The external photodetection of cavity radiation is considered as a continuous quantum measurement in the sense of Srinivas and Davies [Opt. Acta 28, 981 (1981)]. It is analyzed in terms of three elementary processes: the no-leak process, the one-leak-undetected process, and the one-leak-detected process. The first two form a no-count process and the last one, a one-count process. Superoperators for these elementary processes are postulated, following the examples of Srinivas and Davies. The superoperators for the one-count process, the no-count process, the m-count process, and the nonreferring process are then derived based on the postulates. The following implications of these superoperators are found: (1) the change of average photon number due to the one-count process is identical to the well-known Q parameter introduced by Mandel [Opt. Lett. 4, 205 (1979)]; (2) the no-count process is governed by a pseudomaster equation; (3) The probability for the m-count process is the Poisson transform of the initial P function of the cavity radiation; and (4) the nonreferring measurement process is governed by a master equation.

We present experimental results of ac-Stark-effect-enhanced four-wave mixing in a dense sample of two-level atoms. The mixing efficiency exhibits strong maxima when the beams fulfill resonance and phase-matching conditions for the transitions in a dressed atom. The experimental arrangement enabled the verification of recent theories of parametric interactions in strongly driven systems. Good agreement of these theories with the experimental results allows one to use the wave mixing in the studies of properties and dynamics of strongly driven, dense, two-level systems. In particular, the possible role of parametric interaction in the phenomenon of conical emission has been analyzed in this manner.

Classical and quantum fluctuations are analyzed in the system of type-II harmonic generation where two frequency-degenerate subharmonic fields with orthogonal polarizations are required for the generation of a harmonic field. The two subharmonic fields as well as the harmonic fields are on resonance in a cavity. It is found that there is no self-pulsing behavior as predicted for the type-I case where the intensities of both the subharmonic and the harmonic fields undergo fast oscillation. Instead there exists a threshold that is identified as the onset of an optical parametric oscillator (OPO) formed by a subharmonic mode with its polarization orthogonal to the input polarization (not the original modes). When the loss for the harmonic field is small, most of the input power is converted to the output power of the OPO. Under this circumstance, quantum-nondemolition measurements of the input can be performed at certain frequencies. The spectra of squeezing are calculated for the two subharmonic modes and it is found that both modes are squeezed for a certain range of frequency. The output of the OPO is found to exhibit phase squeezing.

Considering intense two-photon coherent states with minimum phase dispersion, the width of the phase probability distributions based on the Pegg-Barnett formalism, the Wigner function, and the Q function is discussed. Remarkable differences are found in certain regions depending on the mean photon number. These results are compared with the phase uncertainty of phase optimized states.

We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes (l=±1) in a ${\mathrm{CO}}_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the ${\mathit{Z}}_2$ symmetry. The pattern dynamics near this codimension-two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.

A simple holographic technique is used to generate a nondiverging hollow beam, which is similar to a ${\mathit{J}}_1$ Bessel beam. The hollow beam is obtained from a Gaussian beam with a high conversion efficiency (greater than 50%). We describe briefly the merit of this hollow beam, which has potential applications in particle collimation.

We derive the generalized set of Maxwell-Bloch equations which takes into account the dependence of relaxation coefficients on the amplitude and frequency of the coherent field. This has interesting implications in many problems in quantum optics and laser physics, e.g., the problem of lasing without inversion due to a strong coherent generating field.

The time evolution of a quantum harmonic oscillator with a series of sudden jumps of the mass or the frequency is determined in the form of a recursion relation. An approximating method is developed for determining the time evolution of harmonic oscillators with arbitrary derivable functions of the frequency or the mass. The approximate solution is shown to tend to the analytical one in the limiting case. As a demonstration of the approximating method, the solution of the problem of damped oscillation in the square of the oscillator frequency is presented.

A system of N two-level atoms in a resonator is considered interacting with a resonant eigenmode field and with an external coherent field, with a frequency slightly different from the frequency of the atomic transition. A model Hamiltonian is constructed for describing the slow quantum dynamics of the system, and a set of closed c-number equations for time-dependent quantum expectation values is derived in the boson and spin coherent states. In the region of parameters for developed chaos in the semiclassical limit (when the radiation field is considered classically) we show that the semiclassical approximation is violated by quantum effects at the time scale ${\mathrm{\tau }}_{\mathrm{ħ}}$∼lnN. We also show that quantum correlations grow exponentially during the time interval 0<τ<${\mathrm{\tau }}_{\mathrm{ħ}}$. An additional averaging over the initial density matrix is considered. The connection of our model with the Dicke model [Phys. Rev. 93, 99 (1956)] is demonstrated, and the possiblity of measuring the quantum chaos effects considered in this paper is discussed.

Two-mode squeezed coherent states with complex squeeze and displacement parameters are studied, taking advantage of the SU(2) dynamical symmetry underlying two-mode systems. Expressions for the photon distributions in such states are derived using an SU(2) identity and the fact that the two-mode squeeze operator can be viewed as a rotated version of the product of reciprocal single-mode squeeze operators. An important U(1)×U(1) invariance of this photon distribution is established. As a consequence, the three phases of the complex squeeze and displacement parameters enter the photon distribution through just one U(1)×U(1) invariant combination. An associated Gouy effect is noted. Numerical examples of two-mode photon distributions are shown, and interesting new features demonstrated. Second-order coherence properties and their nonclassical nature are briefly studied.

