Stochastic dynamics of a laser-driven four-level system serving as a model for a single guest chromophore molecule in an amorphous polymer host is studied. The dynamics of “slow” transitions (spectral jumps), accompanied by instantaneous changes in the fluorescence frequency, is simulated on the basis of continuous measurement theory. It is shown that there is an opportunity to control the statistics of “bright” and “dark” periods by using laser fields to drive molecules having different tunneling rates for the ground and excited electronic states. The effect of population cycling in a four-level system and related effects of local heating or cooling of the environment are discussed.

High-efficiency coherent high-frequency generation via resonant four-wave mixing is investigated in a dressed states analysis of a bichromatically driven three-level system. We propose the existence of exponential gain due to population transfer at the anticrossings of closely spaced inverted dressed states. This occurs when the Rabi frequency of the weaker detuned driving field is much smaller than the leading resonant Rabi frequency and simultaneously comparable to the largest atomic relaxation rate. The dressed population inversion and thus the exponential gain is not affected until the generated field becomes comparable in intensity to one of the two applied fields, when saturation may take place. The analysis is applied to a krypton configuration of interest to current experiments.

The theory for coherent Raman scattering (CRS) with broadband incoherent light is presented for a multiply resonant, multicomponent mixture of molecules that exhibits simultaneous multiple resonances with the frequencies of the driving fields. All possible pairwise hyperpolarizability contributions to the signal intensity are included in the theoretical treatment—(resonant-resonant, resonant-nonresonant, and nonresonant-nonresonant correlations between chromophores) and it is shown how the different types of correlations manifest themselves as differently behaved components of the signal intensity. The Raman resonances are modeled as Lorentzians in the frequency domain, as is the spectral density of the incoherent light. The analytic results for this multiply resonant mixture are presented and applied to a specific binary mixture. These analytic results will be used to recover frequencies and dephasing times in a series of experiments on multiply resonant mixtures.

We measure phase-dependent fluorescence spectra for an elementary system: long-lived coherently driven two-level atoms in an atomic beam. Phase-dependent fluorescence spectra measure quadrature noise in the atomic radiation field. These noise spectra are obtained using a homodyne detection scheme that suppresses excess noise by subtracting signals from two identically prepared atomic samples. Noise spectra are obtained for atomic radiation which is in phase $\left(0\mathrm{}°\right)$ and out of phase $\left(90\mathrm{}°\right)$ with a resonant driving field, as well as $\pm 45°$ out of phase with an off-resonant driving field. The measured phase-dependent fluorescence spectra are much richer than ordinary fluorescence spectra, and exhibit many novel features. Particularly interesting are phase-dependent noise spectra for off-resonant excitation. These strikingly exhibit direct manifestations of time ordering, which appear as large differences between the measured $45°$ and $-45°$ quadrature noise spectra. The measured noise spectra are in excellent agreement in magnitude and shape with the results of a quantum treatment using no free parameters.

${\mathrm{He}}^0{+\mathrm{N}}_2$ collisions are studied at an energy of 1.0 keV and in an angular range from 0.2° to 2°. Time-of-flight techniques are used to identify the dominant collision processes. Electronically elastic collisions are found to dominate the scattering for angles out to 1.3°. In ${\mathrm{He}}^0{+\mathrm{N}}_2,$ ${\mathrm{H}}_2,$ and ${\mathrm{O}}_2$ collisions the electronically elastic processes were found to be weak beyond the smallest angles, in sharp contrast to the present results. Excitation of ${\mathrm{N}}_2$ $\left(a{}^1{\Pi }_g\right)$ is found to be the dominant small-angle inelastic process. Our results also show excitation of ${\mathrm{N}}_2^{+}$ $(A{}^2{\Pi }_u$ and $B{}^2{\Sigma }_u^{+})$ but at most very weak excitation of the ${\mathrm{N}}_2^{+}$ $\left(X{}^2{\Sigma }_g^{+}\right)$ ground state. The excitation of an electron from the $3{\sigma }_g$ molecular orbital of ${\mathrm{N}}_2$ is found to be generally quite specific and takes place primarily through a transition to a $1{\pi }_g$ orbital.

The quantum phase distributions and variances of strong coherent and phase-squeezed states mixed with thermal light are calculated. We find that the effect of thermal light on the coherent phase distribution becomes important only when the number of thermal photons is of order one-half. Its effect on the phase distribution of phase-squeezed states (for the case where the number of photons is very large compared to $e^{2r})$ becomes important when the number of thermal photons is of order $\frac{1}{2}{e}^{-2r}$, where $r$ is the squeezing parameter.

We show spatial localized structures in degenerate optical parametric oscillators associated with bistability between two homogeneous solutions of the same amplitude and the opposite phase. These localized structures are principally different from the ones analyzed previously in nonlinear optics (including optical parametric oscillators), where bistability between different patterns (most often zero- and nonzero-field states) was at the root.

