We have observed excess quantum noise in a geometrically stable He-Xe laser. This was achieved by insertion of an aperture in front of one of the laser mirrors, the aperture diameter being considerably smaller than the beam waist of the lowest-loss Gaussian mode. The measured excess noise is as large as a factor of 15 for the smallest aperture. A simple model is introduced to calculate the transverse excess noise factor using a far-field approximation. We have studied the square and circularly shaped aperture case, both theoretically and experimentally. Our experimental data demonstrate that the overall excess noise factor is given by the product of the transverse and longitudinal excess noise factors, except for the smallest circular apertures, where the results suggest that possible effects of gain guiding and waveguiding need to be considered.

We present experimental and theoretical results of spontaneous optical pattern formation in a nonlinear optical system. The nonlinear optical system we considered had a controllable phase-only spatial Fourier filter placed in the system’s diffractive feedback loop. A change in feedback field spatial spectral component phase resulted in a transition between dynamic regimes, as observed in both experiments and numerics. Patterns originating from interactions between spatial modes belonging to different instability bands (black-eye patterns, decagons, etc.) were observed, as well as localized states and shock traveling waves.

In the Huttner-Barnett theory of QED in linear dispersive dielectrics with absorption [Europhys. Lett. 18, 487 (1992); Phys Rev. A 46, 4306 (1992)], a certain function of frequency $\varepsilon \left(\omega \right)$ is interpreted as the dielectric permittivity of the medium. As the concept of permittivity is independent of the quantum nature of radiation, to fully justify their interpretation it should be demonstrated that the Huttner-Barnett $\varepsilon \left(\omega \right)$ coincides with the result of a classical calculation of the permittivity for the microscopic model adopted. We give such a demonstration here. In addition, we show that the expression for $\varepsilon \left(\omega \right)$ given by Huttner and Barnett can be considerably simplified. The simplified expression makes evident what classes of dielectric permittivity can be described within the Huttner-Barnett theory.

We predict the existence of cavity-induced two-photon absorption in unidentical atoms, and demonstrate the nonclassical character of this two-photon absorption. We show the effects of photon statistics on cavity induced two-photon absorption. We also note the possibility of trapping states in the present system.

An atomic Dicke system is coupled to a photonic band-gap continuum, which we model by a Fano-profile density of states. By introduction of two pseudomodes, a Markovian master equation can be derived governing only the degrees of freedom of the atoms plus the two pseudomodes. One of the modes can be adiabatically eliminated, and effectively we then have an atomic Dicke system coupled to a harmonic oscillator and both systems coupled to the same flat continuum. We find that following the superradiant regime, a metastable state is reached for the atomic system. The decay of the metastable state is nonexponential, and we derive an analytical expression for the decay based on perturbation theory and trapping states identified by the Monte Carlo wave-function method. Further, we investigate mean-value equations of motion for the operators of the system and discuss different decorrelation approximations of the operator expectation values.

From the microscopic quantum Langevin equations (QLEs) we derive the effective semiconductor QLEs and the associated noise correlations which are valid at a low-injection level and in real devices. Applying the semiconductor QLEs to semiconductor light-emitting devices (LEDs), we obtain a formula for the Fano factor of photons that gives the photon-number statistics as a function of the pump statistics and several parameters of LEDs. Key ingredients are nonradiative processes, carrier-number dependence of the radiative and nonradiative lifetimes, and multimodeness of LEDs. The formula is applicable to the actual cases where the quantum efficiency $\eta$ differs from the differential quantum efficiency ${\eta }_d,$ whereas previous theories implicitly assumed $\eta ={\eta }_d.$ It is also applicable to the cases where photons in each mode of the cavity are emitted and/or detected inhomogeneously. When ${\eta }_d<\eta$ at a running point, in particular, our formula predicts that even a Poissonian pump can produce sub-Poissonian light. This mechanism for generation of sub-Poissonian light is completely different from those of previous theories, which assumed sub-Poissonian statistics for the current injected into the active layers of LEDs. Our results agree with recent experiments. We also discuss frequency dependence of the photon statistics.

A nonlinear spectroscopic investigation of a strongly coupled atom-cavity system is presented. A two-field pump-probe experiment is employed to study nonlinear structure as the average number of intracavity atoms is varied from $\overline{N}\approx 4.2$ to $\overline{N}\approx 0.8$. Nonlinear effects are observed for as few as $0.1$ intracavity pump photons. A detailed semiclassical simulation of the atomic beam experiment gives reasonable agreement with the data for $\overline{N}\gtrsim 2$ atoms. The simulation procedure accounts for fluctuations in atom-field coupling which have important effects on both the linear and nonlinear probe transmission spectra. A discrepancy between the simulations and the experiments is observed for small numbers of atoms $(\overline{N}\lesssim 1)$. Unfortunately, it is difficult to determine if this discrepancy is a definitive consequence of the quantum nature of the atom-cavity coupling or a result of the severe technical complications of the experiment.

