We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.

Phase properties of a damped anharmonic oscillator are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the phase distribution function, the expectation value and variance of the phase operator, and the expectation value and variance of the cosine of the phase operator are obtained assuming the zero-temperature reservoir and a coherent initial state of the system. It is shown that quantum periodicity in the evolution of phase quantities is destroyed by damping. The effect of damping on the formation of discrete superpositions of coherent states is discussed. A comparison is made between different phase approaches.

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times τ larger than the deterministic relaxation time ${\mathit{t}}_{\mathit{d}}$, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Angular distributions for energy-resolved photoemitted electrons from resonantly enhanced multiphoton ionization (REMPI) via the two-photon allowed 6p[j=1/2${]}_{\mathit{J}=0\mathrm{}}$, 6p[3/2${]}_2$, 6p’[1/2${]}_0$, 6p’[3/2${]}_2$, 7p[1/2${]}_0$, 7p[3/2${]}_2$, and 7p[5/2${]}_2$ states and the three-photon allowed 7s[3/2${]}_1$, 8s[3/2${]}_1$, 9s[3/2${]}_1$, 5d[3/2${]}_1$, 5d’[5/2${]}_3$, and 5d’[3/2${]}_1$ states of xenon and the three-photon allowed 5s[3/2${]}_1$, 6s[3/2${]}_1$, 4d[3/2${]}_1$, 4d[5/2${]}_3$, and 4d[7/2${]}_3$ states of krypton are reported. In one case, two-photon resonant, three photon ionization [(2+1) REMPI] of the 6p’[1/2${]}_0$ state of xenon, a dramatic laser-power dependence (power ∼1.5×${10}^{10}$ to ∼3×${10}^{10}$ W/${\mathrm{cm}}^2$), was observed. The measured angular distributions for electrons leaving either ion core ${(}^2$${\mathit{P}}_{1/2}$ or ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$) are compared with those calculated from multichannel quantum-defect theory.

Reasonable agreement is obtained in reproducing the general features of the angular distributions for the p and d states in the rare gases. However, discrepancies are observed for some of the s states. Comparison of the measured and calculated branching ratios for leaving either ion core also shows good agreement for the p and d states, but shows that there are inadequacies in the theory for describing the s states. We also report the photoelectron energy and angular distributions for the (4+1) REMPI process via the 6p[1/2${]}_0$ and 6p[3/2${]}_2$ states of xenon. Photoelectrons due to above-threshold ionization, (4+2), resonantly enhanced via the four-photon allowed 6p[1/2${]}_0$ state, are also observed.

We consider the quantum correlations between fields generated through cross-phase-modulational instability in an optical fiber. Two examples of this instability are addressed, one relating to the linear-polarization eigenstates in a high-birefringence fiber, and the other to two-color propagation in a fiber. The degrees of second-order coherence of the quantum noise sidebands generated in this ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ process are calculated, and the violation of a classical Cauchy-Schwarz inequality and intensity-difference squeezing is reported for light transmitted by a passive filter. Around 50% intensity-difference squeezing is possible in the case of the two-color instability. This illustrates the quantum-statistical nature of the sideband correlations and how passive processing may in some circumstances help accentuate quantum correlations.

We study the temporal profile of the time-resolved four-wave-mixing signal in media with strong polarization interactions, assuming a stochastic modulation of the optical-transition frequency. The model is exactly solvable and interpolates smoothly between Lorentzian (fast modulation) and Gaussian (slow modulation) broadening. We show that recently predicted and observed four-wave-mixing signals persist even in the latter limit, albeit with a different temporal profile.

Nonlinear pulse propagation in simple as well as composite glass optical fibers is investigated in detail using the invariant of motion method. It is shown that this approach enables one to have a clear picture of the complicated interplay between dispersion and nonlinearity and its effects on the pulse width variation during propagation. This method is algebraically simple, and it allows one to obtain the needed differential equation for the pulse width faster. It is also shown that the model equation for nonlinear pulse propagation in composite glass fibers is capable of supporting soliton propagation.

