A variety of complex spectral features occurs in multichannel Rydberg systems when the ionization thresholds vary in a simple manner with a tunable parameter such as the magnetic-field strength. We develop an analytical description of these features, identifying the key dynamical quantities controlling the appearance of ‘‘complex resonances’’ and their evolution with the parameter. The analysis predicts a ubiquitous occurrence of states with vanishing autoionization width, and of multiple q reversals associated with perturbing configurations. This description can be used to interpret some features of the diamagnetic spectrum of lithium near the zero-field ionization threshold.

An approach has been developed to study the excitation of a ground-state H atom to the n=2 level under the simultaneous action of fast-electron impact and a monochromatic, linearly polarized, homogeneous laser beam. The laser frequency is assumed to be low (soft-photon limit) so that a stationary-state perturbation theory can be applied as is done in the adiabatic theory. An elegant method has been developed in the present work to construct the dressed excited-state wave functions of the H atom using first-order perturbation theory in the parabolic coordinate representation. By virtue of this method, the problem arising due to the degeneracy of the excited states of the H atom has been successfully overcome. The main advantage of the present approach is that the dressed wave function has been obtained in terms of a finite number of Laguerre polynomials instead of an infinite summation occurring in the usual perturbative treatment. The amplitude for direct excitation (without exchange) has been obtained in closed form. Numerical results for differential cross sections are presented for individual excitations to different Stark manifolds as well as for excitations to the n=2 level at high energies (100 and 200 eV) and for field directions both parallel and perpendicular to the incident electron momentum. Extension to a higher order of perturbation is also possible in the present approach for the construction of the dressed states, and the electron-exchange effect can also be taken into account without any further approximation.

This paper reports on the investigation of excitation spectra of rubidium Rydberg atoms in crossed electric and magnetic fields. The quasi-Landau spectra were evaluated and their Fourier transforms calculated. The scaled spectral scans used for this purpose were obtained by changing the electric and magnetic fields as well as the laser frequency in an appropriate way. The observed resonances could be explained completely by semiclassical orbits. Only orbits showing overlap with the ground-state wave function are observed. The polarization dependence of certain components in the Fourier spectra can be explained by the shape of the semiclassical orbits. The electric dipole moments of the atoms resulting from the shift of the quasi-Landau structures in a changing electric field agree quite well with the corresponding semiclassical orbits.

We have experimentally studied the interaction of a collimated thermal rubidium beam with a two-dimensional intense standing wave generated in the intersection area of the ${\mathrm{TEM}}_{00}$ modes of two mutually orthogonal linear optical resonators. The relative time-phase difference of the two resonator modes was controlled. We observe transverse confinement of the atoms in the node or antinode structure of the standing wave and a deflection of the atoms after their passage through the light field. In both cases the time-phase difference can be identified as an important parameter for the kinematics of the interaction process between atoms and standing waves. Our experimental data are in qualitative agreement with the results of a Monte Carlo simulation based on a two-level atom.

Using Caves’s theory on the quantum-noise limit in an amplifier, we consider the quantum limit on noise in a Raman amplifier. We show explicitly that the full quantum equations for the Raman interaction can be transformed into the general form for a quantum amplifier. In addition, we show that in the steady-state limit the Raman amplifier becomes a phase-insensitive amplifier. At this limit we find that the output signal-to-noise ratio is unity when one photon per mode is input. Thus we conclude that the Raman amplifier, in the phase-insensitive limit, will operate at the quantum-noise limit.

A three-level atom with two competing transitions can sense correlations between modes of an electromagnetic field with which it interacts. We examine the sensitivity of three-level atoms in ladder, Λ, and V configurations to correlations between modes in a broadband correlated reservoir of field modes. Our model of a correlated reservoir includes pairwise mode correlations around a center frequency. When such correlations are set to zero, the reservoir becomes a simple thermal heat bath, but in the opposite extreme when the modes are perfectly correlated, we recover a minimum-uncertainty broadband squeezed vacuum. We show that atomic populations are extremely sensitive to these correlations, and can, in the ladder system, become inverted as a result of the phase-sensitive noise. We also show how atomic population trapping is affected by mode correlations.

