Phase measurements on a single-mode radiation field of annihilation operator a^ are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator, exp^(iφ)==(a^a${\mathrm{^}}^{\mathrm{°}}$${)}^{\mathrm{-}1/2}$a^; its phase eigenkets generate the probability operator measure (POM) for maximum-likelihood phase estimation. When used with an optimum input state, the SG-POM produces a local phase accuracy δφ∼1/${\mathit{N}}^2$, where N is the average photon number of the state. This performance is far superior to the δφ∼1/ √N and δφ∼1/N behaviors of coherent-state and optimized squeezed-state interferometers, respectively. A commuting-observables description for the SG-POM on an extended, signal×apparatus, state space is derived. It is analogous to the signal-band×image-band formulation for optical heterodyne detection. Because heterodyne detection realizes the a^-POM, this analogy may help realize the SG-POM. Two new classes of nonclassical states are identified through study of the SG operator—the coherent phase states and the squeezed phase states. These are direct analogs of the familiar coherent and squeezed states associated with the annihilation operator. Linear system theory is used to elicit a broader class of states—the rational phase states—which includes the coherent and squeezed phase states as special cases, and affords a filter-theory derivation of the minimum average-energy quantum state with prescribed phase-measurement statistics. Fourier theory is also used to prove a number-phase uncertainty relation without recourse to the usual linearization procedures, and to show that the Pegg-Barnett phase operator has the same measurement statistics as the SG-POM for arbitrary quantum states.

We discuss effects of quantized electromagnetic fields upon the electronic conduction in interferometers of semiconductor microstructures. An optical field in an arbitrary quantum state is assumed to hit the interferometer, and the time evolution of the coupled photon-electron system is evaluated. It is found that the interferometer works as a quantum nondemolition photodetector if the interferometer is designed such that the interaction is switched adiabatically.

We report the results of a theoretical study of line shapes obtained in frequency-domain four-wave mixing in systems inhomogeneously broadened due to random fields in the presence of spectral diffusion. The results are based on a solution of the modified optical Bloch equations solved perturbatively to third order in the applied optical fields, assuming a strong redistribution model for the spectral diffusion. The results show that the redistribution of excitation can be directly observed in the line-shape function and can also lead to the presence of interference effects in the line shape.

We propose a measurement scheme to detect the multiphoton coherences inherent in the macroscopic quantum superpositions that can be generated in a superconducting micromaser cavity. The scheme is a nonlinear version of a single-atom homodyne detector. It is shown that the ionization probability of a single test atom is given in terms of the Wigner characteristic function of the field.

The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.

We investigate the problem of resonant reflection and transmission of an ultrashort light pulse passing through a thin layer consisting of two-level atoms. The local-field correction that leads to an inversion-dependent resonance frequency generates a new mechanism of nonlinear transparency. When the excitation frequency is somewhat larger than the original resonant frequency, then the transmission of the layer exhibits a transient bistable behavior on the time scale of superradiation, which can be much shorter than the relaxation times. This type of bistability is essentially different from the ordinary stationary intrinsic bistability investigated earlier by other authors.

We derive the joint photon-number distribution for two-mode squeezed states with coherent amplitudes. For certain ranges of the parameters, the joint distribution exhibits nonclassical oscillations, which are the two-mode analog of the oscillations found in the single-mode case. These nonclassical oscillations are absent from the marginal distributions for each mode. The nonclassical features of the joint distribution may be explained using the interference–in–phase-space concept in four-dimensional phase space.

We study the effects of white additive noise on a transverse pattern of the laser formed by the combination of three degenerate transverse modes. In the semiclassical description, the formation of this pattern corresponds to a process of spontaneous breaking of the cylindrical symmetry. The stationary probability distribution is calculated analytically within the adiabatic elimination of the atomic variables and the cubic approximation. Noise induces a slow random rotation of the pattern around the laser axis and a random distortion. The angular rotation is characterized by a diffusive evolution and restores completely the broken symmetry. We study the random motion of the four phase singularities of the pattern. We analyze the transverse process given by the decay of the unstable cylindrically symmetrical configuration and show that it is accompanied by anomalous fluctuations.

The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].

New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ‘‘white.’’ Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.

We discuss the relationship between fully quantized and semiclassical approaches to input-output theory that connect asymptotically free fields prior to and following interactions that we describe in terms of canonical transformations. We demonstrate the utility of the Wigner function in describing the connection between input and output fields, and show how it is particularly well suited to describe many quantum-optical systems in terms of positive quasiprobability permitting classical stochastic simulation.

