It is shown that fundamental uncertainty relations between photon number and canonical phase of a single-mode optical field can be verified by means of a balanced homodyne measurement. All the relevant quantities can be sampled directly from the measured phase-dependent quadrature distribution.

The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.

In this work we demonstrate a possibility to reconstruct a density matrix of a single-mode signal state of radiation field using a two-detector measurement scheme with fixed position of beam splitter and identical probe states for both ideal and nonideal detectors. It is also shown that by using different probe states in this measurement scheme it is possible to make the reconstruction measuring only the probability of no photon registration on both nonideal detectors.

We investigate the coupled microscopic and macroscopic nonequilibrium spatiotemporal dynamics of broad-area semiconductor lasers. Characteristic nonequilibrium Wigner distributions of the charge carriers and the interband polarization reveal spatially inhomogeneous field-induced heating and cooling as a consequence of the coupling of the optical field to the carrier and phononic systems. The numerical simulations are performed on the basis of microscopic spatially resolved Maxwell-Bloch equations in which the spatiotemporal variation of thermal properties of the active laser medium are self-consistently included. In particular, the spatiotemporal light-matter interactions are determined by the temporal and spatial transport of the electron-hole plasma, its dependence on carrier-carrier, carrier-phonon, and phonon-phonon scattering processes as well as on the optical properties and macroscopic boundary conditions. In resonantly and nonresonantly excited broad-area semiconductor lasers, the microscopically computed Wigner distributions of the charge carriers and the interband polarization reveal the spatiospectral dependence of the laser gain, the induced refractive index, as well as the electron and hole plasma temperatures. The spatiotemporal nature of these processes explains macroscopic effects such as dynamic thermal lensing and formation of spatiospectral optical structures.

Lasing without inversion (LWI) in specific models of closed three-level systems is analyzed in terms of nonlinear dynamics. From a linear stability analysis of the trivial nonlasing solution of the homogeneously broadened systems with on-resonance driving and laser fields, we find that, near lasing threshold, resonant closed $\Lambda$ and $V$ schemes yield continuous-wave LWI while resonant cascade schemes can give rise to self-pulsing LWI. The origin of this different behavior is discussed. For parameters of a real cascade system in atomic ${}^{138}\mathrm{Ba}$ we check numerically that the self-pulsing solution is stable in a broad range of nonzero detunings. It is shown that the self-pulsing emission can still be observed when the typical residual Doppler broadening of an atomic beam is taken into account.

The phase of a single-mode field can be measured in a single-shot measurement by interfering the field with an effectively classical local oscillator of known phase. The standard technique is to have the local oscillator detuned from the system (heterodyne detection) so that it is sometimes in phase and sometimes in quadrature with the system over the course of the measurement. This enables both quadratures of the system to be measured, from which the phase can be estimated. One of us [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] has shown recently that it is possible to make a much better estimate of the phase by using an adaptive technique in which a resonant local oscillator has its phase adjusted by a feedback loop during the single-shot measurement. In a previous work [H. M. Wiseman and R. B. Killip, Phys. Rev. A 56, 944 (1997)] we presented a semiclassical analysis of a particular adaptive scheme, which yielded asymptotic results for the phase variance of strong fields. In this paper we present an exact quantum mechanical treatment. This is necessary for calculating the phase variance for fields with small photon numbers, and also for considering figures of merit other than the phase variance. Our results show that an adaptive scheme is always superior to heterodyne detection as far as the variance is concerned. However, the tails of the probability distribution are surprisingly high for this adaptive measurement, so that it does not always result in a smaller probability of error in phase-based optical communication.

The spectral and temporal dynamics of a multimode dye laser has been studied theoretically and experimentally. The analytical model includes quantum fluctuations as well as four-wave mixingdue to population pulsations, stimulated Brillouin scattering, and Rayleigh scattering both in a standing-wave linear laser, and in a unidirectional ring laser. The nonlinearity found most important in the multimode dye laser is four-wave mixing due to pulsations of the populationof the upper laser level. Numerical simulations show features that characterize this particular type of mode coupling: broadening of the emission spectrum, oscillations of the light flux in individual laser modes, suppression of certain beat notes. Observations of these features confirm population pulsations dominating the laser dynamics. Four-wave mixing due to population pulsations tends to arrange the phases of the laser modes such as to minimize the pulsations and to limit its own strength.

Recently, the author [Phys. Rev. A 49, 2839 (1994)] proposed a quantum-mechanical theory of a photon, in which negative energy states can be dismissed from physical photon states without causing any difficulties. In this Brief Report the physical meaning of a photon wave function is investigated more precisely. The interpretation of a photon wave function as a probability amplitude is guaranteed by requiring the coarse-grained condition that the linear dimensions of a volume or a surface concerned in the configuration space are large compared to the photon wavelengths. The calculation made here is essentially based on that presented by Mandel [Phys. Rev. 144, 1071 (1966)] in his analysis of the photon number operator. But our calculation includes that of Mandel as the zeroth-order approximation. As a result, it is shown that although the position operator ◯ in the ordinary quantum mechanics be considered a correct photon operator strictly cannot, it becomes meaningful to some extent under the coarse-grained condition. In connection with ◯, we also examine the velocity operator $[\mathbf{◯},Ĥ]/iħ$ ($Ĥ$ is the photon Hamiltonian), and show that the probability current density is definable under the coarse-grained condition.

