The thermofield introduced by Takahashi and Umezawa [Collect. Phenom. 2, 55 (1975)] is used to represent the thermal noise; it is generated from the absolute vacuum by a so-called thermalizing operator and serves as the initial state for generating two-mode squeezed states by squeeze and displacement operators. The ones obtained by applying the squeeze operator first followed by the displacement operator are called coherent squeezed states, while the others obtained by applying the displacement operator first are called squeezed coherent states. A criterion for the existence of nonclassical photon statistics in a two-mode radiation introduced by us in a previous paper [Phys. Rev. A 42, 1609 (1990)] is then used to study the conditions for the two types of squeezed states to be nonclassical states. Several three-dimensional plots are presented to illustrate the effects of thermal noise on squeezed states.

We consider squeezing of the electromagnetic field resulting from the interaction of the three-level ssV-shaped atom with two modes initially taken in coherent-state representation. We also consider higher-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and then in the sense of Hillery [Phys. Rev. A 36, 3796 (1987)]. We calculate the two-mode squeezing proposed in [J. Mod. Opt. 34, 709 (1987)] and the sum squeezing defined by Hillery [Phys. Rev. A 40, 3147 (1989)] for an atom starting initially at its ground state.

The statistical noise properties of the laser radiation in a low-Q (bad) cavity are theoretically investigated. The bad-cavity laser system is shown to be exactly equivalent to the stochastic Toda oscillator (STO) in the case of negligible polarization noise. Transforming the STO Langevin equation to the Fokker-Planck equation with a position-dependent diffusion coefficient, analytical expressions of the probability distribution are obtained as particular solutions in a stationary state with the aid of the expansion into a complete orthogonal set. We predict novel statistical features of the laser light, e.g., a power tail of the intensity distribution function, non-Gaussian nature of the field fluctuation, and super-Poissonian photoelectron statistics. General solutions are also given in a closed form in terms of the matrix continued fraction to compare with the particular solutions. The good-cavity case is reanalyzed in our formalism to root out differences between them.

The resonance behavior of magnetic and optical two-level systems under the influence of strong modulated fields is studied in detail by solving the Bloch equations in the limit of vanishing damping, namely, in terms of matrix continued fractions. Thus both analytical and numerical results are obtained for the positions of the various multiple quantum resonances in the time-averaged as well as modulated interaction components. Specifically, the role of the orientation of the optical pump beam in magnetic-resonance configurations is investigated, and it is shown that there are several classes of resonances for which the behavior of the system is independent of the orientation of the pump beam. These are the geometries in which the static and oscillating magnetic fields are either orthogonal or parallel, the geometries leading to Haroche-like resonances (which, however, play a special role in modulated interaction components also), and a previously unknown class, labeled saddle-point resonances. However, other than for these special classes, the behavior of the system depends generally on the orientation of the optical pump beam, unlike as implied in some previous work on this problem. As in the recently studied case of a fully amplitude-modulated optical interaction [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], it is found that the resonances in modulated interaction components are generally doubly branched, with one branch duplicating the resonances found in the time-averaged component. A new feature found for not-fully-amplitude-modulated and phase-modulated, off-resonance optical excitation (or magnetic resonance with nonparallel or nonorthogonal static and oscillating magnetic fields) is the occurrence of an extra type of resonance in modulated components of the interaction that cannot, like all other resonances of the system, be classified as power-shifted multiple quantum transitions.

It is shown that, in modulated magnetic resonance on spin-1/2 systems, the time-averaged absorption signal of the optical pump beam can be obtained directly from the dressed-atom energy eigenvalues of the Floquet Hamiltonian for arbitrary orientations of the optical pump beam, namely, by a straightforward generalization of Shirley’s well-known result [Phys. Rev. 138, B979 (1965)]. Analytical and numerical results derived from this generalized diagonalization technique are compared with the vanishing damping solution of the Bloch equations from the preceding paper [W. M. Ruyten, Phys. Rev. A 42, 4226 (1990)] and are shown to be in complete agreement with the latter.

