The relationship between the multipolar and minimal Hamiltonians through a canonical transformation is used to analyze the time dependence of quantum operators in the two formalisms. It is shown that operators dependent on particle position, the vector potential, and their time derivatives have the same time dependence. However, operators such as the photon number and the atomic population number evolve differently in the two cases. Expressions correct to second order in the electric-dipole moments for these are given. The expectation values of the photon number operator are calculated in the two formalisms and are used to predict natural line shapes. These theoretical shapes differ. The observed shape will depend on the particular setup of the experiment involving the radiative decay of an excited atom. A comparison with the theoretical predictions will determine which of the two frameworks is most appropriate to describe the decay. Finally, the energy density of the electromagnetic field in the neighborhood of an atom is calculated within the two formalisms.

Methods for the enhancement of optical quantum nondemolition (QND) measurements are discussed. We review the use of meter squeezing as a QND enhancement tool and present a method of QND enhancement using an electro-optic feed-forward amplifier. By applying a linearized theory it is shown that these techniques work very well together. The combined effect of these enhancement methods is modeled for two QND systems, a squeezed light beam splitter and an optical parametric amplifier. We also discuss the conflict between the normal QND criteria and QND systems that involve noiseless amplification. We use an additional parameter to quantify the problem. A method for correcting the effects of noiseless amplification is discussed and modeled. We also discuss a special case of QND that eliminates the optical interaction between the meter and signal input beams. This system is shown to be a very effective QND device.

We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\lambda /2\mathrm{}$ and $\lambda /4.\mathrm{}$ Particular attention is given to the parallel dipole in the $\lambda /2\mathrm{}$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.

We investigate the effects of photodetector imperfections on a recently proposed device designed to truncate physically a state of light. We find that the mixed state produced in the presence of the imperfections has a surprisingly good fidelity with the required state. For convenience and mathematical simplicity, we make use of the quantum-mechanical retrodictive formalism but show that the results are equivalent to those obtainable from more usual predictive formalism.

We propose a method for quantum nondemolition (QND) measurement of one component of spin by the measurement of polarization rotation of the off-resonant light induced by a paramagnetic Faraday rotation effect. We show that nonclassical states of spins such as the squeezed spin state, the Dicke state, and macroscopic quantum superposed state of spin can be realized corresponding to particular results of QND measurements. Furthermore, it is shown that a nonclassical state of light such as the twin photon state can also be realized with this method.

We present the results of a comprehensive investigation of the quantum-noise properties of a continuous-wave phase-conjugate mirror (PCM) formed using backward-four-wave mixing in potassium vapor. We characterize the quantum-noise properties of the PCM as functions of the vapor density, pump detuning from resonance, and relative frequency detuning of the signal beam from the probe beam. We compare the noise measurements of the PCM with the predicted noise of an ideal quantum-noise-limited PCM and determine the value of the minimum signal that can be used to perform phase conjugation with unity signal-to-noise ratio. For the range of vapor densities studied, we find that the PCM operates nearest the quantum-noise limit and that the value of the minimum signal is lowest under conditions in which the reflectivity is maximized. These results demonstrate that it is possible to perform phase conjugation with signals as weak as 14 fW with near-unity reflectivity. Our measurements are in qualitative agreement with the predictions of a quantum theory of phase conjugation via nearly degenerate four-wave mixing in a two-level system.

We sketch the theory of a laser based on quantum dots which are pumped by a surface acoustic wave. Collective emission in the sense of superradiance is possible if the dots are identical and arranged along a straight line. In that case strong noise suppression is possible in the photocurrent spectrum, even for high output intensity.

We present a theory of a continuous-wave light propagation in a medium of atoms with a double-$\Lambda$ configuration of levels. This is a configuration with a closed cycle of radiation-induced transitions. An interference of excitation channels in such closed-loop systems leads to a strong dependence of the atomic state on the relative phase and the relative amplitudes of applied electromagnetic waves. Therefore, the medium response may be controlled by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the propagation of four-frequency laser radiation through the double-$\Lambda$ medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the field evolve into a nonabsorbing state. This state implies specific coherent superposition for atoms (“dark state”), and particular relations for the field phases, amplitudes, and frequencies. In this way, the propagation results in the phase, amplitude, and frequency matching of the laser waves. In the second case, one $\Lambda$ system in double-$\Lambda$ atoms is excited resonantly, while the second $\Lambda$ system is far off resonance. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dissipated very weakly, whereas each individual laser wave can vary considerably along the propagation path. We have found that the resonant fields change as much as the far-detuned ones. The intensities oscillate sinusoidally with the optical length, with the energy being transferred back and forth between two waves in each frequency pair, resonant and far detuned. This gives the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them.

We study experimentally how to control and improve phase matching of high-order harmonic generation. We use a birefringent lens and a birefringent compensator to obtain a fundamental laser pulse (150 fs, 800 nm, ∼4 mJ) with two foci separated by 6.2 mm along the propagation axis and with a controllable phase delay between the polarizations along the optic axes of the birefringent optical components. This enables us to enhance the high-order harmonic conversion efficiency for the high-order harmonics in neon to $3\times {10}^{-8},$ a factor of 4 higher compared to a single-focus setup in similar conditions. The enhancement is achieved by improving the phase matching and at the same time maintaining a high intensity in a large generating volume.