We find the observables that can be determined by two practical schemes based on atom-field resonant interaction. In the first example, the interaction is followed by photon-number and atomic-population measurements. In the second scheme the directly measured quantity is the atomic deflection. In particular, we show that they provide the measurement of the atom-field relative phase. When the initial field state is known, the atomic density matrix can be reconstructed.

The quantum fluctuation-dissipation theorem is generally manifested in the equation of motion through the appearance of a dissipative (frictional) term as well as a fluctuating force. Here it is shown that the equation of motion for a free electron interacting with the radiation field, when expressed in terms of the renormalized (observed) mass, displays fluctuations without dissipation. Despite this apparent contradiction, the equation is consistent with the fluctuation-dissipation theorem.

We demonstrate that the Bethe, and therefore the Thomas-Reiche-Kuhn, sum rule is unaffected by the presence of an applied external electromagnetic field in the exact case. We use the consequence that the first-order perturbation contribution must also vanish to derive a necessary condition for the completeness of computational one-electron basis sets.

We propose a technique which is suitable for calculations of resonant energies of three-body systems. It is based on a smooth exterior complex scaling procedure and the three-dimensional finite-element method. Accuracy dependencies on an exterior radius and on a curvature of the rotated path are examined. $S$-wave resonances of helium are calculated with an accuracy better than ${10}^{-5}$ a.u.

We show that the two-photon state generated in the process of spontaneous parametric down-conversion in a thin crystal carries information about the angular spectrum of the pump beam. This information transfer allows one to control the transverse correlation properties of the down-converted fields by manipulating the pump field, with consequences for a broad class of experiments. The effect is demonstrated theoretically and experimentally, in connection with the formation of fourth-order images by the down-converted beams.

We have produced squeezed states of light using a degenerate optical parametric amplifier pumped by an all-solid-state cw mode-locked laser source. The process resulted in squeezed light pulses of less than 3 ps in duration. Up to 0.7 dB of amplitude-squeezed light at 1047 nm and 0.5 dB of noise reduction in vacuum were observed directly. The inferred squeezing level in both cases, after all propagation losses in the detection system and the effects of spatial and temporal mode overlap had been taken into account, was 1.8 dB.

In the two papers [T. Kiss, U. Herzog, and U. Leonhardt, Phys. Rev. A 52, 2433 (1995); U. Herzog, Phys. Rev. A 53, 1245 (1996)] with titles similar to the one given above, the authors assert that in some cases it is possible to compensate a quantum efficiency $\eta <~1/2$ in quantum-state measurements, violating the lower bound $1/2$ proved in a preceding paper [G. M. D’Ariano, U. Leonhardt, and H. Paul, Phys. Rev. A 52, R1801 (1995)]. Here we reestablish the bound for homodyning any quantum state, and show how the proposed loss-compensation method would fail in a real measurement outside the $\eta >1/2\mathrm{}$ regime.

The authors of the preceding Comment [G. M. D’Ariano and C. Macchiavello, preceding paper, Phys. Rev. A 57, 3131 (1998)] tried to reestablish a $0.5$ efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D’Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].

Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT’s) defined in terms of a wave function $\psi \mathrm{}\left(x\right)\mathrm{}$ do not form a group. To get a group property one has to consider transformations that act differently on different branches of the complex argument function and the knowledge of the value of $\psi \mathrm{}\left(x\right)\mathrm{}$ is not sufficient for a well-defined NGT. NGT’s that are well defined in terms of $\psi \mathrm{}\left(x\right)\mathrm{}$ form a semigroup parametrized by a real number γ and a nonzero λ that is either an integer or $-1<~\lambda <~1.$ An extension of NGT’s to projectors and general density matrices leads to NGT’s with complex γ. Both the linearity of evolution and Hermiticity of density matrices are gauge-dependent properties.

We show that the photon pair collection efficiency in coincidence measurements can be maximized when the two-photon state is generated in the process of spontaneous parametric down-conversion in a thin crystal. This effect can be used to close part of the so-called detection loophole in Bell's inequalities experiments. The effect is also demonstrated experimentally.

$P$-wave autodissociating resonances in positronium-hydrogen scattering are calculated using the method of complex-coordinate rotation. The two lowest $P$-wave resonance energies and widths are determined by employing extensive Hylleraas-type wave functions. A comparison with published results is made.