We examine coherent sum and difference-frequency generation in dilute suspensions of metallic or n-type semiconductor microspheres embedded in a passive linear dielectric host using quasihydrodynamic theory within the quasistatic and single-scattering approximations. If one or both of the incident laser-beam frequencies are near the surface dipole resonance, the medium exhibits an enhanced response. Enhancement of the sum-frequency wave is also possible if this frequency coincides with the surface quadrupole resonance of the microsphere. It is shown that a coherent second-order response is possible only if the symmetry of the system is reduced. Detailed calculations are presented for the dynamic response of the individual particles as well as the macroscopic electrodynamics of the composite as a whole. Numerical results for the perturbed electron density and drift velocity as well as the laser-induced, microparticle quadrupole moment of a single microsphere are displayed. Numerical results for the coherent and incoherent intensities are calculated for a 1-mm-thick slab of microparticles embedded in an artificial glass host. The microparticles are silver spheres of 100 Å radius with ${10}^{\mathrm{-}4}$ volume fraction. The coherent intensity for a mm-thick microparticle composite is nonvanishing only for a noncollinear configuration under perfect phase matching. If both of the incident laser-beam frequencies are near the surface dipole resonances, the conversion efficiencies of the coherent (incoherent) radiation at the sum and difference frequencies are ${10}^{\mathrm{-}6}$ (${10}^{\mathrm{-}7}$) and ${10}^{\mathrm{-}11}$ (${10}^{\mathrm{-}16}$), respectively. The conversion efficiencies for the sum-frequency generation at the surface quadrupole resonance are ${10}^{\mathrm{-}7}$ and ${10}^{\mathrm{-}10}$ for the coherent and incoherent intensities.

The mode-locking structure near the threshold, Arnol’d tongues in the quasiperiodic region, and the route to chaos have been investigated in a hybrid optical system with competing interactions. A devil’s staircase and fractional dimensionality on the critical line are found, and the generalized dimension and singularity f(α) spectrum are calculated.

We evaluate the ionization rate from a recent (adiabatic) theory of multiphoton ionization for the case of a recent experiment: a circularly polarized ${\mathrm{CO}}_2$ laser at an intensity of about ${10}^{14}$ W/${\mathrm{cm}}^2$. For S states we obtain a rate ${10}^4$–${10}^5$ times larger than the Keldysh-Faisal-Reiss theory. For P states we obtain a rate about ${10}^9$ times larger. We also make a prediction about the angular distribution from S states.

The dynamics of an initially bare pair of two-level atoms at distance R is investigated. The pair is coupled to the vacuum radiation field in the multipolar scheme and in the dipole approximation. The Heisenberg equations of motion for various atomic operators are obtained neglecting terms O(${\mathit{e}}^3$) and for t smaller than the spontaneous relaxation time. A rigorous proof of causality in the atom-atom interaction is given. Interatomic correlations, however, are shown to develop for t<R/c. This early development is shown to be compatible with the principle of relativistic causality, and to be related to the peculiar form of the vacuum zero-point fluctuations. The techniques adopted are applied to study dynamics and correlations of a superradiant state.

Photon operators that obey commutation relations form Lie algebras. By identifying the Hamiltonian of an interacting system of one electron and a multimode many-photon field in a momentum representation as an element of a Cartan subalgebra, we are able to find the automorphism that maps the Hamiltonian on to that of the noninteracting system. By this method we find the exact solutions as new solutions of the Schrödinger equation for the case of one electron in a multimode many-photon field. The solutions show the existence of both ponderomotive energy and momentum, which obey the rules of linear superposition among the photon modes.