The behavior of a two-level atom confined within a cavity, pumped by an intense external field, and damped by a squeezed vacuum reservoir is studied. When the lowest squeezed quadrature of the vacuum is in phase with the pumping field, the relaxation time of the population inversion and of the polarization quadratures of the atom are appreciably enlarged, and hence the atom is decoupled from the reservoir. The effects of finite bandwidth of the squeezing are analyzed and it is shown that they can be used to improve the decoupling.

A bare bound state is modeled as a ground-state two-level atom which at t=0 is deprived of most of the low-frequency components of its virtual radiation field. This state is expected to evolve into a fully dressed ground state through reconstruction of the full cloud of virtual quanta. The quantum theory of measurement is used to show that the dynamics of the two-level atom due to this reconstruction can be detected experimentally under appropriate conditions. The measuring apparatus is modeled by a pointer coupled to the atom. The theory predicts that for sufficiently short measurements the bound state can be used as a probe of the dressing process. This result is discussed in connection with the theory of the excitonic polaron in a semiconductor.

The change of dynamics in a quantum system under frequent or continuous observation, known as the quantum Zeno effect, is generally derived from the projection or reduction of the wave-packet hypothesis that is the central postulate in the theory of quantum measurements. The only experiment in which the Zeno effect has yet been clearly demonstrated, though, allows no conclusion on the necessity or validity of the projection postulate. This is shown by calculating, in detail, the outcome of the experiment on the basis of the standard three-level Bloch equations. These equations follow from the quantum theory of irreversible processes with no additional assumptions necessary, such as which part of the system serves as measuring apparatus or how efficient the measurement would be.

The theory of the laser linewidth is formulated to account for arbitrarily large output couplings and spatial hole burning. We show explicitly that the linewidth can be interpreted in terms of either spontaneous-emission noise or the amplification of vacuum field modes leaking into the cavity, depending on the ordering of operators in the correlation function determining the laser spectrum. This allows us to derive the Petermann K factor associated with ‘‘excess spontaneous-emission noise’’ in a physically transparent and mathematically simple way, without the need to introduce adjoint modes of the resonator. It also allows us to straightforwardly include spatial-hole-burning effects, which are found to increase the K factor and the linewidth in high-gain systems appreciably.

The three-wave parametric down-conversion in an uniaxial crystal with type-II phase matching is considered. It is established that by these conditions the spatial-multimode broadband squeezed states of light are generated with two orthogonal elliptical polarizations. The eigen-polarization-vectors of multimode squeezed light on the entry and at the exit of the crystal are found. It is shown that the homodyne reception of such light can reduce the photodetection noise of the surface current density below the shot noise in some time and space regions for both eigen-polarization-vectors of light. The frequency and spatial-frequency spectrum of the current density for both eigen-polarization-vectors is calculated. A clear explanation of multimode squeezing for both polarizations is given.

We present analytical and numerical results for the line shapes for a two-level atom interacting with pump and probe fields. We focus our attention on a time regime which is small enough that relaxation effects could be neglected, but sufficiently large that one could integrate the signal over a large number of population oscillations between the excited and ground states. As in our earlier work [J. H. Eberly and V. D. Popov, Phys. Rev. A 37, 2012 (1988)], we consider situations where the signal is determined by the atomic inversion, and identify the transient line shape with the time-averaged inversion considered as a function of the probe frequency. We present a formulation, based on the Floquet approach, that allows us to obtain formal expressions for the transient line shape in terms of infinite continued fractions, which can be evaluated numerically. We also present line shapes computed by directly solving the equations of motion numerically and integrating the inversion numerically over long times to compare with our continued-fraction results. We discuss the dependence on initial conditions, the relative pump-probe phase, and the non-Lorentzian character of these line shapes.