A study of multiatom effects, i.e., dipole-dipole interactions and phase-interrupting collisions between atoms in the Jaynes-Cummings model, is presented here. For this purpose we consider two identical two-level atoms interacting with a single-mode field in a lossless cavity and study the effect of the dipole-dipole interaction between these two atoms on the collapse-and-revival phenomenon of Rabi oscillations by calculating the analytical expression of the excitation probability in the coherent field. We also consider another situation in which a single atom interacting with a single-mode field in a damped cavity undergoes phase-interrupting collisions. The effect of phase-interrupting collisions along with the usual cavity damping on the collapse-and-revival phenomenon has been explicitly calculated using the dressed-atom approach under the secular approximation.

This is the first of two papers studying multiphoton ionization (MPI) in superintense, high-frequency laser fields. They are based on a general iteration scheme in increasing powers of the inverse frequency. To lowest order in the frequency, i.e., the high-frequency limit, the atom was shown to be stable against decay by MPI, though distorted. To next order in the iteration, an expression for the MPI amplitude was obtained. In the present paper, we present general developments from this expression, valid for arbitrary polarization, binding potential, intensity, and initial state. First we analyze the symmetry of the angular distributions of photoelectrons determined by this expression for the MPI amplitude. This expression can explain the asymmetries in the angular distributions of photoelectrons occurring in the case of elliptic polarization that were recently reported in experiments. In the radiation regime where our theory applies these asymmetries are, however, weak. In certain instances our theory yields asymmetries in cases where lowest-order perturbation theory (LOPT) fails to predict them. We prove that at low intensities our expression for the MPI amplitude yields results in agreement with LOPT evaluated at high frequencies. An important part of this paper consists, however, of the derivation of an alternative form for the MPI amplitude of atomic hydrogen, which is substantially simpler, though somewhat less accurate. We study the consequences of this simplified expression for the case of linearly polarized fields in the following paper [Phys. Rev. A 44, xxxx (1991)].

This is the second of two papers studying the multiphoton ionization (MPI) in superintense, high-frequency laser fields. They are based on a general iteration scheme in increasing powers of the inverse frequency. To lowest order in the frequency, i.e., the high-frequency limit, the atom is stable against decay by MPI, though distorted. To next order in the iteration, an expression for the MPI amplitude was obtained. In our first paper [preceding paper, Phys. Rev. A 44, 2160 (1991)], an alternative expression for the MPI amplitude was obtained for atomic hydrogen, which is substantially simpler, though somewhat less accurate. In the present paper, we study its consequences for the case of atomic hydrogen in superintense, linearly polarized fields with the emphasis on the ground state. Special attention is paid to the case in which the de Broglie wavelength of the photoelectrons is small with respect to the amplitude of oscillation of the (distorted) electronic cloud. Most importantly, the total decay rate decreases with increasing intensity at given (high) frequency (‘‘high-intensity stabilization’’). This condition defines a radiation regime which yields features in sharp contrast to those obtained in weak fields. The angular distributions of photoelectrons are found to be characterized by rapid oscillations with the polar angle, arising from a peculiar way in which outgoing electron waves interfere.

At the same time, the overall behavior of the photoelectrons is to be ejected in directions nearly perpendicular to the polarization axis. We have solved the limit of extremely high intensities at fixed, but otherwise arbitrarily chosen, frequency analytically. We find that in ‘‘ultrastrong fields’’ the branching ratios for decay by absorption of the various number of photons possible are only weakly dependent on the values of the intensity and frequency of the laser field, yet excess-photon ionization constitutes a sizable part of the decay modes of the atom (typically 30%). At very high intensities, the hydrogen atom tends to stabilize at fixed, but otherwise arbitrarily chosen frequency. The (a priori unexpected) relative stability of the hydrogen atom in ultrastrong fields is explained as a result of ‘‘radiative distortion’’ of the electron cloud and ‘‘destructive interference’’ of outgoing electron waves. Although the lifetime of the atom turns out to be extremely short for values of the intensity around the atomic unit, for low enough frequencies and very high intensities, it can be remarkably long. Finally, we discuss the problem of how the atom subject to these extreme radiation conditions could be observed experimentally.

The quantum-mechanical superposition of two coherent states of identical mean photon number but different phases yields a state that can exhibit sub-Poissonian and oscillatory photon statistics, as well as squeezing.

