We calculate the effect of the local-field correction (LFC) on the local response at ${\mathrm{\omega }}_{\mathit{s}}$ and 2${\mathrm{\omega }}_{\mathit{p}}$-${\mathrm{\omega }}_{\mathit{s}}$ of a medium consisting of two-level systems when subject to a pump of arbitrary intensity at ${\mathrm{\omega }}_{\mathit{p}}$ and a weak probe at ${\mathrm{\omega }}_{\mathit{s}}$. The pump is considered strong if its reduced intensity I=${\mathrm{\omega }}_{\mathit{R}}^2$/${\gamma }_1$${\gamma }_2$ is large compared to unity. Here ${\mathrm{\omega }}_{\mathit{R}}$ is the Rabi frequency and ${\gamma }_1$ and ${\gamma }_2$ are the longitudinal and transverse relaxation rates. In the weak pump case the LFC manifests itself as a fixed or static frequency shift. When the pump is strong, the response is independent of the LFC. At intermediate pump intensities the effect of LFC is dependent on the intensity of the pump. Both line-shift and line-shape distortions are present. The LFC thus gives rise to a shift in the resonance response that varies according to the intensity and frequency of the applied radiation. We call this effect the dynamic Lorentz shift.

The process of n-photon down conversion is considered both with a quantized pump and in the parametric approximation. In the parametric approximation it is formally found that the photon number diverges at a finite time for n>2. This divergence limits the times for which the parametric approximation is useful. The divergence does not occur if the pump is quantized. Furthermore, it is shown that the Hamiltonian with a quantized pump is essentially self-adjoint. This means that the questions that have been raised about the existence of the time-development operator in the parametric approximation do not arise when the pump is quantized.

The problem of spectral filtering of quantized light fields is studied, based on the recently developed quantum-optical theory of the action of passive, lossless optical systems [L. Knöll, W. Vogel, and D.-G. Welsch, Phys. Rev. A 36, 3803 (1987)]. Expressions for the operator of the electric field strength of the light and the normally and time-ordered field-correlation functions are derived for the case of a Fabry-Pérot interferometer being present. Various kinds of field decomposition that are usually considered in classical optics are studied. The results are compared with the Fourier approach to spectral properties of light. It is shown that, dependent on the experimental scheme used, new quantum effects appear, which may prevent the observation of the Fourier structure of the light as predicted from classical optics. Quantitatively this is demonstrated for the example of spectral squeezing in resonance fluorescence, where significant discrepancies between the measured and the full Fourier spectrum are found.

We study the propagation of a bichromatic field in three-level and four-level media. In the case of a three-level medium, we consider the Λ configuration and demonstrate that if the upper level is not empty there is a critical value for the low-frequency coherence such that below this threshold and for intense fields, coherent bleaching occurs. This implies a sharp reduction of the field absorption and the fluorescence emission whereas above this threshold a parametric instability takes place. It corresponds to an amplification of the field that does not need a population inversion between the optical transitions. Finally we prove that the field alone cannot create a low-frequency coherence exceeding this threshold. Therefore we analyze the double-Λ configuration involving a four-level medium in which the upper and lower pairs of atomic levels have a low-frequency separation while optical transitions take place between the two pairs of states. An intense bichromatic field that is resonant with one upper state and the lower levels and a weak bichromatic field resonant with the other upper state and the same two lower states are sent into the medium. We analyze the limit in which the low-frequency coherence created between the lower pair of states has a relaxation time which is large. Then there will be population trapping in the lower states leading to coherent bleaching if there is no inversion between the upper levels but there will be amplification if there is inversion between the upper levels. In this way amplification at the optical transitions without population inversion between these states is realized.

Thin layered gain media in a ring cavity can lead to detection devices free of spontaneous-emission noise. A theoretical analysis and a physical explanation for the destructive interference of the spontaneous emission in one of the laser outputs are presented.

We present a theoretical study of doubly resonant three-photon ionization with radiation of sufficiently broad bandwidth to overlap all hyperfine levels of the resonant intermediate states. We demonstrate that isotopic selectivity in ionization is apt to occur under a variety of circumstances, although the degree may vary from negligible to quite significant, depending on the relative values of atomic and radiation parameters. Our theory provides a satisfactory quantitative interpretation of recent experimental data in Sn.

A light particle is assumed to move in the field of two heavy particles that separate with constant velocity. The resulting field of the two-heavy fragments is approximated by two moving, one-dimensional zero-range potentials. The propagator for this problem is derived in closed form for arbitrary potential strengths. The resulting integral representation is suitable for numerical evaluation.