The spectroscopic squeezing characteristics of the angular-momentum state exp(θ${\mathit{S}}_{\mathit{z}}$)exp[-(iπ/2)${\mathit{S}}_{\mathit{y}}$]‖S,m〉 are calculated. The parameter √2S Δ${\mathit{S}}_{\mathit{x}}$/‖〈${\mathit{S}}_{\mathit{z}}$〉‖ is shown to be less than or equal to 1 and takes the asymptotic value (1+S${)}^{\mathrm{-}1/2}$ as θ→0 if m≊0. This small value makes those states especially useful in applications where quantum noise reduction is required. Also, the spin-spin correlations of those states are nonzero and negative.

We investigate the dynamics of an arbitrary atomic system (n-level atom or many n-level atoms) interacting with a resonant quantized mode of an electromagnetic field in a lossless cavity. Initially, the field is taken in a coherent state with a large average photon number. If the initial atomic state is chosen as an eigenstate of the atomic Hamiltonian in the classical field limit (semiclassical eigenstates), then the evolution of the system wave function is approximately factorized into the field and atomic parts. Explicit analytical expressions are given for the factorized wave functions. The time evolution of an arbitrary initial atomic state can be fully described in terms of factorized states. As examples, we discuss trapping states, and collapses and revivals of the atomic energy.

We investigate an optically pumped four-level laser in which both the laser and the pump form resonant cavity modes. We find that the system can exhibit absorptive bistability under conditions typical of solid-state lasers. Under conditions of high pump-cavity finesse, a bistability exists between below-threshold operation and maximum laser output.

We examine the effects of linear amplification and attenuation on the quantum-mechanical phase properties of light for fields with mean photon numbers of at least the order of 10. The phase probability density is found to satisfy a diffusion equation for both phase-insensitive and phase-sensitive amplifiers and attenuators. The solution is a convolution of the initial phase probability density with an infinite series of expanding Gaussians which clearly illustrates the diffusion of the phase. In particular, we find that for phase-insensitive amplification the phase of the field undergoes time-dependent uniform diffusion. In the limit of large amplification the diffusion ceases and the phase variance of the amplified light is given by the input phase variance plus an extra term which is equal to the phase variance of a coherent state of the same intensity as the initial field. We show that the reduced phase variance of phase-optimized states (relative to coherent states of the same intensity) is lost for power gains greater than the photon-cloning value of 2. In contrast, phase-sensitive amplifiers give rise to time-dependent nonuniform phase diffusion. The amount of phase diffusion depends on the relative phase angle between the light and the amplifier. If the peak of a relatively narrow phase probability density is near a minimum in the phase diffusion coefficient, then the phase noise added by the amplifier will be less than that found for a phase-insensitive amplifier. Further squeezing of the amplifier reduces the added phase noise proportionally. We find that it is possible, using phase-sensitive amplifiers, to amplify phase-optimized states by power gains considerably larger than 2 and still retain a reduced phase variance.

While, for a long time, steady-state second-harmonic generation has provided important information concerning optical nonlinearities and dynamics of molecular systems, either isolated or adsorbed, time-resolved measurements are now becoming very productive. It is the aim of the present work to introduce a theoretical model of time-resolved second-harmonic generation involving a detailed description of the electronic and vibrational structures of the molecular system. It will be of interest to obtain a better understanding of the dynamics taking place in these systems in terms of their internal parameters.

We examine the growth of a cavity field built up from a vacuum in a micromaser in terms of a ‘‘physical spectrum’’ or a time-dependent spectrum and the photon distributions. We find that the photon distribution attains the steady state earlier than the spectrum becomes steady. The short-time decrease of the half-width at half maximum of the spectrum obeys a power-law behavior with time.

We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.

Driving is applied to an optical system consisting of a Kerr medium combined with a second-order parametric process driven by a pump field which is sinusoidally modulated in amplitude. The coherent tunneling in this system is found to be both enhanced and suppressed by this, depending on the frequency of the driving chosen. A variation of time-independent perturbation theory is applied to this system and found to successfully describe this behavior.

We present a simple approximate description of systems involving cross-phase modulation in highly dispersive media. Optical pulses in such systems suffer large frequency shifts and correspondingly experience large variations in group velocity dispersion so that a simple nonlinear Schrödinger equation description is not valid. We take the frequency shift into account in a moments based model that extends the standard Schrödinger description, and apply the model to the particular case of optical pulse compression in nonlinear Bragg gratings. The model is tested against full numerical simulations. Finally, we consider some of the difficulties involved in observing the pulse-compression effect.

We investigate various measures of phase uncertainty in their dependence on the average number of photons for the case of a phase squeezed state. We use the following three measures: (i) the geometrical uncertainty (δ${\mathit{cphi}}_{\mathit{g}}$${)}^2$, (ii) the dispersion (δ${\mathit{cphi}}_{\mathit{d}}$${)}^2$, and (iii) the rotational width (δ${\mathit{cphi}}_{\mathit{r}}$${)}^2$. Whereas (δ${\mathit{cphi}}_{\mathit{g}}$${)}^2$ and (δ${\mathit{cphi}}_{\mathit{r}}$${)}^2$ decay quadratically with the average number of photons 〈n〉, the dependence of (δ${\mathit{cphi}}_{\mathit{d}}$${)}^2$ is only of the form ln〈n〉/〈n${\mathrm{〉}}^2$. We give physical pictures for these scaling laws.