In higher orders of the Rayleigh-Schrödinger-type perturbation theory for nonlinear time-independent Hamiltonians care should be taken about the normalization in the wave-function-dependent perturbation operator. Low-order results, which have been presented earlier [P. R. Surján and J. Ángyán, Phys. Rev. A 28, 45 (1983)], remain valid; nevertheless, small corrections appear for higher orders (n≥3). Explicit expressions are given for the energy correction in the generalized reaction-field theory in terms of nonlocal polarizabilities and reaction-field response functions.

I report the results of a calculation of the spin asymmetry in the electron-impact ionization of hydrogen atoms for incident energies between 14 and 20 eV. The work involves a variational close-coupling calculation with a pseudostate basis, supplemented by an optical potential procedure for higher partial waves.

Using an exact evaluation of the relativistic second-order Oppenheimer-Brinkman-Kramers approximation, total and differential cross sections for electron capture in ${\mathrm{U}}^{92+}$+${\mathrm{U}}^{91+}$ collisions are calculated for projectile energies between 0.5 and 100 GeV/u. It is shown that (a) at 100 GeV/u the asymptotic cross-section behavior is not yet reached, (b) spin-flip transitions and negative-energy intermediate states become important at high energies, and (c) the Thomas peak in the differential cross section is relativistically suppressed.

Our earlier measurements [Shatindra, Allawadhi, and Sood, Phys. Rev. A 31, 2918 (1985)] of Ll, Lα, Lβ, and Lγ x-ray production cross sections in elements with 73≤Z≤92 by 60-keV photons have been extended to 11 rare-earth elements in the range 57≤Z≤68 in order to examine enhancement in L-subshell x-ray production due to transfer of vacancies from the K to the L shell. The measured values of absolute cross sections have been interpreted in terms of K-shell photoelectric cross sections, probabilities of K→L radiative and nonradiative transitions, L-subshell photoelectric cross sections, fluorescence yields, Coster-Kronig transition probabilities, and radiative decay rates. Fairly good agreement between the experimental and calculated values indicates indirectly the correctness of the theoretical calculations of the atomic parameters in terms of which the experimental results have been interpreted.

This paper analyzes the influence of a Wollaston beam splitter on photodetection statistics when a coherent light beam in an elliptically polarized state penetrates through the Wollaston prism. Also included as an application is a study of a heterodyne experiment on a squeezed signal with a much stronger local oscillation in a coherent state after splitting by the Wollaston prism. The calculations indicate that the quantum noise from the subtraction may be reduced to below the standard quantum limit.

We derive a generalized master equation on the basis of system-reservoir theory where the system is a two-level atom interacting with a superintense classical electromagnetic field within the Born and Markov approximations. We show that the usual assumption of independence of the atom-field coupling and the atomic decay processes breaks down and the relaxation becomes field dependent in the superintense regime. This results in significant deviation from the exponential decay of the Bloch vector components.

We present the solution of the time-dependent Schrödinger equation describing an electron bound in a zero-range potential in three-dimensional space, subject to linearly polarized light. This solution is used to study the survival probability of the initial bound state and the above-threshold photodetachment spectra, as well as the total ionizaton rate of the model negative ion. In contrast to the circularly polarized field case, the rate exhibits variations caused by the closing ionization channels in agreement with the recent experiment.

Higher-order squeezing in nondegenerate four-wave mixing is evaluated by using the steady-state solution of the Fokker-Planck equation in the Q representation. It is shown that under suitable conditions the amount of squeezing increases with the order of squeezing.

A recent theoretical paper [Guo, Wrinn, and Whitehead, Phys. Rev. A 40, 6685 (1989)] predicted the existence of ground-state bound negative ions of all the noble gases. In addition, experimental observations [Haberland, Kolar, and Reiners, Phys. Rev. Lett. 63, 1219 (1989)] suggest the existence of long-lived ${\mathrm{Xe}}^{\mathrm{-}}$. We have examined the cases of ${\mathrm{He}}^{\mathrm{-}}$ and ${\mathrm{Xe}}^{\mathrm{-}}$. For ${\mathrm{He}}^{\mathrm{-}}$, we employed Levinson’s theorem in conjunction with published and reliable theoretical e-He elastic-scattering phase-shift results. For ${\mathrm{Xe}}^{\mathrm{-}}$, we employed electron-correlation theory in conjunction with multiconfigurational Hartree-Fock and variational bound-state calculations of total energies. We conclude that these ions do not exist in a ground configuration.