In this paper we investigate the sensitivity of coupled atomic transitions to correlations between field modes. In particular, we show that a three-level atom interacting with a cavity field supporting two quantized modes can be highly sensitive to the nature of the correlations between the modes. Correlated two-mode states include the two-mode squeezed state, whereas the SU(2) coherent state is an example of an anticorrelated state. We study in detail the dynamics of a three-level atom in the λ configuration, interacting with the two modes of an SU(2) coherent state. We show that for certain choices of the atom-field coupling constants, the generalized two-photon Rabi frequency for the system becomes independent of the photon number, leading to a purely periodic behavior in time of the atomic population probabilities; for other choices of the atom-field coupling constants, we observe the usual collapse and revival of the Rabi oscillations. We study also the dynamics of the field, in particular the correlations between the modes. Finally, for comparison purposes, we present a parallel study of the case in which the field modes are initially uncorrelated.

The generation of squeezed light in a single-pass parametric amplifier pumped by Gaussian beams is analyzed. Limits to the degree of squeezing that can be obtained are found that arise from spatial distortion of the signal beam that is significant for parametric gains greater than 3 dB. It is found that squeezing is limited to approximately 6 dB for typical experimental configurations. These limits severely constrain the design of quantum noise experiments unless high finesse cavities or waveguides are used.

The Raman-enhanced third-order optical nonlinearity of calcite potentially can support resonant back-action-evading measurement of the optical-field amplitude. In a preliminary experiment, we have observed cross-quadrature modulation transfer between an amplitude-modulated pump beam and an unmodulated probe beam tuned near the Stokes frequency. The theory of Holland et al. [Phys. Rev. A 42, 2995 (1990)] is extended to the case for which intracavity losses are significant in an attempt to account for the observations.

We present consistent transient theory of lasing without inversion and show by numerical analysis that pulse-mode lasing is feasible in a two-level system with split upper levels coupled by an external high-frequency electromagnetic field.

From the quantum-optics point of view the problem of a charged particle in the presence of a constant magnetic field is presented. The photon numbers as well as bunching and antibunching are considered. Statistical investigations are carried out for the quasiprobability distribution function (Wigner function). The phenomenon of squeezing is also discussed.

The steady-state bistability and the evolution of the field envelope of a ring-cavity optical-bistable system including the effect of the transverse radiation field and the effect of an inhomogeneously broadened atomic medium are studied by means of the mean-field approximation and dressed-mode theory in this paper. Our study shows that the bistable region enlarges with an increase of the ratio ${\mathit{r}}_0$/${\mathit{w}}_0$ (${\mathit{r}}_0$ is the radius of the cylindrical atomic sample and ${\mathit{w}}_0$ the beam waist of the Gaussian beam), and decreases with increasing width of the inhomogeneously broadened line. The transverse-field effect has more impact on the magnitude of the bistable region than the inhomogeneous broadening under certain conditions. In the case of two unstable modes, the evolution of the field envelope before reaching the stable oscillation regime differs remarkably from that in the case of the plane-wave approximation with a homogeneously broadened atomic medium.

We investigate the classical and quantum oscillator with time-dependent mass and frequency, in the framework of the Lie group theory. Our analysis shows that both systems possess five time-dependent Noether invariants, where only two of them are functionally independent. In the classical case, three of these invariants form the su(1,1) Lie algebra under the Poisson bracket operation, while in the quantum case the corresponding invariants form the su(1,1) Lie algebra under the commutator operation. Since this algebra underlies the noncompact group SU(1,1), we are thus able to define unambiguously the dynamical group related to the generalized quantum oscillator. Furthermore, the Hamiltonian of this system can be expressed in terms of the Noether invariant operators satisfying the su(1,1) Lie algebra. This form is useful in the evaluation of the energy spectrum and in the study of coherence and squeezing. Some particular cases are briefly illustrated. The other two Noether invariants can be interpreted as the quadrature-phase amplitudes involved in the quantum nondemolition measurements and in the problem of the generation of coherent and squeezed states.

A reformulation of the well-known maximum-entropy principle in the interaction picture is shown. The advantage of this approach for the case in which the relevant operators in the interaction picture do not depend explicitly on time is stated. As an example, we study the dynamical evolution of the dispersions of the so-called slowly varying quadrature operators for the degenerate parametric amplifier and the temporal behavior of the squeezed states associated with this system.