We present detailed calculations for two-and three-photon above-threshold ionization of the negative hydrogen ion. In addition to calculated values for partial wave amplitudes and phase shifts pertaining to recent experimental results [Xin Miao Zhao et al., Phys. Rev. Lett. 78, 1656 (1997)], we also address the question of the asymmetry of photoelectron angular distributions in ionization under elliptically polarized radiation, which has been studied experimentally in other negative ions [C. Blondel and C. Delsart, Laser Phys. 3, 3 (1993); Nucl. Instrum. Methods Phys. Res. B 79, 156 (1993); F. Dulieu, C. Blondel, and C. Delsart, J. Phys. B 28, 3861 (1995)].

Operating in Laplace language and making use of a representation based on photon-number states, we find the exact solution for the density operator that belongs to the Jaynes-Cummings model with cavity damping. The detuning parameter is set equal to zero and the optical resonator does not contain any thermal photons. It is shown that the master equation for the density operator can be replaced by two algebraic recursion relations for vectors of dimension 2 and 4. These vectors are built up from suitably chosen matrix elements of the density operator. By performing an iterative procedure, the exact solution for each matrix element is found in the form of an infinite series. We demonstrate that all series are convergent and discuss how they can be truncated when carrying out numerical work. With the help of techniques from function theory, it is proved that our solutions respect the following conditions on the density operator: conservation of trace, Hermiticity, convergence to the initial state for small times, and convergence to the ground state for large times. We compute some matrix elements of the density operator for the case of weak damping and find that their analytic structure becomes much simpler. Finally, it is shown that the exact atomic density matrix converges to the state of maximum von Neumann entropy if the time, the square of the initial electromagnetic energy density, and the inverse of the cavity-damping parameter tend to infinity equally fast. The initial condition for the atom can be chosen freely, whereas the field may start from either a coherent or a photon-number state.

An advanced wave model is applied to a two-photon interference experiment to show that the observed interference effect is due to the geometrical phase of a two-photon state produced in spontaneous parametric down-conversion. The polarization state of the signal-idler pair is changed adiabatically so that the “loop” on the Poincaré sphere is opened in the signal channel and closed in the idler channel. Therefore, we observed an essentially nonlocal geometrical phase, shared by the entangled photon pair, or a biphoton.

We reconsider the determination of the operational defined phase difference between two weak optical fields based on photon counting when the small number of possible experimental outcomes makes it harder to derive a continuous phase distribution. We show that the experimental procedure introduced to overcome this difficulty, namely, an external phase shifting of one input state, is not necessary. Indeed, all measuring data conditioned on the phase shift can be obtained from the data recorded without the external phase shift. Moreover, we investigate the effect of retaining ambiguous data or discarding even more data than only the ambiguous ones, respectively, and discuss the influence of a nonunit efficiency of the photodetectors.

In this paper, we study a Jaynes-Cummings model (JCM) with phase damping, by introducing a master equation describing phase damping under the Markovian approximation. With the help of the superoperator technique, we find an analytic solution of the master equation for a nonresonant multiphoton JCM with phase damping. We investigate the influence of phase damping on nonclassical effects in the JCM, such as revivals of the atomic inversion, oscillations of the photon-number distribution, the quadrature squeezing of the cavity field, and sub-Poissonian photon statistics. It is shown that phase damping suppresses the revivals of the atomic inversion and nonclassical effects of the cavity field in the JCM.

Two-dimensional (2D) “chaotic” localized structures are observed in the transverse profile of light with a delay model of a ring cavity with strongly dispersive two-level atoms. Near nascent optical bistability, the 2D homogeneous solution undergoes a subcritical transition to a spatiotemporal chaos. The inhomogeneous pattern coexisting with the homogeneous solution is filled with large-intensity peaks, oscillating with time. In the subcritical domain, localized structures are observed, with isolated peaks more stable and more coherent than the ones in the filled structure. The order is easily recovered by a filtering procedure that reduces the wave-vector bandwidth.

