spectrum of a cavity filled with a collection of two-level atoms. For very weak excitation the peaks behave like simple harmonic oscillators, but become anharmonic as the excitation increases. The anharmonicity grows to a point where hysteresis appears in the transmission spectrum, eventually causing the two peaks to merge into one.

A unified theory of two-level atom coupling to vacuum field reservoirs with arbitrary mode-density spectra is used to demonstrate that the quantum Zeno effect on excitation decay of the atom (and, correspondingly, inhibition of spontaneous emission) is observable in open cavities and waveguides, using a sequence of evolution-interrupting pulses on a nanosecond scale.

The bosonic strictly isospectral problem for Demkov-Ostrovsky (DO) effective potentials in the radially nodeless sector is first solved in the supersymmetric Darboux-Witten (DW) half line (or l-changing) procedure. As an application, for the κ=1 class, if one goes back to optics examples, it might be possible to think of a one-parameter family of Maxwell lenses having the same optical scattering properties in the nodeless radial sector. Although the relative changes in the index of refraction that one may introduce in this way are at the level of several percent, at most, for all DO orbital quantum numbers l⩾0, the index profiles are different from the original Maxwell one, possessing an inflection point within the lens. I pass then to the DW full line (or N-changing) procedure, obtaining the corresponding Morse-type problem for which the supersymmetric results are well established, and finally come back to the half line with well-defined results. © 1996 The American Physical Society.

The eigenstates of a charged particle with spin 1/2 in the magnetic field surrounding a rectilinear current filament are determined numerically. As they differ only slightly from local Landau levels, the wave functions may be approximated analytically using stationary perturbation theory. The expectation values of the component parallel to the wire of the velocity operator are calculated for both the exact and the approximated wave functions. They are a measure for the drift of the gyration center parallel to the wire, which is predicted by classical mechanics. Taking into account the quantization of the cyclotron rotation, this drift motion can also be derived by applying the method of adiabatic expansion of the particle propagator. The resulting values for the drift velocities are in excellent agreement with those from classical mechanics if, in the latter, one takes into account energy quantization. © 1996 The American Physical Society.

Several practical implications of the noncrossing property of one-dimensional Bohm trajectories are examined. It is shown that the position of a Bohm particle, the average transmission, reflection and dwell times, and the probability distribution of these tunneling times, can all be obtained without actually calculating trajectories. On the other hand, the intuitive interpretation of the scattering of wave packets by potential barriers is discussed within the framework of Bohm’s interpretation of quantum mechanics. In this regard, claims that Bohm’s approach leads to counterintuitive results are shown to be subjective. © 1996 The American Physical Society.

We describe an array of quantum gates implementing Shor’s algorithm [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 116; (unpublished); Phys. Rev. A 53, R2493 (1995)] for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers and adders) that are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer that is running the program to factor N=15 while interacting with a dissipative environment. As a consequence of this interaction, randomly selected quantum bits (qubits) may spontaneously decay. Using the results of our numerical simulations, we analyze the efficiency of some simple error correction techniques. © 1996 The American Physical Society.