We calculate the spectrum of the micromaser for a wide range of pump parameters and propose a multiple microwave field method similar to the Ramsey fringe technique to measure this spectrum. Thus it becomes possible to investigate the phase diffusion in a fundamental system such as the micromaser.

We describe in detail some properties of a one-dimensional model atom that has been used for the study of multiphoton processes. We discuss static properties of the atom such as its energy eigenvalues, dipole moment matrix elements, and dipole sum rule, and also some aspects of its time-dependent response to a weak laser field, including second-order level shifts, and exact polarizability.

We consider the generation of four-wave-mixing signals by an ensemble of two-level atoms interacting with broadband, correlated, pump and probe fields in the forward geometry. We show how the calculation of the four-wave-mixing signal reduces to the solution of six coupled Langevin equations that are numerically integrated using Monte Carlo methods. We account for the pump-induced saturation effects although the probe is weak. The finite correlation time of the pump and probe fields is also included. For weak and δ-correlated pump fields, we reproduce the results of Morita and Yajima [Phys. Rev. A 30, 2525 (1984)]. We find that even for short correlation times of the fields, the four-wave-mixing signal, as a function of the delay between the pump and the probe fields, starts reviving with increase in the pump intensity. This revival as a function of the pump-probe delay time becomes more pronounced with further increase in the pump intensity.

The phenomenon of amplitude-squared squeezing is investigated for the one- and two-photon Jaynes-Cummings model. The relative phase between the atomic coherent state and the coherent field state is found to affect this phenomenon with larger amounts of squeezing that can be found by changing the angles (θ) for fixed relative phase.

We use the eigenstates of the reduced density operators to give an explicit form of the entangled atom-field state in the Jaynes-Cummings model. We relate the expansion coefficients to physical quantities and discuss the effect of atomic coherence on this entangled state.

We discuss the consequences of the interaction of a broadband squeezed vacuum on the photon statistics of a coherently driven two-level atom. The statistics is described in terms of the Mandel function Q(T) and the probability P(n,T) of counting n photons in a time interval T. The phase-dependent decay in the squeezed vacuum is highlighted with these functions.

Without making the nondepleted pump approximation, we solve the problem of four-wave mixing (FWM) in a nondissipative ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ medium. Instead of describing the dynamics of FWM in terms of coupled wave amplitudes, we base our solution on canonical equations that describe the propagation of the field’s intensities. This structure clearly identifies the conservative exchange of energy in the FWM process. Consequently, analysis of the FWM process is reduced to a single propagation equation that describes the energy exchange between the pump and amplified waves. This equation yields an elliptic integral solution. The conversion efficiency reduces to the simple analysis of a fourth-order polynomial, which we analyze to determine the conditions for optimization. The destructive influence of the optical Kerr effect on the phase-matching condition is shown to be eliminated by proper choice of nonzero initial wave-vector mismatch, dependent on the input intensity. Furthermore, we show that the conversion efficiency for pulses is limited by the splitting of the pulses into a set of subpulses.

In this paper we study the dynamics of a three-level atom interacting with a two-mode squeezed vacuum, a highly correlated state in which each mode contains the same number of quanta yet exhibits a thermal photon distribution. Under exact resonance, the Rabi oscillations exhibit an irregular behavior reminiscent of those in the thermal-state Jaynes-Cummings model. If the individual field modes are sufficiently detuned from the intermediate atomic level, the Rabi oscillations become quasiperiodic. The three-level system in this case reduces to an effective two-level system in which two-photon processes dominate. The times of revivals of the Rabi oscillations in this limit depend only on the atom-field coupling constants and the detuning. For comparison, we present a parallel study of the case in which the initial field is prepared in an uncorrelated two-mode state, such as a two-mode thermal state or a two-mode coherent state. Under the full resonance condition, the former leads to an irregular evolution of the Rabi oscillations, while the latter leads to the usual collapse and revival phenomena. If the individual modes are sufficiently detuned from the intermediate atomic level, we observe the same quasiperiodicity of the Rabi oscillations as in the case of the two-mode squeezed vacuum but with a doubling of revival times (for equal atom-field coupling constants). Whereas the two-mode squeezed vacuum and the two-mode thermal-state transition dynamics lead to correlation between the field modes, the two-mode coherent state leads to anticorrelation (when sufficiently detuned from the intermediate atomic level).

Exact analytic solutions of the stimulated-Raman-scattering equations are obtained using group-theoretical methods. Special attention is devoted to a self-similar solution in terms of the fifth Painlevé transcendent ${\mathit{P}}_{\mathrm{V}}$. Its asymptotic behavior is established and shown to agree with experimental data and with earlier numerical calculations.

Amplitude-squared squeezing is investigated for the two-photon Jaynes-Cummings model with the field initially in a squeezed vacuum or a more general squeezed state. For small values of the coherence parameter and large values of the squeeze parameter, the amplitude-squared variances show threefold oscillatory behavior on the long time scale. It is found that a ground-state atom (as against an excited one) leads to considerable enhancement of the input amplitude-squared squeezing. The behavior of photon number squared and its relationship to the amplitude-squared squeezing is commented upon.

An analysis of the amplitude-squared squeezing is presented for the lossless anharmonic-oscillator, Jaynes-Cummings, and intensity-dependent coupling Jaynes-Cummings models using coherent and squeezed inputs. Periodic revivals of the amplitude-squared squeezing are shown to exist in the anharmonic-oscillator and intensity-dependent coupling Jaynes-Cummings models for any value of the initial average photon number n¯. The Jaynes-Cummings model, on the other hand, displays this characteristic for small n¯ only. The effect of the squeezing angle on the amplitude-squared squeezing is studied. A comparison with the normal-order squeezing is presented.