We study the interaction of co- and contrapropagating modes in the presence of an intensity-dependent refractive index, and find that, under suitable conditions, these processes can be described by the nonlinear Schrödinger equation.

A monolithic doubly resonant optical parametric oscillator produced signal and idler modes at widely separated wavelengths whose amplitude fluctuations were correlated (53.6±1.0)% below the vacuum-noise level. The system was used to detect modulated signals well below the shot-noise limit.

The Wigner phase-space representation of quantum mechanics is used to understand simply the squeezing of quantum states by any pulsating harmonic potential well that acts as a classical amplifier. The typical case is a harmonic potential whose width alternates between two different values at each quarter of a period.

A system of coupled nonlinear Schrödinger equations (NLS) governs the interaction of propagating pulses in two-mode nonlinear optical fibers and directional couplers. Using NLS solitons as trial functions in an averaged Lagrangian formulation, ordinary-differential-equation (ODE) approximations for the pulse dynamics are derived. These ODE’s give a criterion for two pulses to attract one another and form a bound state; they also describe the dynamics of the complicated oscillations these pulses undergo in this bound state. In addition, the ODE dynamics show that collisions between these pulses are generally inelastic, in that there is an exchange between translational energy and internal energy (due to pulse-width oscillations). The results of the ODE theory are verified by comparison with numerical solutions of the governing partial differential equations.

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_0$ ${}_{}{}^3{}_{}{}^{}$S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_0$=25–32, we use a quasistatic analysis that employs integration of the time-dependent Schrödinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_0$ ${}_{}{}^3{}_{}{}^{}$S→${\mathit{n}}_0$ ${}_{}{}^3{}_{}{}^{}$L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

Transient photoelectron-counting statistics of a degenerate parametric oscillator (DPO) operating below threshold are studied. A generating-function technique has been used and analytical expressions for photon-counting distribution, factorial moments, and waiting-time distribution have been derived. These results are compared with the steady-state results for the DPO and thermal light.

Using analytic estimates we compare the relative merits of resonant photoexcitation pumping with other excitation methods of x-ray lasers, specifically electron-collision and -recombination pumping. It is shown that the potential of line pumping to achieve high gain in the x-ray region (including the range 2.3<λ<4.4 nm) is higher than that of the other methods using high-power lasers or Z-pinch plasmas as pump sources. In the second part of the paper, we investigate the conditions required to obtain an inversion if the pumping ion and the lasing ion are of the same kind. The analysis is performed for laser transitions of the type Δn≠0 as well as for Δn=0.

The origin of certain anomalies of the Schwinger variational phase shifts in momentum space is investigated. It is demonstrated that these anomalies are related to the appearance of continuum bound states in the approximate calculation.

For the bare Coulomb potential energy -${\mathit{Ze}}^2$/r, it is shown that the total electron momentum density Π${\mathrm{¯}}_0$(p) for an arbitrary number of closed shells is a monotonically decreasing function of p. Since it is known that Π(p) is nonmonotonic for all atomic ground states with completely closed shells except helium, the implication of this result is that the observed nonmonotonicity is due to terms of higher order than ${\mathrm{\Pi }}_0$(p) in ${\mathit{Z}}^{\mathrm{-}1}$ perturbation theory. Numerical calculations are presented and analyzed for the ten-electron isoelectronic series.

Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.

We present a density-matrix method, based on information theory, which makes it possible to find nonzero-temperature coherent and squeezed states for the harmonic oscillator with time-dependent frequency. We establish a connection between the appearance of squeezed states and the relevant operators included in the density matrix, compare our results with previous ones that were obtained using wave functions, and analyze the particular case of a sudden jump in the oscillator’s frequency.

For a quantum-mechanical model of dispersive optical bistability we derive in the classical limit, i.e., for large photon numbers, a two-variable Fokker-Planck equation. For low cavity damping this Fokker-Planck equation can be approximated by a one-variable Fokker-Planck equation which is solved numerically. If, in addition, the number of thermal photons is small compared with the number of photons inside the cavity, an analytical result for the transition rate is obtained.

A nonlinear generalization of quantum mechanics for internal (spin) degrees of freedom has recently been developed by Weinberg [Phys. Rev. Lett. 62, 485 (1989); Ann. Phys. (N.Y.) 194, 336 (1989)]. We extend this theory to systems of composite, or multivalued, spin, such as atoms and molecules. Results for the generalized Hamiltonian function, energy eigenvalues, and state-vector time dependence are found to be similar for single- and multivalued spin systems, with the important difference that states of spin 0 or 1/2 can exhibit observable nonlinear behavior in a composite spin system. Examples of the application of the composite spin analysis are given for the ground-state hyperfine structure of the hydrogen and deuterium atoms.