We derive a generalized master equation, which describes the quantized cooling of identical atoms in the laser fields. The effects of the dipole-dipole interaction between the atoms are included explicitly in the master equation. We then calculate the steady-state density matrix of two atoms cooled by a one-dimensional optical molasses. It is shown that when the mean separation between these atoms reduces below the optical wavelength λ/2π, cooling will be significantly limited due to the enhanced atom-atom interaction. Based on the quantum regression theorem, we also calculate the resonance fluorescence spectrum emitted by these two atoms, which exhibits features different from those of isolated atoms.

It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom’s internal state, a band structure, and a time-dependent dissipative process.

We present results from numerical simulations of the interaction of an intense ultrashort (100 fs) laser pulse with a neutral helium (He) atom and its ion ${\mathrm{He}}^{+}$. The simulations are done for a number of laser intensities in the range of ${10}^{14}$–${10}^{16}$ W/${\mathrm{cm}}^2$ at the KrF-laser wavelength. These intensities range from close to well above the saturation intensity of the neutral atoms and it is therefore necessary to study the contribution to harmonics from neutral atoms as well as ions. Our approach is based on a two-step procedure where we first calculated the neutral-atom response in the single active electron approximation. We observe that harmonics are still produced by the neutral atoms above the saturation intensity, but the simple classical law for the cutoff is not obeyed. In the second step we calculated the response of ions. We show that the contribution from ions extends through and beyond the region where the contribution from the neutral atoms disappears. We find good agreement between our numerical results and the experimental ones. We also present some ideas about the importance of the laser defocusing and phase matching at such high intensities.

Within a fully analytically solvable model, we discuss the mechanisms of strong-field suppression of ionization from the initial s state via a family of p Rydberg states to s and d continua. Both Raman coupling via a continuum between different p Rydberg states and Raman migration of population via d continuum from p to higher angular momentum f Rydberg states are considered. The results are compared with those obtained neglecting Raman couplings via the continuum between Rydberg states of the same and different angular momenta. A profound effect of Raman couplings on ionization is demonstrated.

We show that the parametric superfluorescence generated by a 200-fs pulse at 0.6 μm in a β-barium borate crystal occurs in directions, and at wavelengths, that minimize the group-velocity mismatch between pump and generated pulses. Favorable conditions for generation of tunable femtosecond pulses are found in noncollinear phase matching, a geometry of interaction which is worth exploiting in parametric devices.

We present a very simple theoretical framework for extracting spectroscopic data on an atom via stochastic probing with a fluctuating laser source. By exploiting the fact that the linear susceptibility contains all the atomic structure information in it, we show that the power spectrum of the fluctuations in the intensity radiated from an atomic sample provides the relevant, atomic-level information. The analysis we present is very general and can be applied to a wide variety of atomic and molecular systems.

In this paper, we calculate the sum-frequency generation (SFG) signal for molecules adsorbed on a surface. The expression is established as a function of the molecular microscopic constants and for different polarization combinations of the input beams. Next, this result is applied to reproduce simultaneously experimental SFG spectra of pentadecanoic acid molecules on a water surface obtained for different polarizations of the input beams. From the fit, we have been able to determine unambiguously the microscopic parameters of the adsorbate.

We investigate theoretically the quantum-noise properties of optical phase conjugation via four-wave mixing of nonclassical signal fields. We show that while the field generated at a phase-conjugate mirror (PCM) can be in a nonclassical state, the generated field is not necessarily useful within the context of phase conjugation. For the case in which a quadrature-squeezed signal field is incident at a PCM, we determine that the signal-to-noise ratio of one of the quadrature components of the generated field can approach the signal-to-noise ratio of the corresponding quadrature component of the signal field as the amount of squeezing of the vacuum field injected at the rear of the PCM is increased. For the case in which the signal field is amplitude squeezed, we determine that the signal-to-noise ratio of the conjugate field is always much smaller than that of the signal field. These results demonstrate that the phase-conjugation process can preserve the desirable quantum-noise properties of quadrature-squeezed fields but not those of amplitude-squeezed fields.