An alternative approach is proposed to discuss mode coupling in bidirectional ring lasers that is induced by backscattering. It is shown that various features can be simply discussed in terms of the mode structure of the corresponding passive ring cavity. The nature of the backscattering is found to play a crucial role in determining the normal-mode structure. For instance, we show theoretically that, for a rotating ring laser (gyro), the characteristics of frequency locking are already present in the passive-mode structure if the mode coupling has a dissipative nature, i.e., if the backscattering originates in localized losses. If, on the other hand, the backscattering has a conservative nature, i.e., originates in steps of the refractive index, a frequency splitting is found in the passive-mode structure, making so-called oscillatory instability possible. Experimental observations are reported to support this point of view. The recently reported π-phase jumps in He-Ne ring lasers are shown to fit naturally into this scheme. These jumps can be described as transitions between the normal modes of the passive ring cavity.

Using the maximum-entropy approach, we analyze the appearance of coherent and squeezed states for the Kanai-Caldirola Hamiltonian, making it possible to extend the analysis easily to the so-called generalized harmonic oscillator and a sort of two-photon Hamiltonian, for both the zero and nonzero temperature cases. A connection between the possibility of obtaining squeezing and the relevant operators included in the density matrix is shown. Finally, a comparison with pertinent previous results in the literature is also presented.

The phenomenon of collapses and revivals of Rabi oscillations is studied for a two-level atom undergoing either one- or two-photon transitions in the two-mode squeezed state field inside a lossless cavity. The qualitative behavior of this phenomenon is found to be different as compared with corresponding coherent-state fields. Analytic expressions for excitation probabilities are obtained. Also, the statistical aspect of the field in terms of intensity-intensity correlations is discussed.

We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel’s Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.

We examine resonance fluorescence of a two-level atom in a squeezed vacuum, under the condition that the squeezing bandwidth is much narrower than the Rabi splitting of the Mollow triplet. For a suitable choice of the relative phase between the squeezed vacuum and coherent driving field, we find significant narrowing of the Rabi peaks and inhibited population decay. These results are in marked contrast to previous broadband squeezing analyses, which predict strong broadening of the Rabi peaks and enhanced population decay. We explore the connection between our work and that on the dynamical suppression of spontaneous emission via strongly driven resonance fluorescence in a cavity [Lewenstein, Mossberg, and Glauber, Phys. Rev. Lett. 59, 775 (1987)]. By modifying this work to incorporate squeezing of the cavity modes, we are able to combine the features of both systems, and thereby predict strong inhibition of the decay of all three components of the Bloch vector in a possible experimental configuration.

We consider lasers with intracavity nonlinear elements, e.g., two-photon absorption, second-harmonic generation, as a possible means to reduce the amplitude fluctuations in a laser. While amplitude squeezing up to 37% may be obtained for the internal field, only a modest amount of noise reduction (10% for two-photon absorption, effectively zero for second-harmonic generation) is found in the output field at the laser frequency. In the second-harmonic field an amplitude-noise reduction of 50% below the shot-noise level may be achieved.

We derive the semiclassical quantization rule for the external system in two interacting systems for a nonadiabatic process. It is shown that this semiclassical quantization rule accommodates the contribution of the averaged value of the geometrical phase per one evolution of the external system.

A unitary operator U, which can transform the Fock space of a four-dimensional oscillator into the space in which the Hamiltonian of four harmonically coupled identical one-dimensional harmonic oscillators is diagonalized, is found. The coordinate representation of U is presented and is used to directly derive the wave function of the energy eigenstate of the coupled oscillators. The normally ordered form of U is also deduced with the use of integration within an ordered product.

Broad resonance states associated with unstable periodic orbits in the two-center Coulomb problem are studied using a quantization scheme in which the real part of each resonance energy is determined by a Bohr-Sommerfeld-type loop integral over a periodic orbit and the imaginary part of the resonance energy is related to the Lyapunov index of the periodic orbit.

In this paper we discuss an improved strategy for variational versions of the coupled-cluster response approach for the study of static properties. This takes care of different truncation levels for the cluster amplitudes and their derivatives required for this calculation.