We construct an effective Hamiltonian for an atom interacting with an oscillating electric field. This Hamiltonian yields a quasienergy eigenvalue that exactly reproduces the perturbation series through a given order, and that is also accurate in the high-intensity regime in the absence of resonances.

A recent proposal of a ‘‘quantum eraser’’ by Ingraham [Phys. Rev. A 50, 4502 (1994); 51, 4295(E) (1995)] is analyzed. It is shown that Ingraham’s predictions contradict relativistic causality and, therefore, cannot be right. A subtle quantum effect that was overlooked by Ingraham is explained.

We present an experimental scheme that achieves ideal phase detection on a two-mode field. The two modes a and b are the signal and image band modes of a heterodyne detector, with the field approaching an eigenstate of the photocurrent Z^=a+${\mathit{b}}^{\mathrm{°}}$. The field is obtained by means of a high-gain phase-insensitive amplifier followed by a high-transmissivity beam splitter with a strong local oscillator at the frequency of one of the two modes.

It is shown that the exact difference between the ground-state and first-excited-state electronic energies can be obtained, in principle, as the difference of highest occupied orbital energies from two separate Kohn-Sham calculations. Alternatively, this excitation energy may be taken as the difference between the lowest unoccupied and highest occupied orbital energies of a single Kohn-Sham calculation, provided that one corrects for a certain derivative discontinuity in the exchange-correlation potential that is analogous to the one for the band gap in solids.

The oscillator strengths for the lithium 2${\mathrm{}}^2$S→2${\mathrm{}}^2$P and 2${\mathrm{}}^2$P→3${\mathrm{}}^2$D transitions are calculated to high precision using variational wave functions in Hylleraas coordinates. The calculated oscillator strengths for these transitions are 0.746 957 2(10) and 0.638 570 5(30), respectively. The results resolve disagreements among existing theoretical values and provide definitive predictions. A discrepancy of five standard deviations between the theoretical value and the most accurate measurement of Gaupp et al. [Phys. Rev. A 26, 3351 (1982)] for the 2${\mathrm{}}^2$S→2${\mathrm{}}^2$P transition remains.

Absolute cross sections for dissociative recombination of ${\mathrm{HD}}^{+}$ were measured in the ion storage CRYRING for incident electron energies in the range 0.01–20 eV. The ions were stored for about 25 s before data taking, which is several orders of magnitude longer than their vibrational lifetimes towards spontaneous emission of infrared radiation. A broad resonance in the cross section at 5–12 eV is due to recombination into a manifold of doubly excited states. Multichannel quantum-defect theory was used to calculate the absolute cross section of this resonance. The calculations required inclusion of different mechanisms, such as dissociative autoionization, and many molecular states in order to reproduce the resonance region. Very good agreement of experiment and theory is found, and the results strongly reinforce that vibrationally cold ions were used in the experiment.

Ultracold ionizing collisions of laser-cooled Kr isotopes in the 1${\mathit{s}}_5$[4${\mathit{p}}^5$5s${:}^3$${\mathit{P}}_2$] metastable state are investigated. When the collision energy is reduced below the p-wave centrifugal barrier of 80 μK, the ratio of the ionizing collision rate between polarized and unpolarized ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ atoms is found to decrease. This is a direct evidence of the quantum interference of two identical Fermi particles. The experimental results are compared with the calculation based on the simplified inelastic collision theory.

The structure of ${\mathrm{C}}_3$${\mathrm{H}}_3^{+}$ and ${\mathrm{C}}_3$${\mathrm{H}}_4^{+}$ ions produced by nonresonant multiphoton ionization is determined using laser-induced Coulomb explosion and associated multicharged atomic ion momenta correlations. Both cations exhibit the same ${\mathrm{C}}_3$ average elongated linear carbon geometry. Stretched and bent nuclear configurations around the average structure are included in the calculations in order to reproduce the observed ion-ion correlation peak shapes.

We report the observation of direct, two-color photoassociative ionization (PAI) in collisions between ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ atoms optically cooled and confined in a magneto-optical trap. We also measure the resulting ${\mathrm{R}}_2^{+}$ ion spectrum and compare it to earlier trap-loss fluoresecence spectra. Unlike PAI in Na, which ionizes principally by collisional autoionization, the ${\mathrm{Rb}}_2^{\mathrm{*}}$ intermediate photoionizes directly to ${\mathrm{Rb}}_2^{+}$ in a fixed optical field. These observations confirm PAI as a sensitive and broadly applicable spectroscopic tool.

We show that high harmonic generation in ionizing atomic gases should be accompanied by an intensity-dependent harmonic phase that under realistic experimental conditions will lead to a readily observable blue shift and line splitting in the midplateau harmonics. The origins of the observed blue shift and line splitting are detailed. We also show that midplateau harmonics with a duration of only a few femtoseconds can be generated by combining the intensity dependences of the atomic nonlinear polarizability and the free-electron-induced phase mismatch.