Using just polarizing beam splitters and half-wave plates, we present a practical experimental scheme, by which one can conveniently identify two of the three-particle Greenberger-Horne-Zeilinger (GHZ) states. The scheme can easily be generalized to the $N$-particle case. The GHZ-state analyzer is essential for multiparticle generalizations of quantum dense coding, quantum teleportation, and entanglement swapping.

A complete and accurate scheme to calculate relativistic corrections to the generalized oscillator strength sum rules is presented. We discuss the relations between ours and previous schemes used to solve this old problem. A calculation of the relativistic correction to the sum rule $S_2,$ up to the order ${\mathrm{}(v/c)\mathrm{}}^2,$ is given. Our method could also be used to calculate relativistic corrections of molecular properties.

We report on a measurement of the photodetachment of the Li${}^{-}$ ion via the Li$\mathrm{}\left(4s\right)+{\mathrm{e}}^{-}\left(\epsilon p\right)$ channel. The partial photodetachment cross section below the Li$\mathrm{}\left(4p\right)\mathrm{}$ threshold is dominated by resonance structure. The resonance spectrum in this region is compared to the spectrum of the same resonances recently observed in the Li$\mathrm{}\left(3s\right)+{\mathrm{e}}^{-}\left(\epsilon p\right)$ cross section. The two spectra were found to be mirror images of each other. The parameters for the two resonances obtained in the $3s\epsilon p$ measurement were confirmed. In addition, using the $4s\epsilon p$ spectrum, we were able to assign parameters to a third resonance.

We approach classically the dynamic evolution of ${\mathrm{H}}_2^{+}$ interacting with an ultrashort intense laser pulse, and calculate the probabilities of survival, dissociation, ionization, and dissociative ionization in one dimension, and explain the calculated results.

We perform the calculation of proton-hydrogen ionizing collisions based on the ${\Phi }_2$ model recently proposed to describe the three-body final wave function. The transition matrix was evaluated analytically for a Born and a continuum distorted-wave initial state. The double-differential cross section was computed for the Born-${\Phi }_2$ approximation. Even when this is an undistorted initial-state theory, it introduces the asymmetries of the electron capture to continuum and soft electron peaks. It also takes into account the saddle electrons production in a more realistic way than other distorted-wave theories, presents the expected behavior in the forward direction for large electron energies, and shows the correct shift of the binary peak. Numerical results are compared with experimental data and other theoretical values.

We have developed an analytic model within the “orbital-locking and -following” approximation to explain the observed polarization spectrum in the metal-atom–rare-gas fractional collision experiments of Olsgaard and co-workers [Phys. Rev. A 48, 1987 (1993)]. We obtain an expression for the observed polarization spectrum that can be interpreted in terms of the evolution of the electronic orbital alignment from point to point on the intermediate excited-state potential-energy curve. The results, using model potentials for the metal-atom–rare-gas interaction, are in good agreement with the experimental polarization data.

The dependence of energy pooling cross sections on the alignment of atomic angular momentum with respect to the collision axis is investigated. In a vapor cell, excitation with counter-propagating polarized laser beams that define the collision axis prepares aligned strontium atoms in the $5s5p{}^3{P}_1$ level. Excited-state energy pooling collision products from the endothermic $5s5p{}^3{P}_1+5s5p{}^3{P}_1\to 5s6s{}^1{S}_0{+5s}^2{}^1{S}_0$ reaction and the exothermic $5s5p{}^3{P}_1+5s5p{}^3{P}_1\to 5s5p{}^1{P}_1{+5s}^2{}^1{S}_0$ reaction are studied. Alignment effects are studied as a function of collision energy, using pulsed laser excitation followed by delayed fluorescence detection to lower the transverse collision velocity and laser detuning to vary the collision velocity in the laser-beam direction. The rate coefficient for energy transfer to the $6{}^1{S}_0$ state is enhanced by $38\pm 13\%$ when the $M_J$ alignment of the collision partners is perpendicular to the collision axis and parallel to each other compared to when there is no alignment of the collision partners. No alignment dependence is observed for energy transfer to the $5{}^1{P}_1$ state. This experiment offers the unique capability of simultaneously and independently controlling collision velocity and angular momentum alignment.

Electric-field effects on the ${}^1{P}^o$ shape resonance of ${\mathrm{H}}^{\mathrm{-}}$ lying above the $\mathrm{H}\mathrm{}(N=2\mathrm{})\mathrm{}$ threshold is investigated theoretically using a method of complex-coordinate rotation. Products of Slater-type orbitals are used to represent the two-electron wave functions, with block matrices up to $L_{\max }=6\mathrm{}$ ($I$ states) are used when the external field is turned on. Comparisons are made with the available experimental and theoretical results.

We study the influence of a weak magnetic field on time evolution of a quantum state that is a coherent superposition of two counter-rotating Trojan wave packets in a linearly polarized electromagnetic field. We demonstrate that both the interference pattern of the electron probability density and differential cross section for half-cycle pulse ionization exhibit periodic modulation as a function of magnetic flux cutting the plane of packet motion. The shift is proportional to the magnetic flux in a way characteristic for the Aharonov-Bohm effect.

Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.

Collective atomic Schrödinger-cat states are superpositions of distinct atomic coherent states (or Bloch states). We show how even and odd atomic states can be generated in cavity QED by the use of a dispersive interaction between the atoms and the field along with state reduction.

It is argued that the proof of Cohen [Phys. Rev. A 51, 4373 (1995)] which shows that an application of the Aharonov-Bergmann-Lebowitz (ABL) rule leads to contradiction with predictions of quantum theory is erroneous. A generalization of the ABL rule for the case of an incomplete final measurement (which is needed for the analysis of Cohen’s proof) is presented.