The steady-state intensity correlation functions C(t) of the single-mode laser are analyzed with the generalized-moment-expansion method proposed by Nadler and Schulten [Z. Phys. B 59, 53 (1985); J. Chem. Phys. 82, 151 (1985)]. This method approximates C(t) by a superposition of N exponentials that exactly reproduces n derivatives of C(t) at t=0 and m relaxation moments (n+m+1=2N). In this way, the short- and long-time regimes of C(t) are well described even near threshold. With the use of relaxation moments we develop a method to obtain the eigenvalues of the Fokker-Planck operator. This method is applied to the single-mode laser. We show that the knowledge of only two relaxation moments is enough to obtain good results for the two first eigenvalues. The method gives excellent results when the eigenvalues are well separated (below threshold).

We study the influence of the atomic spontaneous-emission decay on the collapse-revival phenomena in the optical region. We demonstrate that revivals of the atomic inversion are much more sensitive to cavity-field damping than to spontaneous emission. This suggests that the additional dissipation caused by spontaneous emission would not offer an insurmountable obstacle to the experimental observation of optical revivals in high-Q cavities.

In a series of experiments performed by Mandel and co-workers, nonclassical effects have been demonstrated in the interference of two photons generated in a process of parametric down-conversion. The nonclassical effects in the two-photon interference effects can be discussed in the framework of two different descriptions. In the first description, a stochastic theory of electromagnetic field fluctuations can be used in order to calculate the interference pattern. In the second description, a theory of hidden-variable fluctuations can be applied in order to calculate correlations of the interference pattern. A stochastic theory leads to statistical inequalities for the light intensities, while a local hidden-variable theory leads to Bell’s inequalities. Using the Schwinger-boson representation of the angular momentum, we show that the two-photon interference effects can be described in terms of spin-correlated states. In particular, we show that the action of a beam splitter on the photons in a parametric down-conversion is equivalent to the production of an entangled state that is very similar to the well-known Einstein, Podolsky, and Rosen spin-singlet state. We show that the stochastic theory of two-photon fluctuations is not equivalent to a hidden-variable theory of photon correlations. We establish a range for which the stochastic theory fails but the hidden-variable theory is still possible. We compare our theoretical predictions with the experimental results and conclude that a violation of the stochastic theory has been clearly observed, while the violation of the hidden-variable theory is less pronounced.

Fields generated in a large number of nonlinear-optical processes (including those with losses) have a Wigner distribution that is Gaussian centered around the mean value of the field. We show that the Bell inequality for an optical-correlation experiment with two coupled modes generated in a nonlinear process can be expressed as an inequality relating to the parameters of the underlying Wigner distribution function. We consider examples of parametric down-conversion and a two-mode squeezed laser, which can be used in experiments to demonstrate quantum nonlocality.

The fluorescence of a forbidden transition from the ground state ${(}^5$I, J’’=4) to the 18 249.275-${\mathrm{cm}}^{\mathrm{-}1}$ (J=6) level in Nd i was directly observed by atomic-beam laser spectroscopy. This transition was found to be caused by the second-order hyperfine perturbation from the close-lying 18 249.784-${\mathrm{cm}}^{\mathrm{-}1}$ (J’=5) level. Thus the fluorescence peaks were observed only for odd isotopes of ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$ and ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$, and no peaks for even isotopes. Both the relative frequencies and the relative intensities of all the observed forbidden transitions agree well with the theoretical calculation.

The partial photoionization cross sections and asymmetry parameter of the excited state 2${\mathit{p}}^2$3p ${}_{}{}^2{}_{}{}^{}$S of nitrogen have been calculated using the multiconfiguration Hartree-Fock method for continuum wave functions. The effects of electron correlation on the excited initial state, the ionic core state, and the final continuum state have been taken into account in an ab initio manner through the configuration-interaction procedure. It is found that the correlations do not change the result significantly from that obtained with Hartree-Slater and Hartree-Fock calculations. The present result of the asymmetry parameter is seen to be in excellent agreement with the experimental measurement of Pratt, Dehmer, and Dehmer [Phys. Rev. A 36, 1702 (1987)] performed at a single photon energy.

Certain significant features in the collision strengths for electron-impact excitation of the fine-structure transition ${}_{}{}^2{}_{}{}^{}$P${\mathrm{°}}_{1/2\mathrm{-}}^2$P${\mathrm{°}}_{3/2}$ and the resonance transition ${}_{}{}^2{}_{}{}^{}$P°${\mathrm{-}}^2$D in ${\mathrm{C}}^{+}$ are discussed based on improved calculations.

Two resonances in the photodetachment spectrum of ${\mathrm{H}}^{\mathrm{-}}$, one just below the n=3 threshold and the other just below the n=4 threshold, were observed decaying into ${\mathrm{H}}^0$(n’=2)+e. The n=3 resonance shows a preference for the n’=2 channel when compared with total-detachment measurements. Fano-line-shape fits give central energies of 12.652±0.003 eV for ${\mathrm{H}}^{\mathrm{-}\mathrm{*}\mathrm{*}}$(3) and 13.338±0.004 eV for ${\mathrm{H}}^{\mathrm{-}\mathrm{*}\mathrm{*}}$(4). These values are in good agreement with current theoretical calculations.

We have calculated probabilities, orientation parameters, and alignment angles for 2p excitation and capture in proton-hydrogen collisions at 50- and 100-keV projectile energy. The results, obtained from solving the Schrödinger equation in a multistate atomic-orbital expansion, are compared to those of a similar, recently published investigation. In both studies, similar results for excitation are found, and also for capture at large impact parameters. The origin of different predictions for capture at intermediate impact parameters is discussed.