We have produced a magneto-optical trap that simultaneously confines two different atomic species: sodium and potassium. A measurement of the sodium trap loss rate constant due to collisions with cold potassium atoms was performed. We extract this rate constant by measuring the temporal behavior of the loading process of the sodium trap in the presence and absence of cold potassium. The constant that is obtained can be qualitatively explained using simple existing models. Future applications of simultaneous trapping are discussed.

The quantum fluctuations in a nondegenerate optical parametric oscillator are calculated without the standard linearization assumption. Analytical results are obtained with the help of a mean-field approximation, which is exact in the limit of a fast decaying subharmonic mode. This approach is equivalent to a linearization around a self-consistently determined pump field amplitude that takes into account fluctuations of the subharmonic mode. The range of validity of the mean-field approximation is analyzed, and the influence of the system size on field amplitudes and squeezing is discussed.

The injection of an optical signal into a semiconductor laser biased near or above the lasing threshold modifies the coupling between the free carriers and the intracavity field. The detuning between the frequency of the injected signal and the free-running oscillation frequency and the ratio of the photon lifetime to the carrier lifetime are key parameters in determining the enhancement of the carrier-field resonant coupling frequency and the stability of the output field. Experimental results using a vertical cavity surface emitting laser biased near threshold are in agreement with calculations using a lumped-element oscillator model.

Counterpropagation of two light beams in a resonant medium so dense that the local driving field differs from the external field is considered. It is shown that efficient energy transfer between the two beams occurs if there is some asymmetry between their propagation conditions due to, e.g., their frequency difference or Doppler detuning caused by the motion of the medium. The directional energy flow may predominate over absorption and lead to gain.

Adopting the recently introduced inverses of boson creation and annihilation operators, we construct a nonunitary transformation to solve exactly a generalized Jaynes-Cummings (JC) model. The method reveals that the JC model in a new frame can be viewed simply as a system of a spin-1/2 atom interacting with a magnetic field dependent on the photon number. For the initial state with fixed photon number l, the JC model becomes a cyclic evolution, and exhibits a geometric phase ${\gamma }_{\mathit{g}}$. We discuss the properties of ${\gamma }_{\mathit{g}}$ in the large l limit.

In this paper I study relativistic dynamics on a rotating disk. First, I consider the radial trajectories and then I consider the timelike and null geodesics. In the case of radial motion I will specify the constraints which force a test particle to move on a straight and rigidly rotating pipe and show that there is no reversal of radial motion at the light cylinder as claimed in Machabeli and Rogava [Phys. Rev. A 50, 98 (1994)].

We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,x⊕y)] is universal in the sense that all unitary operations on arbitrarily many bits n [U($2^{\mathit{n}}$)] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical and of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.

Recently, Handy, Appiah, and Bessis (HAB) [Phys. Rev. A 50, 988 (1994)] showed that the local maxima in the energy variable E of the function V(E)≡${\max }_{\mathit{u}}$${\min }_{\mathrm{\sigma }}$${\lambda }_{\mathit{E}}^{\mathrm{\sigma }}$[u→] (where ${\lambda }_{\mathit{E}}^{\mathrm{\sigma }}$[u→] are the smallest eigenvalues of modified Hankel moment matrices) approximate the discrete energy states of Schrödinger Hamiltonians. Their theoretical result was demonstrated by way of two zero-missing-moment problems, the harmonic oscillator and the ${\mathit{x}}^2$+λ[${\mathit{x}}^2$/(1+${\mathit{gx}}^2$)] potentials, for which the corresponding eigenvalue functions ${\lambda }_{\mathit{E}}^{\mathrm{\sigma }}$ are solely energy dependent. We examine the general n-missing-moment problem through an application of gradient optimization techniques that are suitable for piecewise differentiable functions, thereby enabling us to test HAB’s results for anharmonic potentials of missing-moment order 1, 2, and 3, corresponding to the quartic, sextic, and octic anharmonic potentials, respectively.

We define a quasiprobability distribution ${\mathit{S}}_{\mathrm{NP}}$(n,θ) which describes the quantum statistics of the photon number and phase observables of a single-mode field (or, equivalently, a harmonic oscillator). The properties of ${\mathit{S}}_{\mathrm{NP}}$(n,θ) are the photon number and phase analogies of the properties of Wigner’s original function, which describes the position and momentum observables. For example, the marginals of ${\mathit{S}}_{\mathrm{NP}}$(n,θ) are the continuous phase and the discrete photon-number probability distributions. We give examples of the ${\mathit{S}}_{\mathrm{NP}}$(n,θ) representation of various states and show, in particular, that ${\mathit{S}}_{\mathrm{NP}}$(n,θ) displays the quantum interference associated with Schrödinger cat states. We also describe how ${\mathit{S}}_{\mathrm{NP}}$(n,θ) can be determined from quantities that are, in principle, measurable.

We propose an implementation of a quantum computer to solve Deutsch’s problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail quantum-bit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design that we employ also demonstrates a signature for quantum parallelism which unambiguously distinguishes the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.