In this paper, we continue our development of the quantum theory of nondegenerate multiwave mixing in an atomic medium [Phys. Rev. A 37, 2017 (1988)]. In our development, the atomic variables are eliminated using a frequency-domain approach employing a slowly varying amplitude approximation that is more rigorous than the usual adiabatic approximation. We then specialize to the case of four-wave interaction with two strong pump beams and obtain noise correlations of the atomic polarization that are applicable to nondegenerate four-wave mixing. The noise correlations include the effect of atomic collisions that is crucial to the atomic-vapor experiments. After making the usual rotating-wave approximation, the atomic-polarization equations give us a set of temporal coupled-mode equations for the c-number variables corresponding to the annihilation operators. We then further specialize to the single-beam case in which all the relevant modes of interest are collinear and obtain a paired set of coupled-mode equations. In order to apply the theory to experiments employing traveling-wave interaction geometries, in the following paper of this series we will present a formalism to treat the spatial propagation of a quantum field.

The quantum theory of Stokes–anti-Stokes processes in a degenerate system in a cavity is developed. The Raman transition is pumped by a coherent field. Effects of many atoms, cavity losses, and thermal photons are included in the theory. An exact solution for the model is obtained. An explicit expression for the reduced density matrix of the cavity field is given. The spectrum of the cavity field is obtained and is interpreted in terms of the eigenstates of the effective Hamiltonian describing Stokes–anti-Stokes processes. The spectrum develops sidebands due to strong Raman coupling.

We derive a closed-form expression for the number probability distribution of a ‘‘generic’’ two-mode field in a two-mode squeezed state. We discuss its dependence on the average particle number in the two modes and on the amount of squeezing. We show that the distribution exhibits oscillations for particle numbers appropriately greater than the average, similar to the one-mode case, although the conditions under which such an oscillatory behavior occurs are different. These results are directed to the investigation of nonclassical properties in the radiation field produced by a parametric amplifier operated in a two-mode regime.

The chaotic vibrations of a diatomic molecule in an intense monochromatic electromagnetic field are classically and quantum mechanically analyzed. It is shown that the driven motion in a Morse potential is accurately described by a return map–the Morse map, whose derivation in various degrees of approximation is presented in detail. The quantization of the map is also considered. The quantized map, though acting on states in the energy range of bound states only, is shown to be influenced by intermediate states above the dissociation threshold, i.e., effects of the continuum are incorporated. Detailed numerical results are presented and various localization mechanisms are discussed and compared.

The nonlinear coupled wave equations of a free-electron laser in the Compton regime are analyzed numerically and analytically, taking into account the shot noise in the incident electron beam. The influence of the sideband instability and the shot noise on the emitted spectrum are determined.

An interpretation of collision-induced extra resonances in multiwave mixing is constructed using a fully quantum-mechanical calculation carried out in the Schrödinger representation. The phase-matched signal is seen to arise as an interference between the amplitudes for scattering of the incident fields at different atomic sites. When collisions occur, the separation of the signal into a collision-induced resonance plus a background term appears naturally in this approach. The origin of the phase-matching condition, conservation of energy (and breaking of the Manley-Rowe relations), the role played by relaxation mechanisms, and the fact that the fields need not be temporally coherent to produce the extra resonances, all can be easily understood within the context of this calculation.

We consider a single-mode dye-laser model with gain parameter fluctuations modeled by a white noise. The decay of the intensity correlation function C(t) is analyzed with the use of a method based on the combination of the low- and high-frequency expansions of the Laplace transform of C(t). The correlation function is approximated by a superposition of two decaying exponentials. Numerical simulations show that this approximation is accurate. We analyze the relaxation of C(t) in the domain of parameters, gain parameter close to the pump parameter, in which the white-gain-noise model reproduces the initial slow decay of C(t). It is found that the intensity correlation function does not show two separated time scales as observed experimentally.

The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.

We have applied the beam-foil–laser (BFL) method to determine the lifetime of the 2p3s ${}_{}{}^1{}_{}{}^{}$P° level in O iii. The result (τ=0.17±0.01 ns) is in good agreement with most of the theoretical predictions but significantly shorter than the two beam-foil lifetime values reported previously. The oscillator strengths of the 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D–2p3s ${}_{}{}^1{}_{}{}^{}$P° transition deduced from the present lifetime result in O iii and from the very recently reported BFL lifetime in N ii confirm the f-value trend along the carbon sequence calculated by Fawcett [At. Data Nucl. Data Tables 37, 411 (1987)].