We investigate correlations among photons from the components of the resonance fluorescence spectrum of a cooperative system of two-level atoms interacting with a strong field of a single-mode lossless cavity. The properties of the central band are more closely related to the superradiant effect in free space than the sidebands. The central band field has reduced fluctuations and the collective dipole has its largest uncertainty when half the atoms are initially excited. Partial atomic excitation destroys the sub-Poissonian character of the sideband field and leads to a bunching-antibunching transition in the correlation of a sideband photon followed by a central band photon.

In a previous paper, Zhang [Phys. Rev. A 54, 1252 (1996)], among other problems, reconsiders the order ${\alpha }^4{R}_{\infty }$ corrections to the positronium $P$ levels. His calculations confirm our corresponding results, except for the contribution due to the squared spin-orbit interaction. We present here a different derivation of our previous result for this last correction, this derivation being, in our opinion, both simple and convincing.

Both the radial Schrödinger-Coulomb wave function and the radial Dirac-Coulomb wave function can be presented in a similar way using the regular solution $f^0\mathrm{}\left(r\right)\mathrm{}$ and the quantum-defect theory parameters $A$ and $B.\mathrm{}$ The radial wave function normalized per unit energy for the continuum state is $B^{1/2}{f}^0\mathrm{}\left(r\right)\mathrm{}$ and the radial wave function normalized to unity for a bound state is ${\mathrm{NA}}^{1/2}{f}^0\mathrm{}\left(r\right),$ where $N$ is the normalization factor. The photoionization cross section of the hydrogen atom can be expressed analytically in terms of algebraic forms using the ground state and continuum states.

We discuss the interaction between a microscopic electric dipole oscillator and a long solenoid which are separated by a small distance. The solenoid belongs to a simple $\mathrm{RLC}$ circuit and the zero point and thermal current fluctuations within the solenoid coils are taken into account. We describe how they affect the equilibrium state and the excited states of the oscillator, thus providing a description of the Casimir interaction of the system. We calculate the modification in the lifetime of the oscillator excited states as a function of the parameters of the circuit, the dipole orientation, and the distance between the dipole and the solenoid. The Casimir force between the solenoid and the electric dipole is calculated, and it is shown that this Casimir interaction always exists, that is, it occurs even when the macroscopic current in the solenoid is zero. We suggest experiments which can exhibit these effects related to the electromagnetic interactions between atoms or molecules and simple circuits.

A Hermitean phase operator is constructed for two-state systems by means of an antiunitary transformation. The phase information is obtained from this operator by calculating a “phase vector,” in close analogy to the way the vector of expectation values (Bloch vector) is calculated from the projection operator of a state. This construction is applied to two issues of quantum physics where phases are of crucial importance, i.e., the superposition principle and geometric phases. It is shown by these examples how the phase vector representation of these issues, offering a very useful visualization, derives from the algebraic properties of the phase operator.

Decoherence in quantum-computer memory due to the inevitable coupling to the external environment is examined. We make the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits decohere collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory, even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.

We consider quantum systems, whose dynamical symmetry groups are semisimple Lie groups, which can be split or decay into two subsystems of the same symmetry. We prove that the only states of such a system that factorize upon splitting are the generalized coherent states. Since Bell’s inequality is never violated by the direct product state, when the system prepared in the generalized coherent state is split, no quantum correlations are created. Therefore the generalized coherent states are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell’s inequality upon splitting.

A formalism is developed for calculating the quasienergy states and spectrum for time-periodic quantum systems when a time-periodic dynamical invariant operator with a nondegenerate spectrum is known. The method, which circumvents the integration of the Schrödinger equation, is applied to an integrable class of systems, where the global invariant operator is constructed. Furthermore, a local integrable approximation for more general nonintegrable systems is developed. Numerical results are presented for the double-resonance model.

On the basis of the invariant formulation, we find the quantum and classical exact solutions and corresponding total phase for the relativistic charged Klein-Gordon (KG) field in a time-dependent spatially homogeneous electric field. The total phase includes both the dynamical and geometric phases (Aharonov-Anandan phases). The connection between the quantum and classical solutions is then obtained. From this connection we discuss the condition under which the geometric phase for the KG field can be defined.

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\mathcal{T}^\mathrm{}\left(X\right)\mathrm{}$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive-definite operator $J^{\mathrm{}(+)\mathrm{}}\mathrm{}\left(X\right)\mathrm{}$, which is nothing but a straightforward quantum version of the modulus of the classical current. For quantum states highly localized in momentum space about a certain momentum $p_0\ne 0$, the expectation value of $J^{\mathrm{}(+)\mathrm{}}\mathrm{}\left(X\right)\mathrm{}$ becomes indistinguishable from the quantum probability current. This fact may provide a justification for the common practice of using the latter quantity as a probability distribution of arrival times.

We numerically analyze the influence of separatrices and stochastic webs on the evolution of quantum wave functions in phase space and we compare our findings with the corresponding classical evolution. We study the dynamics in regular and nonregular systems, namely, in a quartic, the pendulum, and the kicked harmonic oscillator potentials. Regardless of the specific potential, there are common features in the dynamics, some of which are revealed when very small parts of the quantum phase-space densities are analyzed.

Two examples are presented where the observation of the emission in parametric down-conversion leads to its enhancement instead of its inhibition. The improvement is analyzed in terms of the quantum features of the observation.