We propose a simple model of an ion-trap laser: A single two-level ion confined to a harmonic trap, subjected to resolved-sideband laser cooling in the presence of external noise, and coupled strongly to an optical cavity. The lasing of the cavity mode results from the quantized treatment of the ion’s motion, and occurs when the cavity is tuned to frequencies of the vibrational sidebands located below the frequency of the cooling laser.

We investigate the interplay of multiwave-mixing processes with the microscopically coupled spatiotemporal light field and charge carrier dynamics in broad-area semiconductor laser amplifiers. Our theoretical description is based on extended spatially resolved Maxwell-Bloch equations including on the microscopic level spatiotemporal multiwave-mixing processes. Performing a third-order expansion in terms of the microscopic carrier distribution, we include in our description both the effects of population pulsations of the total carrier density at the beat frequency and the spatiospectral interactions of the light fields leading to gain nonlinearities as well as spatial and spectral hole burning. Our simulations show that in a broad-area semiconductor laser amplifier, spatiotemporal wave-mixing processes occur in both transverse and propagation directions of the multifrequency optical beams employed in a typical excite-probe configuration.

We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.

We describe a family of solutions of the three-dimensional envelope equation in dispersive media beyond the slowly varying envelope approximation [T. Brabec et al., Phys. Rev. Lett. 78, 3282 (1997)] that represents few-cycle pulsed light beams evolving due to gain (losses), phase and gain dispersion, diffraction, and space-time focusing. We then show that group velocity dispersion tends to bend the propagating pulse front, in the same sense as diffraction in anomalous dispersion, and in the opposite sense in normal dispersion. In the latter case, the diffraction-induced pulse front curvature and the associated pulse broadening can be eliminated along the whole propagation by setting the diffraction length equal to the dispersion length. Simple analytic expressions for these dispersion-diffraction coupled effects are given.

The intensity transverse profile of the light produced in the process of stimulated down-conversion is derived. A quantum-mechanical treatment is used. We show that the angular spectrum of the pump laser can be transferred to the stimulated down-converted beam, so that images can also be transferred from the pump to the down-converted beam. We also show that the transfer can occur from the stimulating beam to the down-converted one. Finally, we study the process of diffraction through an arbitrarily shaped screen. For the special case of a double-slit, the interference pattern is explicitly obtained. The visibility for the spontaneous emitted light is in accordance with the van Cittert–Zernike theorem for incoherent light, while the visibility for the stimulated emitted light is unity. The overall visibility is in accordance with previous experimental results.

We present a method for dealing with quantum systems coupled to a structured reservoir with any density of modes and with more than one excitation. We apply the method to a two-level atom coupled to the edge of a photonic band gap and a defect mode. Results pertaining to this system provide the solution to the problem of two photons in the reservoir, and a possible generalization is discussed.

It is shown that quantum teleportation and entanglement swapping can be easily derived from Einstein-Podolsky-Rosen correlations and special relativity. This raises the question of what is really teleported in a teleportation experiment. It is also shown that the behavior of two photons that arrive together at a beam splitter can be seen as a particular case of a nonlocal effect in which they arrive “together” at two different beam splitters.

We present an interpretation of traversal time results in Josephson junctions, based on a stochastic model of tunneling processes which include dissipative effects. With the use of semiclassical analysis, the experiments performed up until now have supplied a time duration of the order of ${10}^2\mathrm{ps}$ (a remarkably long time, even considering the macroscopic nature of the systems under examination). According to our interpretation, this duration is only the imaginary part of a complex quantity, the real part of which (presumably the true physical duration) lies in the range of a few picoseconds.

Various measures for the accuracy of approximate eigenstates of semibounded self-adjoint operators H in quantum theory, derived, e.g., by some variational technique, are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators with respect to degenerate approximate eigenstates of H obtained by the variational methods are proposed as criteria for the accuracy of variational eigenstates.

Teleportation of continuous variables can be described in two different ways, one in terms of Wigner functions, the other in terms of discrete basis states. The latter formulation provides the connection between the theory of teleportation of continuous degrees of freedom of a light field and the standard description of teleportation of discrete variables.

Relativistic effects in the ground-state energy of positronium hydride up to orders $O\left({\alpha }^4{\mathrm{mc}}^2\right)$ and $O\left(\right(\mu /M\left){\alpha }^4{\mathrm{mc}}^2\right)$ are calculated using fully correlated basis sets in Hylleraas coordinates. The resulting binding energy against the dissociation into a positronium and a hydrogen is $1.06404168\left(27\right)\mathrm{}$ eV. The two-photon annihilation rate is also calculated and the result is $2.472208\left(20\right)\mathrm{}\hspace{0.5em}{\mathrm{nsec}}^{-1}.$