Several 2${\mathit{p}}^5$(3s3p ${}_{}{}^3{}_{}{}^{}$P${)}^2$P, ${}_{}{}^2{}_{}{}^{}$D core-excited levels of Al iii appear to have large radiative branching ratios to 2${\mathit{p}}^6$ 3${\mathit{p}}^2$P. We propose to produce a population inversion between these levels and amplified spontaneous emission at λ≊170 Å by photoionizing the Al ii 2${\mathit{p}}^6$ 3s3p ${}_{}{}^3{}_{}{}^{}$P metastable levels with the N-shell quasicontinuum band of Sb around 125 Å. By pumping with the Sb band, the secondary electron heating of the lasing medium is minimized, which enables a fast collisional depletion of the 2${\mathit{p}}^6$ 3p ${}_{}{}^2{}_{}{}^{}$P levels and a longer-lived inversion. A model of the population kinetics in this scheme indicates that by irradiating a dense and cold Al ii plasma (${\mathit{N}}_{\mathit{e}}$≊3×${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$, ${\mathit{T}}_{\mathit{e}}$≊1.2 eV) with a Sb quasicontinuum pulse of 100–150 ps FWHM and 5×${10}^9$–${10}^{10}$ W/${\mathrm{cm}}^2$ peak intensity, gain coefficients between 1 and 3 ${\mathrm{cm}}^{\mathrm{-}1}$ for a duration of 100–150 ps may be obtained. The target parameters are typical for stabilized arc plasmas. The possible extrapolation of this inversion scheme to shorter wavelengths and the use of neutral targets are briefly discussed.

The transient properties of a single-mode dye laser with correlations between additive and multiplicative white-noise terms are investigated theoretically. The mean, variance, and skewness of first-passage-time distributions for the white-noise-loss model and the white-noise-gain model are obtained. We find that (1) the mean first-passage time for the two models is not affected by the strength λ of the correlation between additive and multiplicative noise terms; (2) as λ is increased, the magnitudes of the variance and skewness of the two models are increased; and (3) under the same λ and the same pump level, the variance and skewness of the white-noise-gain model are larger than those of the white-noise-loss model.

Interactions of solitons generated by a pair of optical pulses in a fiber having bandpass filters, nonlinear amplifiers, sliding filters, and with the self-induced Raman effect are studied numerically by using the perturbed nonlinear Schrödinger equation, and analytically by the perturbed inverse-scattering transform developed by Kaup and Newell [Proc. R. Soc. London Ser. A 361, 413 (1978)] and Karpman and Maslov [Zh. Eksp. Teor. Fiz. 73, 537 (1977)]. The results are also compared with these obtained by the quasiparticle approach developed by Karpman and Solove’v [Physica D 3, 487 (1981)].

We consider four-photon resonant six-wave mixing and show that the efficiency of harmonic generation is limited due to destructive interference between different optical harmonics. Following the idea of ‘‘induced transparency’’ of Harris et al. [Phys. Rev. Lett. 64, 1107 (1990)], it is shown that in the presence of an auxiliary electromagnetic coupling between the four-photon excited level and a third level, the interference between various excitation channels can be made constructive. Depending upon the strength of the auxiliary wave, absorption and dispersion-free propagation of the generated wave lead to high conversion efficiency.

Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.

We present the details of an experimental observation of excited-state enhancement of the degenerate-four-wave-mixing (DFWM) susceptibility ${\gamma }_{\mathit{n}}^{\mathit{S}}$(-ω;ω,ω,-ω) of a conjugated linear chain, diphenylexatriene (DPH), when the first π-electron excited state is populated for nanosecond time scales and then probed nonresonantly through picosecond DFWM. An increase as large as a factor of 100 in the completely nonresonant 1064-nm DFWM signal from the highest DPH concentrations (8 mM) is observed when the 355-nm pump beam saturates the ${\mathit{S}}_2$ absorption as compared to when the pump beam is turned off. A large ${\gamma }_2^{\mathit{S}}$(-ω;ω,ω,-ω) of (12 000±1700)×${10}^{\mathrm{-}36}$ esu is found, compared to the ground state ${\gamma }_0^{\mathit{S}}$(-ω;ω,ω,-ω) which is <50×${10}^{\mathrm{-}36}$ esu. Importantly, separate transient absorption experiments show that there is no excited-state absorption at 1064 nm with excitation at 355 nm. Therefore, upon population of the excited state, the electronic third-order optical susceptibility of DPH is increased by orders of magnitude, without introducing any optical loss at the probe wavelength.