We measure the two-dimensional, near-field spatial distribution of a 140-Å nickel-like silver x-ray laser at the output aperture with high magnification using a curved multilayer x-ray mirror to image the output onto an x-ray charge-coupled device camera. Lasing is created by illuminating silver slab targets with a pair of 75 ps laser pulses separated by 2.2 nsec from the Vulcan laser. The two-dimensional, high-resolution, spatial image shows the x-ray laser source size and its position relative to the target surface. A dramatic change in both the position and source size are observed for the refraction compensating curved target as compared with the flat targets.

We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ medium. We show that a 20-period, 12-μm structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2–3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.

A quantum state can be described by its quasiprobability functions or by its density matrix. The quasiprobability functions and density matrix for nonclassical fields have been measured by making use of homodyne detection schemes. We suggest direct photodetection of the amplified signal fields for the quasiprobability function measurements. Linear amplification is described in phase space by a convolution of the signal field to the idler field, which normally determines added noise during amplification. Taking the coherent idler field and using the convolution relation, we show that the direct photodetection of the amplified field results in a quasiprobability function for the signal field. In particular, the probability of there being no photons in the amplified field is the scaled $Q$ function for the signal field.

We report experimental studies of metastable chaos in the far-infrared ammonia ring laser. When the laser pump power is switched from above chaos threshold to slightly below, chaotic intensity pulsations continue for a varying time afterward before decaying to either periodic or cw emission. The behavior is in good qualitative agreement with that predicted by the Lorenz equations, previously used to describe this laser. The statistical distribution of the duration of the chaotic transient is measured and shown to be in excellent agreement with the Lorenz equations in showing a modified exponential distribution. We also give a brief numerical analysis and graphical visualization of the Lorenz equations in phase space illustrating the boundary between the metastable chaotic and the stable fixed point basins of attraction. This provides an intuitive understanding of the metastable dynamics of the Lorenz equations and the experimental system.

We propose a scheme for an optical quantum gate, i.e., a mirror in a quantum superposition state of total transmission and reflection. The model consists of a high-$Q$ optical cavity strongly coupled to a single atom or ion in a quantum superposition state of two long lived internal states. By including spontaneous emission, dissipation, measurement back-action, and the time dependence of the atom-field coupling, we numerically simulate a system very close to experimental reality. The switching and quantum coherence properties are confirmed separately in two steps by using the gate directly and as an entrance beam splitter to an interferometer.

Vertical-cavity surface-emitting lasers have two preferential polarization states related to the crystal axes of the quantum wells. In this work, we consider such a laser extended by means of a polarizer inserted in an external cavity. When the phase of the external-cavity field is modulated, the laser switches from one polarization state to the other. Experimental and theoretical results in which spin interactions are inserted are presented and discussed. A linear stability analysis is applied to the two linearly polarized stationary states in the case of structures with small amplitude anisotropies. It shows how the phase of the reinjected field affects the stability of the mode. Coefficients for gain compression and spontaneous noise are mandatory to obtain polarization flips in the simulations.

We give a local-field calculation of the dynamic response of a single quantum well (QW) inside a cavity pumped by a strong light beam. The starting point of our theory is the microscopic Maxwell-Lorentz equation combined with light-induced nonlinear current densities associated with intersubband transitions in the QW system. The frequency- and space-dependent current densities are derived from the density-matrix formalism in a nonperturbative manner. Assuming only the electromagnetic coupling from the pump beam to the probe beam is important, we solve the wave equation exactly for both the pump and probe fields. In turn we determine the probe absorption coefficient of the QW structure. For a GaAs/Al${}_{0.33}$Ga${}_{0.67}$As QW placed between vacuum and a GaAs/AlAs distributed Bragg reflector followed by a GaAs prism, we calculate the probe absorption spectra for different parameters such as the pump frequency, the incident intensity of the pump field, and the cavity quality. Our results show that the optical absorption and amplification for the probe field are strongly dependent of these parameters. It is also demonstrated that it is of importance to take into account the dynamic screening effect for the pump field in the calculation of the probe spectra.

Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of “biphotons” carrying information about the pump phase.

The effect of high-density pumping on lasing mode spectra is investigated in a laser-diode pumped microchip ${\mathrm{LiNdP}}_4{\mathrm{O}}_{12}$ (LNP) laser. Breakup of multimode oscillations, leading to single-mode oscillations, is observed experimentally. It is shown analytically that the enhanced Auger recombination process among excited Nd ion pairs results in a strong deformation of spatial hole-burning patterns, leading to a destabilization of the multimode laser output via a quadratic-to-quartic transition of the spatial distribution of population inversion. The destabilization threshold is shown to be given by a universal relation which reproduces experimental results quite well. A mode-partition instability is observed above the transition, whose properties are intimately related to the antiphase dynamics.

We present an experimental study on the role of cavity polaritons in laser emissions from a GaAs quantum-well microcavity. We show that cavity polaritons play no role in the laser emission process when the cavity is nearly resonant with the excitons. The laser emissions emerge from the bare cavity mode instead of from a cavity-polariton branch and the threshold density is much higher than the saturation density at which cavity polaritons vanish. We also show that the presence of emission doublets near the lasing threshold, which was previously taken as an evidence for laser emission from cavity polaritons, is primarily the result of spatial and/or temporal variations of exciton densities within the excitation volume.

A generalized complex Swift-Hohenberg equation including diffraction and nonlinear resonance terms is derived for spatially extended nondegenerate optical parametric oscillators (OPOs) with flat end mirrors. For vanishing pump detuning this equation becomes the complex Swift-Hohenberg (SH) equation valid also for lasers. Nevertheless the similarities between OPOs and lasers are limited, since the diffractive character of OPOs is lost when the diffraction coefficients of signal and idler fields are equal. This manifests, e.g., in the absence of advection by traveling waves (TWs), a clear difference with lasers. When pump detuning is nonzero a nonlinear resonance develops, as it occurs in degenerate OPOs. This nonlinear resonance is essential in order to properly describe the TWs that OPOs support, and describes the bistability between TWs. This leads to the appearance of localized structures, which we also report here.

The study of the fluorescence phenomenon by near-field optical techniques requires one to describe precisely the spontaneous emission change occurring when the fluorescing particle is placed in a complex optical environment. For this purpose, the field susceptibility (also called the field propagator) of a planar junction formed by a cavity bounded by two semi-infinite bodies with arbitrary optical constant is derived within the framework of linear-response theory. The field propagator associated with the junction is then modified in a self-consistent manner to account for the presence of any arbitrary object inside the junction. As a first illustration the alteration of the fluorescence lifetime of a molecule by two subwavelength-sized dielectric spheres, placed inside the junction, is presented.

We observe amplification of a linearly polarized laser beam propagating through a Doppler-broadened atomic potassium vapor driven by an intense, linear and orthogonally polarized counterpropagating laser beam. The observed gain spectra are well explained by a model that incoporates only the effects of the coherent driving of the atomic dipole moment and not atomic recoil. Our results suggest that the recently reported observations of amplification and lasing using a laser-driven sodium vapor may not arise from the effects of collective atomic recoil.

We measure the transmission spectrum of an optical cavity filled with two-level atoms. For small intensities, the coupling between atoms and a single mode of the cavity splits the spectrum into two normal modes: the vacuum Rabi peaks. We gradually decouple the system in two ways and study the evolution of the vacuum Rabi peaks. First we lower the atom-cavity coupling frequency through its intensity dependence, showing that the peaks shift, deform, exhibit frequency hysteresis, and eventually merge into a single peak that approaches the empty cavity resonance. Second we detune the atoms and the cavity mode and observe an avoided crossing. The normal modes of the coupled system transform into the two resonances of the uncoupled system. We map out the transition region and find good agreement with theoretical predictions.