The correlation of the quantum-mechanical ground-state fluctuations of the electric-field strength in a dispersive and lossy linear dielectric are studied in terms of the symmetrized autocorrelation function, with special emphasis on the optical frequency domain. Starting from the canonical quantization scheme developed by Huttner and Barnett [Phys. Rev. A 46, 4306 (1992)], the analysis is based on a quantization of the phenomenological Maxwell theory, the effect of the medium being described by a frequency-dependent complex permittivity. In this way, the spectrally resolved ground-state autocorrelation function of the electric-field strength can be expressed in terms of the real and imaginary parts of the refractive index. Both analytical and numerical results are presented and the effects of dispersion and absorption including their dependence on the frequency interval chosen are discussed. A comparison with the vacuum fluctuations in free space is given.

We investigate a single-atom nondegenerate cascade laser model, based on a coherently pumped three-level atom coupled to two independently damped cavity modes. We show that while many features predicted within a recently proposed N-atom superradiant laser model [F. Haake et al., Phys. Rev. Lett. 71, 995 (1993)] can readily be obtained in the single-atom case, some of the quantum noise properties are significantly different. The influence of spontaneous decay and nonadiabatic effects due to the finite spectral width of the lower cavity mode are discussed. Finally, we show that the present model has a large potential for the stationary preparation of various nonclassical states of the atom-field system.

We show that the micromaser, widely studied for its distinct quantum features, has one more remarkable property: unlike conventional lasers and masers it works without population inversion. We study the time-averaged inversion of a single atom passing through a cavity with a field in its stationary state. The result is shown to hold also for the regularly pumped micromaser and for the two-photon micromaser. It even remains partially valid for a semiclassical description of the field.

In this paper the equations for quantum optical pulse propagation in nonlinear and dispersive single-mode fibers are presented in terms of two phase-space formulations based on the positive-P and the Wigner distributions. Included are the effects due to the coupling of the electromagnetic modes to the vibrational states of a vitreous silica fiber. By making use of the well-known equivalence of Fokker-Planck and Ito stochastic equations, we demonstrate two alternative methods for formulating the equations of motion as coupled stochastic c-number equations for the propagating field. The first method involves a representation of the density operator in terms of the positive P distribution function. This leads to exact stochastic equations of motion. The second method makes use of the Wigner distribution function. This method, which requires truncation of third-order derivative terms in the corresponding Fokker-Planck equation, is necessarily approximate. However, we discuss certain advantages to the Wigner approach that have made it the preferable method for exploratory work.

We show how the quantum trajectory method for describing the dissipative evolution of conditioned states can be implemented in a numerically efficient higher-order unraveling that goes beyond the Euler method usually employed in such simulations. We demonstrate its applicability through an analysis of spontaneous emission and find that improvements by two orders of magnitude are possible for the specific example addressed.

A simple formalism is introduced for describing the quantum phase of a single-mode field (or, equivalently, a harmonic oscillator) using a particular infinite-dimensional Hilbert space ${\mathit{H}}_{\mathit{s}\mathit{y}\mathit{m}}$. This space is spanned by vectors which represent states of the single field mode containing non-negative numbers of photons. It has a symmetry in the sense that it contains vectors in the neighborhood of both the vacuum state and the infinite photon number state. A striking property of ${\mathit{H}}_{\mathit{s}\mathit{y}\mathit{m}}$ is that it supports Hermitian and unitary phase operators. Indeed the Pegg-Barnett unitary phase operators are shown to converge strongly on the Hilbert space ${\mathit{H}}_{\mathit{s}\mathit{y}\mathit{m}}$ and so the correponding limit points are ordinary operators on ${\mathit{H}}_{\mathit{s}\mathit{y}\mathit{m}}$. This can be compared with the situation for the infinite-dimensional Hilbert space H conventionally used in quantum optics on which the Pegg-Barnett unitary phase operators converge weakly, in general.